def small_case

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64rint.bend:130

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend as SH
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64light.bend as FL
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as FR

130def small_case(+m: F.RMode, +s: Bool, +w: WU.U64, +j: Nat, +hb: {Nat.is_lt(1n+j, 64n) == True{} : Bool}) -> {F.ri_k(m, s, w, 1n+j, True{}) == G(m, s, C.high(1n+j, SW.value(w)), C.low(1n+j, SW.value(w)), C.shift(j, 1n)) : F.F64}:
131  +V = SW.value(w)
132  +q = X.shr(w, 1n+j)
133  +sq = X.shl(q, 1n+j)
134  +r = X.sub(w, sq)
135  +h = X.shl(WU.U64{1, 0}, Nat.sub(1n+j, 1n))
136  +Hq = C.high(1n+j, V)
137  +Lq = C.low(1n+j, V)
138  +S = C.shift(1n+j, Hq)
139  eq1 = SH.shr_value(w, 1n+j)
140  eq2 = SH.shr_value(w, 1n+j)
141  eq3 = SH.shr_value(w, 1n+j)
142  +hQ = L.subst(Nat, t => {C.fits(63n, t) == True{} : Bool}, Hq, SW.value(q), Equal.sym(Nat, SW.value(q), Hq, eq1), hfit(j, V, FL.vb64(w)))
143  esl0 = SH.shl_value(q, 1n+j, hb)
144  +esl1 = Equal.cong(Nat, Nat, t => C.low(64n, C.shift(1n+j, t)), SW.value(q), Hq, eq2)
145  +eV = WW.low_high(1n+j, V)
146  +eV2 = WW.low_high(1n+j, V)
147  +hSV0 = L.subst(Nat, t => {Nat.is_le(S, t) == True{} : Bool}, Nat.add(S, Lq), Nat.add(Lq, S), NA.add_comm(S, Lq), N.le_add_right(S, Lq))
148  +hSV = L.subst(Nat, t => {Nat.is_le(S, t) == True{} : Bool}, Nat.add(Lq, S), V, Equal.sym(Nat, V, Nat.add(Lq, S), eV), hSV0)
149  +hSf = SH.fits_lek(64n, S, V, hSV, FL.vb64(w))
150  +esl = Equal.trans(Nat, SW.value(sq), C.low(64n, S), S, Equal.trans(Nat, SW.value(sq), C.low(64n, C.shift(1n+j, SW.value(q))), C.low(64n, S), esl0, esl1), WW.low_fit(64n, S, hSf))
151  +esl2 = Equal.trans(Nat, SW.value(sq), C.low(64n, S), S, Equal.trans(Nat, SW.value(sq), C.low(64n, C.shift(1n+j, SW.value(q))), C.low(64n, S), SH.shl_value(q, 1n+j, hb), Equal.cong(Nat, Nat, t => C.low(64n, C.shift(1n+j, t)), SW.value(q), Hq, eq3)), WW.low_fit(64n, S, SH.fits_lek(64n, S, V, L.subst(Nat, t => {Nat.is_le(S, t) == True{} : Bool}, Nat.add(Lq, S), V, Equal.sym(Nat, V, Nat.add(Lq, S), eV2), L.subst(Nat, t => {Nat.is_le(S, t) == True{} : Bool}, Nat.add(S, Lq), Nat.add(Lq, S), NA.add_comm(S, Lq), N.le_add_right(S, Lq))), FL.vb64(w))))
152  +hle = L.subst(Nat, t => {Nat.is_le(t, V) == True{} : Bool}, S, SW.value(sq), Equal.sym(Nat, SW.value(sq), S, esl), hSV)
153  er0 = WA.sub_value(w, sq, hle)
154  +er1 = Equal.cong(Nat, Nat, t => Nat.sub(V, t), SW.value(sq), S, esl2)
155  +eV3 = WW.low_high(1n+j, V)
156  +er2 = Equal.cong(Nat, Nat, t => Nat.sub(t, S), V, Nat.add(Lq, S), eV3)
157  +er3 = FR.sub_add_l(Lq, S)
158  +er = Equal.trans(Nat, SW.value(r), Nat.sub(V, SW.value(sq)), Lq, er0, Equal.trans(Nat, Nat.sub(V, SW.value(sq)), Nat.sub(V, S), Lq, er1, Equal.trans(Nat, Nat.sub(V, S), Nat.sub(Nat.add(Lq, S), S), Lq, er2, er3)))
159  +ehv = half_v(j, hb)
160  +e0 = riq(m, s, q, r, h, hQ)
161  e4 = SH.shr_value(w, 1n+j)
162  Equal.trans(F.F64, F.ri_q(m, s, q, r, h), G(m, s, SW.value(q), SW.value(r), SW.value(h)), G(m, s, Hq, Lq, C.shift(j, 1n)), e0, g3(m, s, SW.value(q), Hq, e4, SW.value(r), Lq, er, SW.value(h), C.shift(j, 1n), ehv))