def fz

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64tools.bend:176

import Base
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/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64light.bend as FL

176def fz(+x: F.F64) -> {X.is_zero(F.frac(x)) == Nat.is_eq(SF.frac(x), 0n) : Bool}:
177  match x:
178    case F.Bits{+xl, +xh}:
179      Equal.trans(Bool, X.is_zero(F.frac(F.Bits{xl, xh})), Nat.is_eq(SW.value(F.frac(F.Bits{xl, xh})), 0n), Nat.is_eq(SF.frac(F.Bits{xl, xh}), 0n), WA.is_zero_value(F.frac(F.Bits{xl, xh})), Equal.cong(Nat, Bool, t => Nat.is_eq(t, 0n), SW.value(F.frac(F.Bits{xl, xh})), SF.frac(F.Bits{xl, xh}), FL.hfr(xl, xh)))