PROOF.ucmp_eq: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3997-3999 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=3997&end_line=3999

import Base
import bend-kit-lemmas@0.1.1.0/lemmas.bend as Lemmas

def ucmp_eq(+x: U32, +y: U32, e: {U32.cmp(x, y) == EQ{} : Cmp}) -> {x == y : U32}:
  Lemmas.u32_to_nat_inj(x, y, ncmp_eq(U32.to_nat(x), U32.to_nat(y),
    Equal.trans(Cmp, Nat.cmp(U32.to_nat(x), U32.to_nat(y)), U32.cmp(x, y), EQ{}, ucmp_nat(x, y), e)))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=ncmp_eq
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=ucmp_nat
  https://jend.leeeet.dev/definition.txt?path=bend-kit-lemmas@0.1.1.0/lemmas.bend&name=u32_to_nat_inj