PROOF.ucmp_flip: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 4001-4004 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=4001&end_line=4004

import Base
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws

def ucmp_flip(+x: U32, +y: U32) -> {U32.cmp(y, x) == Laws.flip(U32.cmp(x, y)) : Cmp}:
  %ucmp_nat(y, x) : {_ == Laws.flip(U32.cmp(x, y)) : Cmp}
  %ucmp_nat(x, y) : {Nat.cmp(U32.to_nat(y), U32.to_nat(x)) == Laws.flip(_) : Cmp}
  ncmp_flip(U32.to_nat(x), U32.to_nat(y))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  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/LAWS.bend&name=flip
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=ncmp_flip
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=ucmp_nat