def bz0

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64exp.bend:70

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/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

70# a zero pattern with sign s (as f64addc.bz)
71def bz0(+one: Nat, +h1: {one == 1n : Nat}, +s: Bool, +c: U32, +hc: {c == U32{WD.pw(32n, 31n)} : U32}) -> {F.Bits{0, U32.from_nat(C.shift(31n, SF.pick(Nat, s, one, 0n)))} == SF.pick(F.F64, s, F.Bits{0, c}, F.Bits{0, 0}) : F.F64}:
72  match s:
73    case True{}:
74      Equal.cong(U32, F.F64, z => F.Bits{0, z}, U32.from_nat(C.shift(31n, one)), c, Equal.trans(U32, U32.from_nat(C.shift(31n, one)), U32.from_nat(U32.to_nat(c)), c, Equal.cong(Nat, U32, z => U32.from_nat(z), C.shift(31n, one), U32.to_nat(c), Equal.sym(Nat, U32.to_nat(c), C.shift(31n, one), FB.pwv(31n, {==}, one, h1, c, hc))), LW.rt(c)))
75    case False{}:
76      {==}