ProofValue.wn.cmp_eq: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_value.bend as ProofValue
Lines 238-247 of bend-osdev-word64@0.1.1.0/proof_value.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&start_line=238&end_line=247

import Base

def wn.cmp_eq(x: Nat, y: Nat, e: {Nat.cmp(x, y) == EQ{} : Cmp}) -> {x == y : Nat}:
  match x y:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      Empty.absurd({0n == 1n+q : Nat}, wn.lt_eq(e))
    case 1n+p 0n:
      Empty.absurd({1n+p == 0n : Nat}, wn.gt_eq(e))
    case 1n+p 1n+q:
      wn.succ_cong(p, q, wn.cmp_eq(p, q, e))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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-osdev-word64@0.1.1.0/proof_value.bend&name=wn.gt_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.lt_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.succ_cong