def take_drop_val

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/poly.bend:323

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

323def take_drop_val(+n: Nat, +xs: List<&2, U32>) -> {FS.value(xs) == Nat.add(FS.value(F.take(n, xs)), LM.sh(F.take(n, xs), FS.value(F.drop(n, xs)))) : Nat}:
324  match n xs:
325    case 0n _:
326      {==}
327    case 1n+m Nil{}:
328      {==}
329    case 1n+ +m Con{+x, +xt}:
330      +T = FS.value(F.take(m, xt))
331      +D = LM.sh(F.take(m, xt), FS.value(F.drop(m, xt)))
332      +ih = take_drop_val(m, xt)
333      +e1 = M.cong_r(v(x), C.shift(8n, FS.value(xt)), C.shift(8n, Nat.add(T, D)), M.cong_sc(8n, FS.value(xt), Nat.add(T, D), ih))
334      +e2 = M.cong_r(v(x), C.shift(8n, Nat.add(T, D)), Nat.add(C.shift(8n, T), C.shift(8n, D)), Equal.sym(Nat, Nat.add(C.shift(8n, T), C.shift(8n, D)), C.shift(8n, Nat.add(T, D)), M.sc_add(8n, T, D)))
335      +e3 = Equal.sym(Nat, Nat.add(Nat.add(v(x), C.shift(8n, T)), C.shift(8n, D)), Nat.add(v(x), Nat.add(C.shift(8n, T), C.shift(8n, D))), NA.add_assoc(v(x), C.shift(8n, T), C.shift(8n, D)))
336      Equal.trans(Nat, Nat.add(v(x), C.shift(8n, FS.value(xt))), Nat.add(v(x), C.shift(8n, Nat.add(T, D))), Nat.add(Nat.add(v(x), C.shift(8n, T)), C.shift(8n, D)), e1,
337        Equal.trans(Nat, Nat.add(v(x), C.shift(8n, Nat.add(T, D))), Nat.add(v(x), Nat.add(C.shift(8n, T), C.shift(8n, D))), Nat.add(Nat.add(v(x), C.shift(8n, T)), C.shift(8n, D)), e2, e3))