F64tools.fz: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend as F64tools
Lines 176-179 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64tools.bend&start_line=176&end_line=179

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

def fz(+x: F.F64) -> {X.is_zero(F.frac(x)) == Nat.is_eq(SF.frac(x), 0n) : Bool}:
  match x:
    case F.Bits{+xl, +xh}:
      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)))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64light.bend&name=hfr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=is_zero_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=frac
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/w64.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=F64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=frac
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=is_zero