U64mont.izv: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64mont.bend as U64mont
Lines 239-240 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64mont.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64mont.bend&start_line=239&end_line=240

import Base
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/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/math/typed/w64add.bend as WA

def izv(+a: WU.U64, +n: Nat, +h: {SW.value(a) == n : Nat}) -> {X.is_zero(a) == Nat.is_eq(n, 0n) : Bool}:
  Equal.trans(Bool, X.is_zero(a), Nat.is_eq(SW.value(a), 0n), Nat.is_eq(n, 0n), WA.is_zero_value(a), Equal.cong(Nat, Bool, t => Nat.is_eq(t, 0n), SW.value(a), n, h))

Uses (9):
  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/w64add.bend&name=is_zero_value
  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/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=is_zero