proofs/crypto/sha/conformance.bend

bend-collections-laws-crypto@1.0.0.0 · 2,760 lines · 76 definitions

1import Base
2import bend-collections-laws-crypto@1.0.0.0/src/crypto/sha/state.bend as S
3import bend-collections-laws-crypto@1.0.0.0/src/crypto/sha/core.bend as C
4import bend-collections-laws-crypto@1.0.0.0/spec/crypto/sha.bend as F
5import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/sha/list_proofs.bend as L
6import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/sha/padding.bend as Padding
7
8law octets_correct:
9  for +width: Nat
10  for +n: Nat
11  for +acc: List<&2, U32>
12  {C.length_octets(width, n, acc) == List.append(&2, U32, F.octets(width, n), acc) : List<&2, U32>}
13
14def octets_correct(width, n, acc):
15  match width:
16    case 0n:
17      {==}
18    case 1n+p:
19      %L.append_assoc_reverse(U32, F.octets(p, Nat.div(n, 256n)),
20        [U32.from_nat(Nat.mod(n, 256n))], acc) :
21        {C.length_octets(p, Nat.div(n, 256n), U32.from_nat(Nat.mod(n, 256n)) <> acc) == _ : List<&2, U32>}
22      octets_correct(p, Nat.div(n, 256n), U32.from_nat(Nat.mod(n, 256n)) <> acc)
23
24law length_correct:
25  for +n: Nat
26  {C.bit_length(n) == F.length_field(n) : List<&2, U32>}
27
28def length_correct(n):
29  octets_correct(7n, Nat.div(n, 32n), [U32.shln(U32.from_nat(Nat.mod(n, 32n)), 3n)])
30
31law nth_correct:
32  for xs: List<&2, U32>
33  for n: Nat
34  {C.get(xs, n) == F.nth(xs, n) : U32}
35
36def nth_correct(xs, n):
37  match xs n:
38    case Nil{} _:
39      {==}
40    case h <> t 0n:
41      {==}
42    case h <> t 1n+p:
43      nth_correct(t, p)
44
45law next_correct:
46  for +hs: List<&2, U32>
47  {C.next_word(hs) == F.recurrence(hs) : U32}
48
49def next_correct(hs):
50  match hs:
51    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> (p <> rest):
52      {==}
53    case Nil{}:
54      {==}
55    case a <> Nil{}:
56      {==}
57    case a <> b <> Nil{}:
58      {==}
59    case a <> b <> c <> Nil{}:
60      {==}
61    case a <> b <> c <> d <> Nil{}:
62      {==}
63    case a <> b <> c <> d <> e <> Nil{}:
64      {==}
65    case a <> b <> c <> d <> e <> f <> Nil{}:
66      {==}
67    case a <> b <> c <> d <> e <> f <> g <> Nil{}:
68      {==}
69    case a <> b <> c <> d <> e <> f <> g <> h <> Nil{}:
70      {==}
71    case a <> b <> c <> d <> e <> f <> g <> h <> i <> Nil{}:
72      {==}
73    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> Nil{}:
74      {==}
75    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> Nil{}:
76      {==}
77    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> Nil{}:
78      {==}
79    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> Nil{}:
80      {==}
81    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> Nil{}:
82      {==}
83    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> Nil{}:
84      {==}
85
86law extension_correct:
87  for +n: Nat
88  for +hs: List<&2, U32>
89  {C.expand(n, hs) == F.extension(n, hs) : List<&2, U32>}
90
91def extension_correct(n, hs):
92  match n:
93    case 0n:
94      {==}
95    case 1n+p:
96      %next_correct(hs) : {C.expand(1n+p, hs) == _ <> F.extension(p, _ <> hs) : List<&2, U32>}
97      %extension_correct(p, C.next_word(hs) <> hs) :
98        {C.expand(1n+p, hs) == C.next_word(hs) <> _ : List<&2, U32>}
99      {==}
100
101law schedule_correct:
102  for +extra: Nat
103  for +block: List<&2, U32>
104  {C.schedule(extra, block) == F.schedule(extra, block) : List<&2, U32>}
105
106def schedule_correct(extra, block):
107  Equal.cong(List<&2, U32>, List<&2, U32>, ext => List.append(&2, U32, block, ext),
108    C.expand(extra, List.reverse(&2, U32, block)), F.extension(extra, List.reverse(&2, U32, block)),
109    extension_correct(extra, List.reverse(&2, U32, block)))
110
111law step_correct:
112  for s: S.State
113  for k: U32
114  for w: U32
115  {C.step(s, k, w) == F.step(s, k, w) : S.State}
116
117def step_correct(s, k, w):
118  match s:
119    case S.H{a, b, c, d, e, f, g, h}:
120      {==}
121
122law rounds_correct:
123  for +ks: List<&2, U32>
124  for +ws: List<&2, U32>
125  for +s: S.State
126  {C.rounds(ks, ws, s) == F.rounds(ks, ws)(s) : S.State}
127
128def rounds_correct(ks, ws, s):
129  match ks ws:
130    case Nil{} _:
131      {==}
132    case k <> kt Nil{}:
133      {==}
134    case k <> kt w <> wt:
135      %step_correct(s, k, w) :
136        {C.rounds(kt, wt, C.step(s, k, w)) == F.rounds(kt, wt)(_) : S.State}
137      rounds_correct(kt, wt, C.step(s, k, w))
138
139law feedforward_correct:
140  for x: S.State
141  for y: S.State
142  {C.feedforward(x, y) == F.feedforward(x, y) : S.State}
143
144def feedforward_correct(x, y):
145  match x y:
146    case S.H{a, b, c, d, e, f, g, h} S.H{i, j, k, l, m, n, o, p}:
147      {==}
148
149law compression_correct:
150  for +ws: List<&2, U32>
151  for +ks: List<&2, U32>
152  for +s: S.State
153  {C.compress(ws, ks, s) == F.compress(ws, ks, s) : S.State}
154
155def compression_correct(ws, ks, s):
156  %feedforward_correct(s, F.rounds(ks, ws)(s)) : {C.compress(ws, ks, s) == _ : S.State}
157  Equal.cong(S.State, S.State, r => C.feedforward(s, r),
158    C.rounds(ks, ws, s), F.rounds(ks, ws)(s), rounds_correct(ks, ws, s))
159
160law expanded_rounds_correct:
161  for +n: Nat
162  for +history: List<&2, U32>
163  for +ks: List<&2, U32>
164  for +s: S.State
165  {C.expanded_rounds(n, history, ks, s) == C.rounds(ks, C.expand(n, history), s) : S.State}
166
167def expanded_rounds_correct(n, history, ks, s):
168  match n ks:
169    case 0n Nil{}:
170      {==}
171    case 0n k <> kt:
172      {==}
173    case 1n+p Nil{}:
174      {==}
175    case 1n+p k <> kt:
176      expanded_rounds_correct(p, C.next_word(history) <> history, kt,
177        C.step(s, k, C.next_word(history)))
178
179law schedule_rounds_correct:
180  for +ws: List<&2, U32>
181  for +extra: Nat
182  for +history: List<&2, U32>
183  for +ks: List<&2, U32>
184  for +s: S.State
185  {C.schedule_rounds(ws, extra, history, ks, s) ==
186    C.rounds(ks, List.append(&2, U32, ws, C.expand(extra, history)), s) : S.State}
187
188def schedule_rounds_correct(ws, extra, history, ks, s):
189  match ws ks:
190    case Nil{} _:
191      expanded_rounds_correct(extra, history, ks, s)
192    case w <> wt Nil{}:
193      {==}
194    case w <> wt k <> kt:
195      schedule_rounds_correct(wt, extra, history, kt, C.step(s, k, w))
196
197law fused_compress_correct:
198  for +block: List<&2, U32>
199  for +extra: Nat
200  for +ks: List<&2, U32>
201  for +s: S.State
202  {C.fused_compress(block, extra, ks, s) == C.compress(C.schedule(extra, block), ks, s) : S.State}
203
204law fused_compress_slow_correct:
205  for +block: List<&2, U32>
206  for +extra: Nat
207  for +ks: List<&2, U32>
208  for +s: S.State
209  {C.fused_compress_slow(block, extra, ks, s) == C.compress(C.schedule(extra, block), ks, s) : S.State}
210
211def fused_compress_slow_correct(block, extra, ks, s):
212  Equal.cong(S.State, S.State, r => C.feedforward(s, r),
213    C.schedule_rounds(block, extra, List.reverse(&2, U32, block), ks, s),
214    C.rounds(ks, List.append(&2, U32, block,
215      C.expand(extra, List.reverse(&2, U32, block))), s),
216    schedule_rounds_correct(block, extra, List.reverse(&2, U32, block), ks, s))
217
218law window_rounds_correct:
219  for +q: Nat
220  for +a: U32
221  for +b: U32
222  for +c: U32
223  for +d: U32
224  for +e: U32
225  for +f: U32
226  for +g: U32
227  for +h: U32
228  for +i: U32
229  for +j: U32
230  for +k: U32
231  for +l: U32
232  for +m: U32
233  for +n: U32
234  for +o: U32
235  for +p: U32
236  for +rest: List<&2, U32>
237  for +ks: List<&2, U32>
238  for +s: S.State
239  {C.window_rounds(q, C.W{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}, ks, s) ==
240    C.expanded_rounds(q, a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> p <> rest, ks, s) : S.State}
241
242def window_rounds_correct(q, a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, rest, ks, s):
243  match q ks:
244    case 0n Nil{}:
245      {==}
246    case 0n x <> xt:
247      {==}
248    case 1n+r Nil{}:
249      {==}
250    case 1n+r x <> xt:
251      window_rounds_correct(r,
252        (C.small1(b) + g + C.small0(o) + p : U32),
253        a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p <> rest, xt,
254        C.step(s, x, (C.small1(b) + g + C.small0(o) + p : U32)))
255
256law window_schedule_rounds_correct:
257  for +ws: List<&2, U32>
258  for +extra: Nat
259  for +a: U32
260  for +b: U32
261  for +c: U32
262  for +d: U32
263  for +e: U32
264  for +f: U32
265  for +g: U32
266  for +h: U32
267  for +i: U32
268  for +j: U32
269  for +k: U32
270  for +l: U32
271  for +m: U32
272  for +n: U32
273  for +o: U32
274  for +p: U32
275  for +rest: List<&2, U32>
276  for +ks: List<&2, U32>
277  for +s: S.State
278  {C.window_schedule_rounds(ws, extra, C.W{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}, ks, s) ==
279    C.schedule_rounds(ws, extra, a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> p <> rest, ks, s) : S.State}
280
281def window_schedule_rounds_correct(ws, extra, a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, rest, ks, s):
282  match ws ks:
283    case Nil{} _:
284      window_rounds_correct(extra, a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, rest, ks, s)
285    case w <> wt Nil{}:
286      {==}
287    case w <> wt x <> xt:
288      window_schedule_rounds_correct(wt, extra, a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,
289        rest, xt, C.step(s, x, w))
290
291def fused_compress_correct(block, extra, ks, s):
292  match block:
293    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> p <> Nil{}:
294      Equal.trans(S.State,
295        C.feedforward(s, C.window_schedule_rounds(
296          [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
297          C.W{p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a}, ks, s)),
298        C.feedforward(s, C.schedule_rounds(
299          [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
300          [p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a], ks, s)),
301        C.feedforward(s, C.rounds(ks, List.append(&2, U32,
302          [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p],
303          C.expand(extra, [p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a])), s)),
304        Equal.cong(S.State, S.State, r => C.feedforward(s, r),
305          C.window_schedule_rounds(
306            [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
307            C.W{p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a}, ks, s),
308          C.schedule_rounds(
309            [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
310            [p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a], ks, s),
311          window_schedule_rounds_correct(
312            [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
313            p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a, Nil{}, ks, s)),
314        Equal.cong(S.State, S.State, r => C.feedforward(s, r),
315          C.schedule_rounds(
316            [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
317            [p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a], ks, s),
318          C.rounds(ks, List.append(&2, U32,
319            [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p],
320            C.expand(extra, [p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a])), s),
321          schedule_rounds_correct(
322            [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra,
323            [p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a], ks, s)))
324    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> p <> q <> rest:
325      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> p <> q <> rest, extra, ks, s)
326    case Nil{}:
327      fused_compress_slow_correct(Nil{}, extra, ks, s)
328    case a <> Nil{}:
329      fused_compress_slow_correct(a <> Nil{}, extra, ks, s)
330    case a <> b <> Nil{}:
331      fused_compress_slow_correct(a <> b <> Nil{}, extra, ks, s)
332    case a <> b <> c <> Nil{}:
333      fused_compress_slow_correct(a <> b <> c <> Nil{}, extra, ks, s)
334    case a <> b <> c <> d <> Nil{}:
335      fused_compress_slow_correct(a <> b <> c <> d <> Nil{}, extra, ks, s)
336    case a <> b <> c <> d <> e <> Nil{}:
337      fused_compress_slow_correct(a <> b <> c <> d <> e <> Nil{}, extra, ks, s)
338    case a <> b <> c <> d <> e <> f <> Nil{}:
339      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> Nil{}, extra, ks, s)
340    case a <> b <> c <> d <> e <> f <> g <> Nil{}:
341      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> Nil{}, extra, ks, s)
342    case a <> b <> c <> d <> e <> f <> g <> h <> Nil{}:
343      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> Nil{}, extra, ks, s)
344    case a <> b <> c <> d <> e <> f <> g <> h <> i <> Nil{}:
345      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> Nil{}, extra, ks, s)
346    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> Nil{}:
347      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> Nil{}, extra, ks, s)
348    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> Nil{}:
349      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> Nil{}, extra, ks, s)
350    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> Nil{}:
351      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> Nil{}, extra, ks, s)
352    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> Nil{}:
353      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> Nil{}, extra, ks, s)
354    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> Nil{}:
355      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> Nil{}, extra, ks, s)
356    case a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> Nil{}:
357      fused_compress_slow_correct(a <> b <> c <> d <> e <> f <> g <> h <> i <> j <> k <> l <> m <> n <> o <> Nil{}, extra, ks, s)
358
359law window_compress16_correct:
360  for +a: U32
361  for +b: U32
362  for +c: U32
363  for +d: U32
364  for +e: U32
365  for +f: U32
366  for +g: U32
367  for +h: U32
368  for +i: U32
369  for +j: U32
370  for +k: U32
371  for +l: U32
372  for +m: U32
373  for +n: U32
374  for +o: U32
375  for +p: U32
376  for +extra: Nat
377  for +ks: List<&2, U32>
378  for +s: S.State
379  {C.window_compress16(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, extra, ks, s) ==
380    C.fused_compress([a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], extra, ks, s) : S.State}
381
382def window_compress16_correct(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, extra, ks, s):
383  match ks:
384    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> k10 <> k11 <> k12 <> k13 <> k14 <> k15 <> kt:
385      {==}
386    case Nil{}:
387      {==}
388    case k0 <> Nil{}:
389      {==}
390    case k0 <> k1 <> Nil{}:
391      {==}
392    case k0 <> k1 <> k2 <> Nil{}:
393      {==}
394    case k0 <> k1 <> k2 <> k3 <> Nil{}:
395      {==}
396    case k0 <> k1 <> k2 <> k3 <> k4 <> Nil{}:
397      {==}
398    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> Nil{}:
399      {==}
400    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> Nil{}:
401      {==}
402    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> Nil{}:
403      {==}
404    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> Nil{}:
405      {==}
406    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> Nil{}:
407      {==}
408    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> k10 <> Nil{}:
409      {==}
410    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> k10 <> k11 <> Nil{}:
411      {==}
412    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> k10 <> k11 <> k12 <> Nil{}:
413      {==}
414    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> k10 <> k11 <> k12 <> k13 <> Nil{}:
415      {==}
416    case k0 <> k1 <> k2 <> k3 <> k4 <> k5 <> k6 <> k7 <> k8 <> k9 <> k10 <> k11 <> k12 <> k13 <> k14 <> Nil{}:
417      {==}
418
419law digest_correct:
420  for s: S.State
421  {C.digest(s) == F.digest(s) : List<&2, U32>}
422
423def digest_correct(s):
424  match s:
425    case S.H{a, b, c, d, e, f, g, h}:
426      {==}
427
428law block_bytes_correct:
429  for +bytes: List<&2, U32>
430  for +extra: Nat
431  for +ks: List<&2, U32>
432  for +s: S.State
433  {C.block_bytes(bytes, extra, ks, s) == F.blocks(F.schedules(F.words(bytes), extra), ks)(s) : S.State}
434
435def block_bytes_correct(bytes, extra, ks, s):
436  match bytes:
437    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> b63 <> rest:
438      +block = {[
439        C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15),
440        C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31),
441        C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47),
442        C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, b63)
443      ] : List<&2, U32>}
444      +fast = C.window_compress16(
445        C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15),
446        C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31),
447        C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47),
448        C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, b63),
449        extra, ks, s)
450      %schedule_correct(extra, block) :
451        {C.block_bytes(rest, extra, ks, fast) == F.blocks(F.schedules(F.words(rest), extra), ks)(F.compress(_, ks, s)) : S.State}
452      %compression_correct(C.schedule(extra, block), ks, s) :
453        {C.block_bytes(rest, extra, ks, fast) == F.blocks(F.schedules(F.words(rest), extra), ks)(_) : S.State}
454      %fused_compress_correct(block, extra, ks, s) :
455        {C.block_bytes(rest, extra, ks, fast) == F.blocks(F.schedules(F.words(rest), extra), ks)(_) : S.State}
456      %window_compress16_correct(
457        C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15),
458        C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31),
459        C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47),
460        C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, b63),
461        extra, ks, s) :
462        {C.block_bytes(rest, extra, ks, fast) == F.blocks(F.schedules(F.words(rest), extra), ks)(_) : S.State}
463      block_bytes_correct(rest, extra, ks, fast)
464    case Nil{}:
465      {==}
466    case b0 <> Nil{}:
467      {==}
468    case b0 <> b1 <> Nil{}:
469      {==}
470    case b0 <> b1 <> b2 <> Nil{}:
471      {==}
472    case b0 <> b1 <> b2 <> b3 <> Nil{}:
473      {==}
474    case b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}:
475      {==}
476    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}:
477      {==}
478    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}:
479      {==}
480    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}:
481      {==}
482    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}:
483      {==}
484    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}:
485      {==}
486    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}:
487      {==}
488    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}:
489      {==}
490    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}:
491      {==}
492    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}:
493      {==}
494    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}:
495      {==}
496    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}:
497      {==}
498    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}:
499      {==}
500    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}:
501      {==}
502    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}:
503      {==}
504    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}:
505      {==}
506    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}:
507      {==}
508    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}:
509      {==}
510    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}:
511      {==}
512    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}:
513      {==}
514    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}:
515      {==}
516    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}:
517      {==}
518    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}:
519      {==}
520    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}:
521      {==}
522    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}:
523      {==}
524    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}:
525      {==}
526    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}:
527      {==}
528    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}:
529      {==}
530    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}:
531      {==}
532    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}:
533      {==}
534    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}:
535      {==}
536    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}:
537      {==}
538    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}:
539      {==}
540    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}:
541      {==}
542    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}:
543      {==}
544    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}:
545      {==}
546    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}:
547      {==}
548    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}:
549      {==}
550    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}:
551      {==}
552    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}:
553      {==}
554    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}:
555      {==}
556    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}:
557      {==}
558    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}:
559      {==}
560    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}:
561      {==}
562    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}:
563      {==}
564    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}:
565      {==}
566    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}:
567      {==}
568    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}:
569      {==}
570    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}:
571      {==}
572    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}:
573      {==}
574    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}:
575      {==}
576    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}:
577      {==}
578    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}:
579      {==}
580    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}:
581      {==}
582    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}:
583      {==}
584    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}:
585      {==}
586    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}:
587      {==}
588    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}:
589      {==}
590    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}:
591      {==}
592
593law suffix_correct:
594  for +n: Nat
595  {C.suffix(n) == F.padding_suffix(n) : List<&2, U32>}
596
597def suffix_correct(n):
598  %Padding.zeros_correct(Nat.mod(n, 64n)) :
599    {C.suffix(n) == 128 <> List.append(&2, U32, List.replicate(U32, _, 0), F.length_field(n)) : List<&2, U32>}
600  %length_correct(n) :
601    {C.suffix(n) == 128 <> List.append(&2, U32,
602      List.replicate(U32, Nat.mod(Nat.sub(119n, Nat.mod(n, 64n)), 64n), 0), _) : List<&2, U32>}
603  {==}
604
605# Byte counts of whole blocks: 64 * k, built the way stream accumulates them.
606def mul64(k: Nat) -> Nat:
607  match k:
608    case 0n:
609      0n
610    case 1n+p:
611      Nat.add(64n, mul64(p))
612
613# The quotient accumulator never affects the remainder computed by divmod.
614law mod_quotient:
615  for +x: Nat
616  for +m: Nat
617  for +d: Nat
618  for +e: Nat
619  for +r: Nat
620  {Pair.snd(Nat, Nat, Nat.divmod.go(x, m, d, r)) == Pair.snd(Nat, Nat, Nat.divmod.go(x, m, e, r)) : Nat}
621
622def mod_quotient(x, m, d, e, r):
623  match x m:
624    case 0n _:
625      {==}
626    case 1n+p 0n:
627      mod_quotient(p, r, 1n+d, 1n+e, 0n)
628    case 1n+p 1n+q:
629      mod_quotient(p, q, d, e, 1n+r)
630
631# Sixty-four divmod steps return to the initial counter state with a larger quotient.
632law mod_shift:
633  for +x: Nat
634  {Nat.mod(Nat.add(64n, x), 64n) == Nat.mod(x, 64n) : Nat}
635
636def mod_shift(x):
637  mod_quotient(x, 63n, 1n, 0n, 0n)
638
639law mod_tail:
640  for +x: Nat
641  for +k: Nat
642  {Nat.mod(Nat.add(x, mul64(k)), 64n) == Nat.mod(x, 64n) : Nat}
643
644def mod_tail(x, k):
645  match k:
646    case 0n:
647      %L.add_zero(x) : {Nat.mod(Nat.add(x, 0n), 64n) == Nat.mod(_, 64n) : Nat}
648      {==}
649    case 1n+p:
650      Equal.trans(Nat, Nat.mod(Nat.add(x, Nat.add(64n, mul64(p))), 64n),
651        Nat.mod(Nat.add(64n, Nat.add(x, mul64(p))), 64n), Nat.mod(x, 64n),
652        Equal.cong(Nat, Nat, y => Nat.mod(y, 64n),
653          Nat.add(x, Nat.add(64n, mul64(p))), Nat.add(64n, Nat.add(x, mul64(p))),
654          L.add_swap(x, 64n, mul64(p))),
655        Equal.trans(Nat, Nat.mod(Nat.add(64n, Nat.add(x, mul64(p))), 64n),
656          Nat.mod(Nat.add(x, mul64(p)), 64n), Nat.mod(x, 64n),
657          mod_shift(Nat.add(x, mul64(p))), mod_tail(x, p)))
658
659# Each literal-constant round refines one step of window_rounds over the
660# remaining FIPS constants; the window variables stay abstract, so every proof
661# is one unfolding followed by the next round's lemma.
662law kr64_correct:
663  for +q: Nat
664  for +win: C.ShaWindow
665  for +s: S.State
666  {C.kr64(q, win, s) == C.window_rounds(q, win, Nil{}, s) : S.State}
667
668def kr64_correct(q, win, s):
669  match q win:
670    case 0n _:
671      {==}
672    case 1n+z C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}:
673      {==}
674
675law kr63_correct:
676  for +q: Nat
677  for +x0: U32
678  for +x1: U32
679  for +x2: U32
680  for +x3: U32
681  for +x4: U32
682  for +x5: U32
683  for +x6: U32
684  for +x7: U32
685  for +x8: U32
686  for +x9: U32
687  for +x10: U32
688  for +x11: U32
689  for +x12: U32
690  for +x13: U32
691  for +x14: U32
692  for +x15: U32
693  for +s: S.State
694  {C.kr63(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
695    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3329325298], s) : S.State}
696
697def kr63_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
698  match q:
699    case 0n:
700      {==}
701    case 1n+z:
702      kr64_correct(z, C.W{(C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14},
703        C.step(s, 3329325298, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
704
705law kr62_correct:
706  for +q: Nat
707  for +x0: U32
708  for +x1: U32
709  for +x2: U32
710  for +x3: U32
711  for +x4: U32
712  for +x5: U32
713  for +x6: U32
714  for +x7: U32
715  for +x8: U32
716  for +x9: U32
717  for +x10: U32
718  for +x11: U32
719  for +x12: U32
720  for +x13: U32
721  for +x14: U32
722  for +x15: U32
723  for +s: S.State
724  {C.kr62(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
725    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3204031479, 3329325298], s) : S.State}
726
727def kr62_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
728  match q:
729    case 0n:
730      {==}
731    case 1n+z:
732      kr63_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
733        C.step(s, 3204031479, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
734
735law kr61_correct:
736  for +q: Nat
737  for +x0: U32
738  for +x1: U32
739  for +x2: U32
740  for +x3: U32
741  for +x4: U32
742  for +x5: U32
743  for +x6: U32
744  for +x7: U32
745  for +x8: U32
746  for +x9: U32
747  for +x10: U32
748  for +x11: U32
749  for +x12: U32
750  for +x13: U32
751  for +x14: U32
752  for +x15: U32
753  for +s: S.State
754  {C.kr61(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
755    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2756734187, 3204031479, 3329325298], s) : S.State}
756
757def kr61_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
758  match q:
759    case 0n:
760      {==}
761    case 1n+z:
762      kr62_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
763        C.step(s, 2756734187, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
764
765law kr60_correct:
766  for +q: Nat
767  for +x0: U32
768  for +x1: U32
769  for +x2: U32
770  for +x3: U32
771  for +x4: U32
772  for +x5: U32
773  for +x6: U32
774  for +x7: U32
775  for +x8: U32
776  for +x9: U32
777  for +x10: U32
778  for +x11: U32
779  for +x12: U32
780  for +x13: U32
781  for +x14: U32
782  for +x15: U32
783  for +s: S.State
784  {C.kr60(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
785    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
786
787def kr60_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
788  match q:
789    case 0n:
790      {==}
791    case 1n+z:
792      kr61_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
793        C.step(s, 2428436474, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
794
795law kr59_correct:
796  for +q: Nat
797  for +x0: U32
798  for +x1: U32
799  for +x2: U32
800  for +x3: U32
801  for +x4: U32
802  for +x5: U32
803  for +x6: U32
804  for +x7: U32
805  for +x8: U32
806  for +x9: U32
807  for +x10: U32
808  for +x11: U32
809  for +x12: U32
810  for +x13: U32
811  for +x14: U32
812  for +x15: U32
813  for +s: S.State
814  {C.kr59(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
815    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
816
817def kr59_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
818  match q:
819    case 0n:
820      {==}
821    case 1n+z:
822      kr60_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
823        C.step(s, 2361852424, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
824
825law kr58_correct:
826  for +q: Nat
827  for +x0: U32
828  for +x1: U32
829  for +x2: U32
830  for +x3: U32
831  for +x4: U32
832  for +x5: U32
833  for +x6: U32
834  for +x7: U32
835  for +x8: U32
836  for +x9: U32
837  for +x10: U32
838  for +x11: U32
839  for +x12: U32
840  for +x13: U32
841  for +x14: U32
842  for +x15: U32
843  for +s: S.State
844  {C.kr58(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
845    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
846
847def kr58_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
848  match q:
849    case 0n:
850      {==}
851    case 1n+z:
852      kr59_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
853        C.step(s, 2227730452, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
854
855law kr57_correct:
856  for +q: Nat
857  for +x0: U32
858  for +x1: U32
859  for +x2: U32
860  for +x3: U32
861  for +x4: U32
862  for +x5: U32
863  for +x6: U32
864  for +x7: U32
865  for +x8: U32
866  for +x9: U32
867  for +x10: U32
868  for +x11: U32
869  for +x12: U32
870  for +x13: U32
871  for +x14: U32
872  for +x15: U32
873  for +s: S.State
874  {C.kr57(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
875    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
876
877def kr57_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
878  match q:
879    case 0n:
880      {==}
881    case 1n+z:
882      kr58_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
883        C.step(s, 2024104815, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
884
885law kr56_correct:
886  for +q: Nat
887  for +x0: U32
888  for +x1: U32
889  for +x2: U32
890  for +x3: U32
891  for +x4: U32
892  for +x5: U32
893  for +x6: U32
894  for +x7: U32
895  for +x8: U32
896  for +x9: U32
897  for +x10: U32
898  for +x11: U32
899  for +x12: U32
900  for +x13: U32
901  for +x14: U32
902  for +x15: U32
903  for +s: S.State
904  {C.kr56(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
905    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
906
907def kr56_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
908  match q:
909    case 0n:
910      {==}
911    case 1n+z:
912      kr57_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
913        C.step(s, 1955562222, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
914
915law kr55_correct:
916  for +q: Nat
917  for +x0: U32
918  for +x1: U32
919  for +x2: U32
920  for +x3: U32
921  for +x4: U32
922  for +x5: U32
923  for +x6: U32
924  for +x7: U32
925  for +x8: U32
926  for +x9: U32
927  for +x10: U32
928  for +x11: U32
929  for +x12: U32
930  for +x13: U32
931  for +x14: U32
932  for +x15: U32
933  for +s: S.State
934  {C.kr55(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
935    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
936
937def kr55_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
938  match q:
939    case 0n:
940      {==}
941    case 1n+z:
942      kr56_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
943        C.step(s, 1747873779, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
944
945law kr54_correct:
946  for +q: Nat
947  for +x0: U32
948  for +x1: U32
949  for +x2: U32
950  for +x3: U32
951  for +x4: U32
952  for +x5: U32
953  for +x6: U32
954  for +x7: U32
955  for +x8: U32
956  for +x9: U32
957  for +x10: U32
958  for +x11: U32
959  for +x12: U32
960  for +x13: U32
961  for +x14: U32
962  for +x15: U32
963  for +s: S.State
964  {C.kr54(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
965    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
966
967def kr54_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
968  match q:
969    case 0n:
970      {==}
971    case 1n+z:
972      kr55_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
973        C.step(s, 1537002063, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
974
975law kr53_correct:
976  for +q: Nat
977  for +x0: U32
978  for +x1: U32
979  for +x2: U32
980  for +x3: U32
981  for +x4: U32
982  for +x5: U32
983  for +x6: U32
984  for +x7: U32
985  for +x8: U32
986  for +x9: U32
987  for +x10: U32
988  for +x11: U32
989  for +x12: U32
990  for +x13: U32
991  for +x14: U32
992  for +x15: U32
993  for +s: S.State
994  {C.kr53(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
995    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
996
997def kr53_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
998  match q:
999    case 0n:
1000      {==}
1001    case 1n+z:
1002      kr54_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1003        C.step(s, 1322822218, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1004
1005law kr52_correct:
1006  for +q: Nat
1007  for +x0: U32
1008  for +x1: U32
1009  for +x2: U32
1010  for +x3: U32
1011  for +x4: U32
1012  for +x5: U32
1013  for +x6: U32
1014  for +x7: U32
1015  for +x8: U32
1016  for +x9: U32
1017  for +x10: U32
1018  for +x11: U32
1019  for +x12: U32
1020  for +x13: U32
1021  for +x14: U32
1022  for +x15: U32
1023  for +s: S.State
1024  {C.kr52(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1025    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1026
1027def kr52_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1028  match q:
1029    case 0n:
1030      {==}
1031    case 1n+z:
1032      kr53_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1033        C.step(s, 958139571, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1034
1035law kr51_correct:
1036  for +q: Nat
1037  for +x0: U32
1038  for +x1: U32
1039  for +x2: U32
1040  for +x3: U32
1041  for +x4: U32
1042  for +x5: U32
1043  for +x6: U32
1044  for +x7: U32
1045  for +x8: U32
1046  for +x9: U32
1047  for +x10: U32
1048  for +x11: U32
1049  for +x12: U32
1050  for +x13: U32
1051  for +x14: U32
1052  for +x15: U32
1053  for +s: S.State
1054  {C.kr51(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1055    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1056
1057def kr51_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1058  match q:
1059    case 0n:
1060      {==}
1061    case 1n+z:
1062      kr52_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1063        C.step(s, 883997877, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1064
1065law kr50_correct:
1066  for +q: Nat
1067  for +x0: U32
1068  for +x1: U32
1069  for +x2: U32
1070  for +x3: U32
1071  for +x4: U32
1072  for +x5: U32
1073  for +x6: U32
1074  for +x7: U32
1075  for +x8: U32
1076  for +x9: U32
1077  for +x10: U32
1078  for +x11: U32
1079  for +x12: U32
1080  for +x13: U32
1081  for +x14: U32
1082  for +x15: U32
1083  for +s: S.State
1084  {C.kr50(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1085    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1086
1087def kr50_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1088  match q:
1089    case 0n:
1090      {==}
1091    case 1n+z:
1092      kr51_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1093        C.step(s, 659060556, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1094
1095law kr49_correct:
1096  for +q: Nat
1097  for +x0: U32
1098  for +x1: U32
1099  for +x2: U32
1100  for +x3: U32
1101  for +x4: U32
1102  for +x5: U32
1103  for +x6: U32
1104  for +x7: U32
1105  for +x8: U32
1106  for +x9: U32
1107  for +x10: U32
1108  for +x11: U32
1109  for +x12: U32
1110  for +x13: U32
1111  for +x14: U32
1112  for +x15: U32
1113  for +s: S.State
1114  {C.kr49(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1115    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1116
1117def kr49_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1118  match q:
1119    case 0n:
1120      {==}
1121    case 1n+z:
1122      kr50_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1123        C.step(s, 506948616, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1124
1125law kr48_correct:
1126  for +q: Nat
1127  for +x0: U32
1128  for +x1: U32
1129  for +x2: U32
1130  for +x3: U32
1131  for +x4: U32
1132  for +x5: U32
1133  for +x6: U32
1134  for +x7: U32
1135  for +x8: U32
1136  for +x9: U32
1137  for +x10: U32
1138  for +x11: U32
1139  for +x12: U32
1140  for +x13: U32
1141  for +x14: U32
1142  for +x15: U32
1143  for +s: S.State
1144  {C.kr48(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1145    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1146
1147def kr48_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1148  match q:
1149    case 0n:
1150      {==}
1151    case 1n+z:
1152      kr49_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1153        C.step(s, 430227734, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1154
1155law kr47_correct:
1156  for +q: Nat
1157  for +x0: U32
1158  for +x1: U32
1159  for +x2: U32
1160  for +x3: U32
1161  for +x4: U32
1162  for +x5: U32
1163  for +x6: U32
1164  for +x7: U32
1165  for +x8: U32
1166  for +x9: U32
1167  for +x10: U32
1168  for +x11: U32
1169  for +x12: U32
1170  for +x13: U32
1171  for +x14: U32
1172  for +x15: U32
1173  for +s: S.State
1174  {C.kr47(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1175    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1176
1177def kr47_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1178  match q:
1179    case 0n:
1180      {==}
1181    case 1n+z:
1182      kr48_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1183        C.step(s, 275423344, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1184
1185law kr46_correct:
1186  for +q: Nat
1187  for +x0: U32
1188  for +x1: U32
1189  for +x2: U32
1190  for +x3: U32
1191  for +x4: U32
1192  for +x5: U32
1193  for +x6: U32
1194  for +x7: U32
1195  for +x8: U32
1196  for +x9: U32
1197  for +x10: U32
1198  for +x11: U32
1199  for +x12: U32
1200  for +x13: U32
1201  for +x14: U32
1202  for +x15: U32
1203  for +s: S.State
1204  {C.kr46(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1205    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1206
1207def kr46_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1208  match q:
1209    case 0n:
1210      {==}
1211    case 1n+z:
1212      kr47_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1213        C.step(s, 4094571909, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1214
1215law kr45_correct:
1216  for +q: Nat
1217  for +x0: U32
1218  for +x1: U32
1219  for +x2: U32
1220  for +x3: U32
1221  for +x4: U32
1222  for +x5: U32
1223  for +x6: U32
1224  for +x7: U32
1225  for +x8: U32
1226  for +x9: U32
1227  for +x10: U32
1228  for +x11: U32
1229  for +x12: U32
1230  for +x13: U32
1231  for +x14: U32
1232  for +x15: U32
1233  for +s: S.State
1234  {C.kr45(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1235    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1236
1237def kr45_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1238  match q:
1239    case 0n:
1240      {==}
1241    case 1n+z:
1242      kr46_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1243        C.step(s, 3600352804, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1244
1245law kr44_correct:
1246  for +q: Nat
1247  for +x0: U32
1248  for +x1: U32
1249  for +x2: U32
1250  for +x3: U32
1251  for +x4: U32
1252  for +x5: U32
1253  for +x6: U32
1254  for +x7: U32
1255  for +x8: U32
1256  for +x9: U32
1257  for +x10: U32
1258  for +x11: U32
1259  for +x12: U32
1260  for +x13: U32
1261  for +x14: U32
1262  for +x15: U32
1263  for +s: S.State
1264  {C.kr44(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1265    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1266
1267def kr44_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1268  match q:
1269    case 0n:
1270      {==}
1271    case 1n+z:
1272      kr45_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1273        C.step(s, 3516065817, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1274
1275law kr43_correct:
1276  for +q: Nat
1277  for +x0: U32
1278  for +x1: U32
1279  for +x2: U32
1280  for +x3: U32
1281  for +x4: U32
1282  for +x5: U32
1283  for +x6: U32
1284  for +x7: U32
1285  for +x8: U32
1286  for +x9: U32
1287  for +x10: U32
1288  for +x11: U32
1289  for +x12: U32
1290  for +x13: U32
1291  for +x14: U32
1292  for +x15: U32
1293  for +s: S.State
1294  {C.kr43(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1295    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1296
1297def kr43_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1298  match q:
1299    case 0n:
1300      {==}
1301    case 1n+z:
1302      kr44_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1303        C.step(s, 3345764771, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1304
1305law kr42_correct:
1306  for +q: Nat
1307  for +x0: U32
1308  for +x1: U32
1309  for +x2: U32
1310  for +x3: U32
1311  for +x4: U32
1312  for +x5: U32
1313  for +x6: U32
1314  for +x7: U32
1315  for +x8: U32
1316  for +x9: U32
1317  for +x10: U32
1318  for +x11: U32
1319  for +x12: U32
1320  for +x13: U32
1321  for +x14: U32
1322  for +x15: U32
1323  for +s: S.State
1324  {C.kr42(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1325    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1326
1327def kr42_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1328  match q:
1329    case 0n:
1330      {==}
1331    case 1n+z:
1332      kr43_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1333        C.step(s, 3259730800, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1334
1335law kr41_correct:
1336  for +q: Nat
1337  for +x0: U32
1338  for +x1: U32
1339  for +x2: U32
1340  for +x3: U32
1341  for +x4: U32
1342  for +x5: U32
1343  for +x6: U32
1344  for +x7: U32
1345  for +x8: U32
1346  for +x9: U32
1347  for +x10: U32
1348  for +x11: U32
1349  for +x12: U32
1350  for +x13: U32
1351  for +x14: U32
1352  for +x15: U32
1353  for +s: S.State
1354  {C.kr41(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1355    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1356
1357def kr41_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1358  match q:
1359    case 0n:
1360      {==}
1361    case 1n+z:
1362      kr42_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1363        C.step(s, 2820302411, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1364
1365law kr40_correct:
1366  for +q: Nat
1367  for +x0: U32
1368  for +x1: U32
1369  for +x2: U32
1370  for +x3: U32
1371  for +x4: U32
1372  for +x5: U32
1373  for +x6: U32
1374  for +x7: U32
1375  for +x8: U32
1376  for +x9: U32
1377  for +x10: U32
1378  for +x11: U32
1379  for +x12: U32
1380  for +x13: U32
1381  for +x14: U32
1382  for +x15: U32
1383  for +s: S.State
1384  {C.kr40(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1385    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1386
1387def kr40_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1388  match q:
1389    case 0n:
1390      {==}
1391    case 1n+z:
1392      kr41_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1393        C.step(s, 2730485921, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1394
1395law kr39_correct:
1396  for +q: Nat
1397  for +x0: U32
1398  for +x1: U32
1399  for +x2: U32
1400  for +x3: U32
1401  for +x4: U32
1402  for +x5: U32
1403  for +x6: U32
1404  for +x7: U32
1405  for +x8: U32
1406  for +x9: U32
1407  for +x10: U32
1408  for +x11: U32
1409  for +x12: U32
1410  for +x13: U32
1411  for +x14: U32
1412  for +x15: U32
1413  for +s: S.State
1414  {C.kr39(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1415    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1416
1417def kr39_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1418  match q:
1419    case 0n:
1420      {==}
1421    case 1n+z:
1422      kr40_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1423        C.step(s, 2456956037, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1424
1425law kr38_correct:
1426  for +q: Nat
1427  for +x0: U32
1428  for +x1: U32
1429  for +x2: U32
1430  for +x3: U32
1431  for +x4: U32
1432  for +x5: U32
1433  for +x6: U32
1434  for +x7: U32
1435  for +x8: U32
1436  for +x9: U32
1437  for +x10: U32
1438  for +x11: U32
1439  for +x12: U32
1440  for +x13: U32
1441  for +x14: U32
1442  for +x15: U32
1443  for +s: S.State
1444  {C.kr38(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1445    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1446
1447def kr38_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1448  match q:
1449    case 0n:
1450      {==}
1451    case 1n+z:
1452      kr39_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1453        C.step(s, 2177026350, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1454
1455law kr37_correct:
1456  for +q: Nat
1457  for +x0: U32
1458  for +x1: U32
1459  for +x2: U32
1460  for +x3: U32
1461  for +x4: U32
1462  for +x5: U32
1463  for +x6: U32
1464  for +x7: U32
1465  for +x8: U32
1466  for +x9: U32
1467  for +x10: U32
1468  for +x11: U32
1469  for +x12: U32
1470  for +x13: U32
1471  for +x14: U32
1472  for +x15: U32
1473  for +s: S.State
1474  {C.kr37(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1475    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1476
1477def kr37_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1478  match q:
1479    case 0n:
1480      {==}
1481    case 1n+z:
1482      kr38_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1483        C.step(s, 1986661051, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1484
1485law kr36_correct:
1486  for +q: Nat
1487  for +x0: U32
1488  for +x1: U32
1489  for +x2: U32
1490  for +x3: U32
1491  for +x4: U32
1492  for +x5: U32
1493  for +x6: U32
1494  for +x7: U32
1495  for +x8: U32
1496  for +x9: U32
1497  for +x10: U32
1498  for +x11: U32
1499  for +x12: U32
1500  for +x13: U32
1501  for +x14: U32
1502  for +x15: U32
1503  for +s: S.State
1504  {C.kr36(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1505    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1506
1507def kr36_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1508  match q:
1509    case 0n:
1510      {==}
1511    case 1n+z:
1512      kr37_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1513        C.step(s, 1695183700, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1514
1515law kr35_correct:
1516  for +q: Nat
1517  for +x0: U32
1518  for +x1: U32
1519  for +x2: U32
1520  for +x3: U32
1521  for +x4: U32
1522  for +x5: U32
1523  for +x6: U32
1524  for +x7: U32
1525  for +x8: U32
1526  for +x9: U32
1527  for +x10: U32
1528  for +x11: U32
1529  for +x12: U32
1530  for +x13: U32
1531  for +x14: U32
1532  for +x15: U32
1533  for +s: S.State
1534  {C.kr35(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1535    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1536
1537def kr35_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1538  match q:
1539    case 0n:
1540      {==}
1541    case 1n+z:
1542      kr36_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1543        C.step(s, 1396182291, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1544
1545law kr34_correct:
1546  for +q: Nat
1547  for +x0: U32
1548  for +x1: U32
1549  for +x2: U32
1550  for +x3: U32
1551  for +x4: U32
1552  for +x5: U32
1553  for +x6: U32
1554  for +x7: U32
1555  for +x8: U32
1556  for +x9: U32
1557  for +x10: U32
1558  for +x11: U32
1559  for +x12: U32
1560  for +x13: U32
1561  for +x14: U32
1562  for +x15: U32
1563  for +s: S.State
1564  {C.kr34(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1565    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1566
1567def kr34_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1568  match q:
1569    case 0n:
1570      {==}
1571    case 1n+z:
1572      kr35_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1573        C.step(s, 1294757372, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1574
1575law kr33_correct:
1576  for +q: Nat
1577  for +x0: U32
1578  for +x1: U32
1579  for +x2: U32
1580  for +x3: U32
1581  for +x4: U32
1582  for +x5: U32
1583  for +x6: U32
1584  for +x7: U32
1585  for +x8: U32
1586  for +x9: U32
1587  for +x10: U32
1588  for +x11: U32
1589  for +x12: U32
1590  for +x13: U32
1591  for +x14: U32
1592  for +x15: U32
1593  for +s: S.State
1594  {C.kr33(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1595    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1596
1597def kr33_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1598  match q:
1599    case 0n:
1600      {==}
1601    case 1n+z:
1602      kr34_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1603        C.step(s, 773529912, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1604
1605law kr32_correct:
1606  for +q: Nat
1607  for +x0: U32
1608  for +x1: U32
1609  for +x2: U32
1610  for +x3: U32
1611  for +x4: U32
1612  for +x5: U32
1613  for +x6: U32
1614  for +x7: U32
1615  for +x8: U32
1616  for +x9: U32
1617  for +x10: U32
1618  for +x11: U32
1619  for +x12: U32
1620  for +x13: U32
1621  for +x14: U32
1622  for +x15: U32
1623  for +s: S.State
1624  {C.kr32(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1625    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1626
1627def kr32_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1628  match q:
1629    case 0n:
1630      {==}
1631    case 1n+z:
1632      kr33_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1633        C.step(s, 666307205, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1634
1635law kr31_correct:
1636  for +q: Nat
1637  for +x0: U32
1638  for +x1: U32
1639  for +x2: U32
1640  for +x3: U32
1641  for +x4: U32
1642  for +x5: U32
1643  for +x6: U32
1644  for +x7: U32
1645  for +x8: U32
1646  for +x9: U32
1647  for +x10: U32
1648  for +x11: U32
1649  for +x12: U32
1650  for +x13: U32
1651  for +x14: U32
1652  for +x15: U32
1653  for +s: S.State
1654  {C.kr31(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1655    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1656
1657def kr31_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1658  match q:
1659    case 0n:
1660      {==}
1661    case 1n+z:
1662      kr32_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1663        C.step(s, 338241895, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1664
1665law kr30_correct:
1666  for +q: Nat
1667  for +x0: U32
1668  for +x1: U32
1669  for +x2: U32
1670  for +x3: U32
1671  for +x4: U32
1672  for +x5: U32
1673  for +x6: U32
1674  for +x7: U32
1675  for +x8: U32
1676  for +x9: U32
1677  for +x10: U32
1678  for +x11: U32
1679  for +x12: U32
1680  for +x13: U32
1681  for +x14: U32
1682  for +x15: U32
1683  for +s: S.State
1684  {C.kr30(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1685    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1686
1687def kr30_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1688  match q:
1689    case 0n:
1690      {==}
1691    case 1n+z:
1692      kr31_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1693        C.step(s, 113926993, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1694
1695law kr29_correct:
1696  for +q: Nat
1697  for +x0: U32
1698  for +x1: U32
1699  for +x2: U32
1700  for +x3: U32
1701  for +x4: U32
1702  for +x5: U32
1703  for +x6: U32
1704  for +x7: U32
1705  for +x8: U32
1706  for +x9: U32
1707  for +x10: U32
1708  for +x11: U32
1709  for +x12: U32
1710  for +x13: U32
1711  for +x14: U32
1712  for +x15: U32
1713  for +s: S.State
1714  {C.kr29(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1715    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1716
1717def kr29_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1718  match q:
1719    case 0n:
1720      {==}
1721    case 1n+z:
1722      kr30_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1723        C.step(s, 3584528711, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1724
1725law kr28_correct:
1726  for +q: Nat
1727  for +x0: U32
1728  for +x1: U32
1729  for +x2: U32
1730  for +x3: U32
1731  for +x4: U32
1732  for +x5: U32
1733  for +x6: U32
1734  for +x7: U32
1735  for +x8: U32
1736  for +x9: U32
1737  for +x10: U32
1738  for +x11: U32
1739  for +x12: U32
1740  for +x13: U32
1741  for +x14: U32
1742  for +x15: U32
1743  for +s: S.State
1744  {C.kr28(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1745    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1746
1747def kr28_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1748  match q:
1749    case 0n:
1750      {==}
1751    case 1n+z:
1752      kr29_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1753        C.step(s, 3336571891, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1754
1755law kr27_correct:
1756  for +q: Nat
1757  for +x0: U32
1758  for +x1: U32
1759  for +x2: U32
1760  for +x3: U32
1761  for +x4: U32
1762  for +x5: U32
1763  for +x6: U32
1764  for +x7: U32
1765  for +x8: U32
1766  for +x9: U32
1767  for +x10: U32
1768  for +x11: U32
1769  for +x12: U32
1770  for +x13: U32
1771  for +x14: U32
1772  for +x15: U32
1773  for +s: S.State
1774  {C.kr27(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1775    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1776
1777def kr27_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1778  match q:
1779    case 0n:
1780      {==}
1781    case 1n+z:
1782      kr28_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1783        C.step(s, 3210313671, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1784
1785law kr26_correct:
1786  for +q: Nat
1787  for +x0: U32
1788  for +x1: U32
1789  for +x2: U32
1790  for +x3: U32
1791  for +x4: U32
1792  for +x5: U32
1793  for +x6: U32
1794  for +x7: U32
1795  for +x8: U32
1796  for +x9: U32
1797  for +x10: U32
1798  for +x11: U32
1799  for +x12: U32
1800  for +x13: U32
1801  for +x14: U32
1802  for +x15: U32
1803  for +s: S.State
1804  {C.kr26(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1805    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1806
1807def kr26_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1808  match q:
1809    case 0n:
1810      {==}
1811    case 1n+z:
1812      kr27_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1813        C.step(s, 2952996808, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1814
1815law kr25_correct:
1816  for +q: Nat
1817  for +x0: U32
1818  for +x1: U32
1819  for +x2: U32
1820  for +x3: U32
1821  for +x4: U32
1822  for +x5: U32
1823  for +x6: U32
1824  for +x7: U32
1825  for +x8: U32
1826  for +x9: U32
1827  for +x10: U32
1828  for +x11: U32
1829  for +x12: U32
1830  for +x13: U32
1831  for +x14: U32
1832  for +x15: U32
1833  for +s: S.State
1834  {C.kr25(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1835    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1836
1837def kr25_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1838  match q:
1839    case 0n:
1840      {==}
1841    case 1n+z:
1842      kr26_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1843        C.step(s, 2821834349, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1844
1845law kr24_correct:
1846  for +q: Nat
1847  for +x0: U32
1848  for +x1: U32
1849  for +x2: U32
1850  for +x3: U32
1851  for +x4: U32
1852  for +x5: U32
1853  for +x6: U32
1854  for +x7: U32
1855  for +x8: U32
1856  for +x9: U32
1857  for +x10: U32
1858  for +x11: U32
1859  for +x12: U32
1860  for +x13: U32
1861  for +x14: U32
1862  for +x15: U32
1863  for +s: S.State
1864  {C.kr24(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1865    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1866
1867def kr24_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1868  match q:
1869    case 0n:
1870      {==}
1871    case 1n+z:
1872      kr25_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1873        C.step(s, 2554220882, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1874
1875law kr23_correct:
1876  for +q: Nat
1877  for +x0: U32
1878  for +x1: U32
1879  for +x2: U32
1880  for +x3: U32
1881  for +x4: U32
1882  for +x5: U32
1883  for +x6: U32
1884  for +x7: U32
1885  for +x8: U32
1886  for +x9: U32
1887  for +x10: U32
1888  for +x11: U32
1889  for +x12: U32
1890  for +x13: U32
1891  for +x14: U32
1892  for +x15: U32
1893  for +s: S.State
1894  {C.kr23(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1895    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1896
1897def kr23_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1898  match q:
1899    case 0n:
1900      {==}
1901    case 1n+z:
1902      kr24_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1903        C.step(s, 1996064986, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1904
1905law kr22_correct:
1906  for +q: Nat
1907  for +x0: U32
1908  for +x1: U32
1909  for +x2: U32
1910  for +x3: U32
1911  for +x4: U32
1912  for +x5: U32
1913  for +x6: U32
1914  for +x7: U32
1915  for +x8: U32
1916  for +x9: U32
1917  for +x10: U32
1918  for +x11: U32
1919  for +x12: U32
1920  for +x13: U32
1921  for +x14: U32
1922  for +x15: U32
1923  for +s: S.State
1924  {C.kr22(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1925    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1926
1927def kr22_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1928  match q:
1929    case 0n:
1930      {==}
1931    case 1n+z:
1932      kr23_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1933        C.step(s, 1555081692, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1934
1935law kr21_correct:
1936  for +q: Nat
1937  for +x0: U32
1938  for +x1: U32
1939  for +x2: U32
1940  for +x3: U32
1941  for +x4: U32
1942  for +x5: U32
1943  for +x6: U32
1944  for +x7: U32
1945  for +x8: U32
1946  for +x9: U32
1947  for +x10: U32
1948  for +x11: U32
1949  for +x12: U32
1950  for +x13: U32
1951  for +x14: U32
1952  for +x15: U32
1953  for +s: S.State
1954  {C.kr21(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1955    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1956
1957def kr21_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1958  match q:
1959    case 0n:
1960      {==}
1961    case 1n+z:
1962      kr22_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1963        C.step(s, 1249150122, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1964
1965law kr20_correct:
1966  for +q: Nat
1967  for +x0: U32
1968  for +x1: U32
1969  for +x2: U32
1970  for +x3: U32
1971  for +x4: U32
1972  for +x5: U32
1973  for +x6: U32
1974  for +x7: U32
1975  for +x8: U32
1976  for +x9: U32
1977  for +x10: U32
1978  for +x11: U32
1979  for +x12: U32
1980  for +x13: U32
1981  for +x14: U32
1982  for +x15: U32
1983  for +s: S.State
1984  {C.kr20(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
1985    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [770255983, 1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
1986
1987def kr20_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
1988  match q:
1989    case 0n:
1990      {==}
1991    case 1n+z:
1992      kr21_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
1993        C.step(s, 770255983, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
1994
1995law kr19_correct:
1996  for +q: Nat
1997  for +x0: U32
1998  for +x1: U32
1999  for +x2: U32
2000  for +x3: U32
2001  for +x4: U32
2002  for +x5: U32
2003  for +x6: U32
2004  for +x7: U32
2005  for +x8: U32
2006  for +x9: U32
2007  for +x10: U32
2008  for +x11: U32
2009  for +x12: U32
2010  for +x13: U32
2011  for +x14: U32
2012  for +x15: U32
2013  for +s: S.State
2014  {C.kr19(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
2015    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [604807628, 770255983, 1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
2016
2017def kr19_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
2018  match q:
2019    case 0n:
2020      {==}
2021    case 1n+z:
2022      kr20_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
2023        C.step(s, 604807628, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
2024
2025law kr18_correct:
2026  for +q: Nat
2027  for +x0: U32
2028  for +x1: U32
2029  for +x2: U32
2030  for +x3: U32
2031  for +x4: U32
2032  for +x5: U32
2033  for +x6: U32
2034  for +x7: U32
2035  for +x8: U32
2036  for +x9: U32
2037  for +x10: U32
2038  for +x11: U32
2039  for +x12: U32
2040  for +x13: U32
2041  for +x14: U32
2042  for +x15: U32
2043  for +s: S.State
2044  {C.kr18(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
2045    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [264347078, 604807628, 770255983, 1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
2046
2047def kr18_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
2048  match q:
2049    case 0n:
2050      {==}
2051    case 1n+z:
2052      kr19_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
2053        C.step(s, 264347078, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
2054
2055law kr17_correct:
2056  for +q: Nat
2057  for +x0: U32
2058  for +x1: U32
2059  for +x2: U32
2060  for +x3: U32
2061  for +x4: U32
2062  for +x5: U32
2063  for +x6: U32
2064  for +x7: U32
2065  for +x8: U32
2066  for +x9: U32
2067  for +x10: U32
2068  for +x11: U32
2069  for +x12: U32
2070  for +x13: U32
2071  for +x14: U32
2072  for +x15: U32
2073  for +s: S.State
2074  {C.kr17(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
2075    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [4022224774, 264347078, 604807628, 770255983, 1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
2076
2077def kr17_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
2078  match q:
2079    case 0n:
2080      {==}
2081    case 1n+z:
2082      kr18_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
2083        C.step(s, 4022224774, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
2084
2085law kr16_correct:
2086  for +q: Nat
2087  for +x0: U32
2088  for +x1: U32
2089  for +x2: U32
2090  for +x3: U32
2091  for +x4: U32
2092  for +x5: U32
2093  for +x6: U32
2094  for +x7: U32
2095  for +x8: U32
2096  for +x9: U32
2097  for +x10: U32
2098  for +x11: U32
2099  for +x12: U32
2100  for +x13: U32
2101  for +x14: U32
2102  for +x15: U32
2103  for +s: S.State
2104  {C.kr16(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, s) ==
2105    C.window_rounds(q, C.W{x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15}, [3835390401, 4022224774, 264347078, 604807628, 770255983, 1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s) : S.State}
2106
2107def kr16_correct(q, x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, s):
2108  match q:
2109    case 0n:
2110      {==}
2111    case 1n+z:
2112      kr17_correct(z, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
2113        C.step(s, 3835390401, (C.small1(x1) + x6 + C.small0(x14) + x15 : U32)))
2114
2115law fips16_correct:
2116  for +a: U32
2117  for +b: U32
2118  for +c: U32
2119  for +d: U32
2120  for +e: U32
2121  for +f: U32
2122  for +g: U32
2123  for +h: U32
2124  for +i: U32
2125  for +j: U32
2126  for +k: U32
2127  for +l: U32
2128  for +m: U32
2129  for +n: U32
2130  for +o: U32
2131  for +p: U32
2132  for +q: Nat
2133  for +s: S.State
2134  {C.fips_compress16(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, s) ==
2135    C.window_compress16(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, C.round_constants(), s) : S.State}
2136
2137def fips16_correct(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, s):
2138  +s16 = C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(C.step(s, 1116352408, a), 1899447441, b), 3049323471, c), 3921009573, d), 961987163, e), 1508970993, f), 2453635748, g), 2870763221, h), 3624381080, i), 310598401, j), 607225278, k), 1426881987, l), 1925078388, m), 2162078206, n), 2614888103, o), 3248222580, p)
2139  Equal.cong(S.State, S.State, y => C.feedforward(s, y),
2140    C.kr16(q, C.W{p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a}, s16),
2141    C.window_rounds(q, C.W{p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a}, [3835390401, 4022224774, 264347078, 604807628, 770255983, 1249150122, 1555081692, 1996064986, 2554220882, 2821834349, 2952996808, 3210313671, 3336571891, 3584528711, 113926993, 338241895, 666307205, 773529912, 1294757372, 1396182291, 1695183700, 1986661051, 2177026350, 2456956037, 2730485921, 2820302411, 3259730800, 3345764771, 3516065817, 3600352804, 4094571909, 275423344, 430227734, 506948616, 659060556, 883997877, 958139571, 1322822218, 1537002063, 1747873779, 1955562222, 2024104815, 2227730452, 2361852424, 2428436474, 2756734187, 3204031479, 3329325298], s16),
2142    kr16_correct(q, p, o, n, m, l, k, j, i, h, g, f, e, d, c, b, a, s16))
2143
2144# Streaming refines the generic block decoder, instantiated with the FIPS
2145# table, applied to the padded message. After a complete block the count grows
2146# by 64 exactly as the remaining length shrinks. For a short tail, count = 64k
2147# fixes n mod 64 to the tail length, so the modular zero count is concrete and
2148# finish_go packs the same 64 or 128 bytes that block_bytes decodes.
2149law stream_correct:
2150  for +bytes: List<&2, U32>
2151  for +k: Nat
2152  for +extra: Nat
2153  for +s: S.State
2154  {C.stream(bytes, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, bytes,
2155    C.suffix(Nat.add(List.length(&2, U32, bytes), mul64(k)))), extra, C.round_constants(), s) : S.State}
2156
2157def stream_correct(bytes, k, extra, s):
2158  match bytes:
2159    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> b63 <> rest:
2160      +fast = C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, b63), extra, s)
2161      %fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, b63), extra, s) :
2162        {C.stream(rest, mul64(1n+k), extra, fast) == C.block_bytes(List.append(&2, U32, rest,
2163          C.suffix(Nat.add(64n, Nat.add(List.length(&2, U32, rest), mul64(k))))), extra, C.round_constants(), _) : S.State}
2164      %L.add_swap(List.length(&2, U32, rest), 64n, mul64(k)) :
2165        {C.stream(rest, mul64(1n+k), extra, fast) == C.block_bytes(List.append(&2, U32, rest,
2166          C.suffix(_)), extra, C.round_constants(), fast) : S.State}
2167      stream_correct(rest, 1n+k, extra, fast)
2168    case Nil{}:
2169      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, Nil{}), mul64(k)), 64n),
2170        Nat.mod(List.length(&2, U32, Nil{}), 64n),
2171        mod_tail(List.length(&2, U32, Nil{}), k)) :
2172        {C.stream(Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, Nil{},
2173          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2174            C.bit_length(Nat.add(List.length(&2, U32, Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2175      fips16_correct(C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, Nil{}), mul64(k))), extra, s)
2176    case b0 <> Nil{}:
2177      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> Nil{}), mul64(k)), 64n),
2178        Nat.mod(List.length(&2, U32, b0 <> Nil{}), 64n),
2179        mod_tail(List.length(&2, U32, b0 <> Nil{}), k)) :
2180        {C.stream(b0 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> Nil{},
2181          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2182            C.bit_length(Nat.add(List.length(&2, U32, b0 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2183      fips16_correct(C.pack(b0, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> Nil{}), mul64(k))), extra, s)
2184    case b0 <> b1 <> Nil{}:
2185      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> Nil{}), mul64(k)), 64n),
2186        Nat.mod(List.length(&2, U32, b0 <> b1 <> Nil{}), 64n),
2187        mod_tail(List.length(&2, U32, b0 <> b1 <> Nil{}), k)) :
2188        {C.stream(b0 <> b1 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> Nil{},
2189          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2190            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2191      fips16_correct(C.pack(b0, b1, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> Nil{}), mul64(k))), extra, s)
2192    case b0 <> b1 <> b2 <> Nil{}:
2193      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> Nil{}), mul64(k)), 64n),
2194        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> Nil{}), 64n),
2195        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> Nil{}), k)) :
2196        {C.stream(b0 <> b1 <> b2 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> Nil{},
2197          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2198            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2199      fips16_correct(C.pack(b0, b1, b2, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> Nil{}), mul64(k))), extra, s)
2200    case b0 <> b1 <> b2 <> b3 <> Nil{}:
2201      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{}), mul64(k)), 64n),
2202        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{}), 64n),
2203        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{}), k)) :
2204        {C.stream(b0 <> b1 <> b2 <> b3 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{},
2205          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2206            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2207      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> Nil{}), mul64(k))), extra, s)
2208    case b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}:
2209      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}), mul64(k)), 64n),
2210        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}), 64n),
2211        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}), k)) :
2212        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{},
2213          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2214            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2215      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> Nil{}), mul64(k))), extra, s)
2216    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}:
2217      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}), mul64(k)), 64n),
2218        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}), 64n),
2219        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}), k)) :
2220        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{},
2221          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2222            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2223      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> Nil{}), mul64(k))), extra, s)
2224    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}:
2225      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}), mul64(k)), 64n),
2226        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}), 64n),
2227        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}), k)) :
2228        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{},
2229          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2230            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2231      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> Nil{}), mul64(k))), extra, s)
2232    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}:
2233      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}), mul64(k)), 64n),
2234        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}), 64n),
2235        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}), k)) :
2236        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{},
2237          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2238            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2239      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> Nil{}), mul64(k))), extra, s)
2240    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}:
2241      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}), mul64(k)), 64n),
2242        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}), 64n),
2243        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}), k)) :
2244        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{},
2245          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2246            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2247      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> Nil{}), mul64(k))), extra, s)
2248    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}:
2249      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}), mul64(k)), 64n),
2250        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}), 64n),
2251        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}), k)) :
2252        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{},
2253          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2254            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2255      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> Nil{}), mul64(k))), extra, s)
2256    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}:
2257      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}), mul64(k)), 64n),
2258        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}), 64n),
2259        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}), k)) :
2260        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{},
2261          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2262            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2263      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> Nil{}), mul64(k))), extra, s)
2264    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}:
2265      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}), mul64(k)), 64n),
2266        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}), 64n),
2267        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}), k)) :
2268        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{},
2269          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2270            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2271      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> Nil{}), mul64(k))), extra, s)
2272    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}:
2273      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}), mul64(k)), 64n),
2274        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}), 64n),
2275        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}), k)) :
2276        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{},
2277          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2278            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2279      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> Nil{}), mul64(k))), extra, s)
2280    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}:
2281      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}), mul64(k)), 64n),
2282        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}), 64n),
2283        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}), k)) :
2284        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{},
2285          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2286            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2287      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> Nil{}), mul64(k))), extra, s)
2288    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}:
2289      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}), mul64(k)), 64n),
2290        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}), 64n),
2291        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}), k)) :
2292        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{},
2293          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2294            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2295      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> Nil{}), mul64(k))), extra, s)
2296    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}:
2297      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}), mul64(k)), 64n),
2298        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}), 64n),
2299        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}), k)) :
2300        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{},
2301          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2302            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2303      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> Nil{}), mul64(k))), extra, s)
2304    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}:
2305      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}), mul64(k)), 64n),
2306        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}), 64n),
2307        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}), k)) :
2308        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{},
2309          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2310            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2311      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> Nil{}), mul64(k))), extra, s)
2312    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}:
2313      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}), mul64(k)), 64n),
2314        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}), 64n),
2315        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}), k)) :
2316        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{},
2317          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2318            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2319      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> Nil{}), mul64(k))), extra, s)
2320    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}:
2321      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}), mul64(k)), 64n),
2322        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}), 64n),
2323        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}), k)) :
2324        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{},
2325          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2326            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2327      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> Nil{}), mul64(k))), extra, s)
2328    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}:
2329      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}), mul64(k)), 64n),
2330        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}), 64n),
2331        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}), k)) :
2332        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{},
2333          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2334            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2335      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> Nil{}), mul64(k))), extra, s)
2336    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}:
2337      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}), mul64(k)), 64n),
2338        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}), 64n),
2339        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}), k)) :
2340        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{},
2341          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2342            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2343      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> Nil{}), mul64(k))), extra, s)
2344    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}:
2345      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}), mul64(k)), 64n),
2346        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}), 64n),
2347        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}), k)) :
2348        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{},
2349          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2350            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2351      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> Nil{}), mul64(k))), extra, s)
2352    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}:
2353      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}), mul64(k)), 64n),
2354        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}), 64n),
2355        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}), k)) :
2356        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{},
2357          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2358            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2359      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> Nil{}), mul64(k))), extra, s)
2360    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}:
2361      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}), mul64(k)), 64n),
2362        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}), 64n),
2363        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}), k)) :
2364        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{},
2365          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2366            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2367      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> Nil{}), mul64(k))), extra, s)
2368    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}:
2369      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}), mul64(k)), 64n),
2370        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}), 64n),
2371        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}), k)) :
2372        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{},
2373          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2374            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2375      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> Nil{}), mul64(k))), extra, s)
2376    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}:
2377      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}), mul64(k)), 64n),
2378        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}), 64n),
2379        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}), k)) :
2380        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{},
2381          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2382            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2383      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> Nil{}), mul64(k))), extra, s)
2384    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}:
2385      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}), mul64(k)), 64n),
2386        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}), 64n),
2387        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}), k)) :
2388        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{},
2389          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2390            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2391      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> Nil{}), mul64(k))), extra, s)
2392    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}:
2393      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}), mul64(k)), 64n),
2394        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}), 64n),
2395        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}), k)) :
2396        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{},
2397          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2398            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2399      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> Nil{}), mul64(k))), extra, s)
2400    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}:
2401      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}), mul64(k)), 64n),
2402        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}), 64n),
2403        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}), k)) :
2404        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{},
2405          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2406            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2407      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> Nil{}), mul64(k))), extra, s)
2408    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}:
2409      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}), mul64(k)), 64n),
2410        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}), 64n),
2411        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}), k)) :
2412        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{},
2413          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2414            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2415      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> Nil{}), mul64(k))), extra, s)
2416    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}:
2417      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}), mul64(k)), 64n),
2418        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}), 64n),
2419        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}), k)) :
2420        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{},
2421          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2422            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2423      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> Nil{}), mul64(k))), extra, s)
2424    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}:
2425      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}), mul64(k)), 64n),
2426        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}), 64n),
2427        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}), k)) :
2428        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{},
2429          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2430            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2431      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> Nil{}), mul64(k))), extra, s)
2432    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}:
2433      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}), mul64(k)), 64n),
2434        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}), 64n),
2435        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}), k)) :
2436        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{},
2437          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2438            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2439      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> Nil{}), mul64(k))), extra, s)
2440    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}:
2441      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}), mul64(k)), 64n),
2442        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}), 64n),
2443        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}), k)) :
2444        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{},
2445          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2446            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2447      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> Nil{}), mul64(k))), extra, s)
2448    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}:
2449      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}), mul64(k)), 64n),
2450        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}), 64n),
2451        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}), k)) :
2452        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{},
2453          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2454            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2455      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> Nil{}), mul64(k))), extra, s)
2456    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}:
2457      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}), mul64(k)), 64n),
2458        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}), 64n),
2459        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}), k)) :
2460        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{},
2461          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2462            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2463      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> Nil{}), mul64(k))), extra, s)
2464    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}:
2465      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}), mul64(k)), 64n),
2466        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}), 64n),
2467        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}), k)) :
2468        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{},
2469          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2470            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2471      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> Nil{}), mul64(k))), extra, s)
2472    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}:
2473      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}), mul64(k)), 64n),
2474        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}), 64n),
2475        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}), k)) :
2476        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{},
2477          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2478            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2479      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> Nil{}), mul64(k))), extra, s)
2480    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}:
2481      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}), mul64(k)), 64n),
2482        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}), 64n),
2483        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}), k)) :
2484        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{},
2485          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2486            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2487      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> Nil{}), mul64(k))), extra, s)
2488    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}:
2489      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}), mul64(k)), 64n),
2490        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}), 64n),
2491        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}), k)) :
2492        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{},
2493          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2494            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2495      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> Nil{}), mul64(k))), extra, s)
2496    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}:
2497      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}), mul64(k)), 64n),
2498        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}), 64n),
2499        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}), k)) :
2500        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{},
2501          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2502            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2503      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> Nil{}), mul64(k))), extra, s)
2504    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}:
2505      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}), mul64(k)), 64n),
2506        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}), 64n),
2507        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}), k)) :
2508        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{},
2509          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2510            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2511      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> Nil{}), mul64(k))), extra, s)
2512    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}:
2513      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}), mul64(k)), 64n),
2514        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}), 64n),
2515        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}), k)) :
2516        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{},
2517          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2518            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2519      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> Nil{}), mul64(k))), extra, s)
2520    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}:
2521      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}), mul64(k)), 64n),
2522        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}), 64n),
2523        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}), k)) :
2524        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{},
2525          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2526            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2527      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> Nil{}), mul64(k))), extra, s)
2528    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}:
2529      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}), mul64(k)), 64n),
2530        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}), 64n),
2531        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}), k)) :
2532        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{},
2533          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2534            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2535      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, 128, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> Nil{}), mul64(k))), extra, s)
2536    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}:
2537      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}), mul64(k)), 64n),
2538        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}), 64n),
2539        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}), k)) :
2540        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{},
2541          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2542            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2543      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, 128, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> Nil{}), mul64(k))), extra, s)
2544    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}:
2545      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}), mul64(k)), 64n),
2546        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}), 64n),
2547        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}), k)) :
2548        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{},
2549          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2550            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2551      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, 128), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> Nil{}), mul64(k))), extra, s)
2552    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}:
2553      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}), mul64(k)), 64n),
2554        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}), 64n),
2555        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}), k)) :
2556        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{},
2557          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2558            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2559      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> Nil{}), mul64(k))), extra, s)
2560    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}:
2561      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}), mul64(k)), 64n),
2562        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}), 64n),
2563        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}), k)) :
2564        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{},
2565          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2566            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2567      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, 128, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> Nil{}), mul64(k))), extra, s)
2568    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}:
2569      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}), mul64(k)), 64n),
2570        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}), 64n),
2571        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}), k)) :
2572        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{},
2573          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2574            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2575      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, 128, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> Nil{}), mul64(k))), extra, s)
2576    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}:
2577      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}), mul64(k)), 64n),
2578        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}), 64n),
2579        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}), k)) :
2580        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{},
2581          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2582            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2583      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, 128), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> Nil{}), mul64(k))), extra, s)
2584    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}:
2585      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}), mul64(k)), 64n),
2586        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}), 64n),
2587        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}), k)) :
2588        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{},
2589          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2590            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2591      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(128, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> Nil{}), mul64(k))), extra, s)
2592    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}:
2593      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}), mul64(k)), 64n),
2594        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}), 64n),
2595        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}), k)) :
2596        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{},
2597          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2598            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2599      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, 128, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> Nil{}), mul64(k))), extra, s)
2600    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}:
2601      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}), mul64(k)), 64n),
2602        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}), 64n),
2603        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}), k)) :
2604        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{},
2605          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2606            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2607      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, 128, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> Nil{}), mul64(k))), extra, s)
2608    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}:
2609      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}), mul64(k)), 64n),
2610        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}), 64n),
2611        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}), k)) :
2612        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{},
2613          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2614            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2615      fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, 128), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> Nil{}), mul64(k))), extra, s)
2616    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}:
2617      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k)), 64n),
2618        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), 64n),
2619        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), k)) :
2620        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{},
2621          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2622            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2623      Equal.trans(S.State,
2624        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, s)),
2625        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, s)),
2626        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, C.round_constants(), s)),
2627        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, s)),
2628        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2629          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, C.round_constants(), s),
2630          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(128, 0, 0, 0), C.pack(0, 0, 0, 0), extra, s)))
2631    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}:
2632      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k)), 64n),
2633        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), 64n),
2634        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), k)) :
2635        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{},
2636          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2637            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2638      Equal.trans(S.State,
2639        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, s)),
2640        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, s)),
2641        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, C.round_constants(), s)),
2642        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, s)),
2643        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2644          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, C.round_constants(), s),
2645          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, 128, 0, 0), C.pack(0, 0, 0, 0), extra, s)))
2646    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}:
2647      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k)), 64n),
2648        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), 64n),
2649        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), k)) :
2650        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{},
2651          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2652            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2653      Equal.trans(S.State,
2654        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, s)),
2655        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, s)),
2656        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, C.round_constants(), s)),
2657        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, s)),
2658        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2659          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, C.round_constants(), s),
2660          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, 128, 0), C.pack(0, 0, 0, 0), extra, s)))
2661    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}:
2662      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k)), 64n),
2663        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), 64n),
2664        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), k)) :
2665        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{},
2666          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2667            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2668      Equal.trans(S.State,
2669        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, s)),
2670        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, s)),
2671        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, C.round_constants(), s)),
2672        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, s)),
2673        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2674          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, C.round_constants(), s),
2675          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, 128), C.pack(0, 0, 0, 0), extra, s)))
2676    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}:
2677      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k)), 64n),
2678        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), 64n),
2679        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), k)) :
2680        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{},
2681          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2682            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2683      Equal.trans(S.State,
2684        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, s)),
2685        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, s)),
2686        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, C.round_constants(), s)),
2687        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, s)),
2688        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2689          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, C.round_constants(), s),
2690          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(128, 0, 0, 0), extra, s)))
2691    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}:
2692      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k)), 64n),
2693        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), 64n),
2694        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), k)) :
2695        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{},
2696          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2697            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2698      Equal.trans(S.State,
2699        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, s)),
2700        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, s)),
2701        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, C.round_constants(), s)),
2702        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, s)),
2703        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2704          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, C.round_constants(), s),
2705          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, 128, 0, 0), extra, s)))
2706    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}:
2707      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k)), 64n),
2708        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), 64n),
2709        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), k)) :
2710        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{},
2711          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2712            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2713      Equal.trans(S.State,
2714        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, s)),
2715        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, s)),
2716        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, C.round_constants(), s)),
2717        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, s)),
2718        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2719          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, C.round_constants(), s),
2720          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, 128, 0), extra, s)))
2721    case b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}:
2722      %Equal.sym(Nat, Nat.mod(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k)), 64n),
2723        Nat.mod(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), 64n),
2724        mod_tail(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), k)) :
2725        {C.stream(b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}, mul64(k), extra, s) == C.block_bytes(List.append(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{},
2726          128 <> List.append(&2, U32, List.replicate(U32, Nat.mod(Nat.sub(119n, _), 64n), 0),
2727            C.bit_length(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))))), extra, C.round_constants(), s) : S.State}
2728      Equal.trans(S.State,
2729        C.fips_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, s)),
2730        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), extra, C.round_constants(), C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, s)),
2731        C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), extra, C.round_constants(), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, C.round_constants(), s)),
2732        fips16_correct(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), extra, C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, s)),
2733        Equal.cong(S.State, S.State, y => C.window_compress16(C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.pack(0, 0, 0, 0), C.len_hi(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), C.len_lo(Nat.add(List.length(&2, U32, b0 <> b1 <> b2 <> b3 <> b4 <> b5 <> b6 <> b7 <> b8 <> b9 <> b10 <> b11 <> b12 <> b13 <> b14 <> b15 <> b16 <> b17 <> b18 <> b19 <> b20 <> b21 <> b22 <> b23 <> b24 <> b25 <> b26 <> b27 <> b28 <> b29 <> b30 <> b31 <> b32 <> b33 <> b34 <> b35 <> b36 <> b37 <> b38 <> b39 <> b40 <> b41 <> b42 <> b43 <> b44 <> b45 <> b46 <> b47 <> b48 <> b49 <> b50 <> b51 <> b52 <> b53 <> b54 <> b55 <> b56 <> b57 <> b58 <> b59 <> b60 <> b61 <> b62 <> Nil{}), mul64(k))), extra, C.round_constants(), y),
2734          C.fips_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, s), C.window_compress16(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, C.round_constants(), s),
2735          fips16_correct(C.pack(b0, b1, b2, b3), C.pack(b4, b5, b6, b7), C.pack(b8, b9, b10, b11), C.pack(b12, b13, b14, b15), C.pack(b16, b17, b18, b19), C.pack(b20, b21, b22, b23), C.pack(b24, b25, b26, b27), C.pack(b28, b29, b30, b31), C.pack(b32, b33, b34, b35), C.pack(b36, b37, b38, b39), C.pack(b40, b41, b42, b43), C.pack(b44, b45, b46, b47), C.pack(b48, b49, b50, b51), C.pack(b52, b53, b54, b55), C.pack(b56, b57, b58, b59), C.pack(b60, b61, b62, 128), extra, s)))
2736
2737# Unlike the old theorem, there is NO arbitrary preprocessing parameter.
2738# This proves the actual implementation pipeline against the independent one.
2739law sha256_correct:
2740  for +bytes: List<&2, U32>
2741  {C.sha256(bytes) == F.hash(bytes, 48n, C.round_constants()) : List<&2, U32>}
2742
2743def sha256_correct(bytes):
2744  %suffix_correct(List.length(&2, U32, bytes)) :
2745    {C.sha256(bytes) == F.digest(F.blocks(F.schedules(F.words(
2746      List.append(&2, U32, bytes, _)), 48n), C.round_constants())(F.initial())) : List<&2, U32>}
2747  %L.add_zero(List.length(&2, U32, bytes)) :
2748    {C.sha256(bytes) == F.digest(F.blocks(F.schedules(F.words(
2749      List.append(&2, U32, bytes, C.suffix(_))), 48n), C.round_constants())(F.initial())) : List<&2, U32>}
2750  +padded = List.append(&2, U32, bytes, C.suffix(Nat.add(List.length(&2, U32, bytes), 0n)))
2751  %digest_correct(F.blocks(F.schedules(F.words(padded), 48n), C.round_constants())(F.initial())) :
2752    {C.sha256(bytes) == _ : List<&2, U32>}
2753  Equal.cong(S.State, List<&2, U32>, s => C.digest(s),
2754    C.stream(bytes, 0n, 48n, C.initial()),
2755    F.blocks(F.schedules(F.words(padded), 48n), C.round_constants())(C.initial()),
2756    Equal.trans(S.State, C.stream(bytes, 0n, 48n, C.initial()),
2757      C.block_bytes(padded, 48n, C.round_constants(), C.initial()),
2758      F.blocks(F.schedules(F.words(padded), 48n), C.round_constants())(C.initial()),
2759      stream_correct(bytes, 0n, 48n, C.initial()),
2760      block_bytes_correct(padded, 48n, C.round_constants(), C.initial())))