PROOF.ncmp_eq: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3952-3962 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=3952&end_line=3962

import Base

def ncmp_eq(a: Nat, b: Nat, e: {Nat.cmp(a, b) == EQ{} : Cmp}) -> {a == b : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      ne_absurd({0n == 1n+q : Nat}, LT{}, {==}, e)
    case 1n+p 0n:
      ne_absurd({1n+p == 0n : Nat}, GT{}, {==}, e)
    case 1n+p 1n+q:
      %ncmp_eq(p, q, e) : {1n+p == 1n+_ : Nat}
      {==}

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/PROOF.bend&name=ne_absurd