PROOF.ncmp_flip: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3964-3973 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=3964&end_line=3973

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

def ncmp_flip(a: Nat, b: Nat) -> {Nat.cmp(b, a) == Laws.flip(Nat.cmp(a, b)) : Cmp}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      ncmp_flip(p, q)

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.cmp
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=flip