def rpfE

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64round.bend:780

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/f64.bend as SF
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/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA

780def rpfE(+s: Bool, +E: Nat, +w: WU.U64, +hS: {C.fits(63n, SW.value(w)) == True{} : Bool}, +hE: {C.fits(11n, E) == True{} : Bool}, +hz: {C.fits(52n, SF.rne(SW.value(w), 10n)) == False{} : Bool}, +hq: {C.fits(63n, Nat.add(SF.rne(SW.value(w), 10n), C.shift(52n, E))) == True{} : Bool}) -> {F.rp_fin(s, E, w) == bits(s, Nat.add(SF.rne(SW.value(w), 10n), C.shift(52n, E))) : F.F64}:
781  +r = X.clear0(X.shr(X.add(w, WU.U64{512, 0}), 10n), U32.is_eq(U32.and(X.lo(w), 1023), 512))
782  +q = SF.rne(SW.value(w), 10n)
783  +ev = rpw(w, hS)
784  z0 = WA.is_zero_value(r)
785  +hzr = Equal.trans(Bool, X.is_zero(r), Nat.is_eq(SW.value(r), 0n), False{}, z0, Equal.trans(Bool, Nat.is_eq(SW.value(r), 0n), Nat.is_eq(q, 0n), False{}, Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), SW.value(r), q, ev), nz_of(52n, q, hz)))
786  +e1 = Equal.cong(Bool, F.F64, t => F.pack(s, F.zero_e(E, t), r), X.is_zero(r), False{}, hzr)
787  +hn = L.subst(Nat, z => {C.fits(63n, Nat.add(z, C.shift(52n, E))) == True{} : Bool}, q, SW.value(r), Equal.sym(Nat, SW.value(r), q, ev), hq)
788  +e2 = pack_v(s, E, hE, r, hn)
789  +e3 = Equal.cong(Nat, F.F64, z => bits(s, Nat.add(z, C.shift(52n, E))), SW.value(r), q, ev)
790  Equal.trans(F.F64, F.pack(s, F.zero_e(E, X.is_zero(r)), r), F.pack(s, E, r), bits(s, Nat.add(q, C.shift(52n, E))), e1, Equal.trans(F.F64, F.pack(s, E, r), bits(s, Nat.add(SW.value(r), C.shift(52n, E))), bits(s, Nat.add(q, C.shift(52n, E))), e2, e3))