def rpf0

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64round.bend:792

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

792def rpf0(+s: Bool, +w: WU.U64, +hS: {C.fits(63n, SW.value(w)) == True{} : Bool}, +hq: {C.fits(63n, Nat.add(SF.rne(SW.value(w), 10n), C.shift(52n, 0n))) == True{} : Bool}) -> {F.rp_fin(s, 0n, w) == bits(s, Nat.add(SF.rne(SW.value(w), 10n), C.shift(52n, 0n))) : F.F64}:
793  +r = X.clear0(X.shr(X.add(w, WU.U64{512, 0}), 10n), U32.is_eq(U32.and(X.lo(w), 1023), 512))
794  +q = SF.rne(SW.value(w), 10n)
795  +ev = rpw(w, hS)
796  +e1 = Equal.cong(Nat, F.F64, t => F.pack(s, t, r), F.zero_e(0n, X.is_zero(r)), 0n, ze0(X.is_zero(r)))
797  +hn = L.subst(Nat, z => {C.fits(63n, Nat.add(z, C.shift(52n, 0n))) == True{} : Bool}, q, SW.value(r), Equal.sym(Nat, SW.value(r), q, ev), hq)
798  +e2 = pack_v(s, 0n, {==}, r, hn)
799  +e3 = Equal.cong(Nat, F.F64, z => bits(s, Nat.add(z, C.shift(52n, 0n))), SW.value(r), q, ev)
800  Equal.trans(F.F64, F.pack(s, F.zero_e(0n, X.is_zero(r)), r), F.pack(s, 0n, r), bits(s, Nat.add(q, C.shift(52n, 0n))), e1, Equal.trans(F.F64, F.pack(s, 0n, r), bits(s, Nat.add(SW.value(r), C.shift(52n, 0n))), bits(s, Nat.add(q, C.shift(52n, 0n))), e2, e3))