U64bgcd.fzh: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64bgcd.bend as U64bgcd
Lines 124-125 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64bgcd.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64bgcd.bend&start_line=124&end_line=125

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/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW

def fzh(+l: U32, +h: U32) -> {U32.is_zero(h) == Nat.is_eq(C.high(32n, v(WU.U64{l, h})), 0n) : Bool}:
  Equal.trans(Bool, U32.is_zero(h), Nat.is_eq(U32.to_nat(h), 0n), Nat.is_eq(C.high(32n, v(WU.U64{l, h})), 0n), LW.zero_nat(h), Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), U32.to_nat(h), C.high(32n, v(WU.U64{l, h})), hv(l, h)))

Uses (13):
  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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend&name=zero_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64bgcd.bend&name=hv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64bgcd.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64