PROOF.word.cmp_nat.d: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 863-904 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=863&end_line=904

import Base

def word.cmp_nat.d(a: Nat, b: Nat, x: Bool, y: Bool) -> {Word.cmp.fin(x, y, Nat.cmp(a, b)) == Nat.cmp(nat.dbit(x, a), nat.dbit(y, b)) : Cmp}:
  match a b:
    case 0n 0n:
      match x y:
        case True{} True{}:
          {==}
        case True{} False{}:
          {==}
        case False{} True{}:
          {==}
        case False{} False{}:
          {==}
    case 0n 1n+bp:
      match x y:
        case True{} True{}:
          {==}
        case True{} False{}:
          {==}
        case False{} True{}:
          {==}
        case False{} False{}:
          {==}
    case 1n+ap 0n:
      match x y:
        case True{} True{}:
          {==}
        case True{} False{}:
          {==}
        case False{} True{}:
          {==}
        case False{} False{}:
          {==}
    case 1n+ +ap 1n+ +bp:
      match x y:
        case True{} True{}:
          word.cmp_nat.d(ap, bp, True{}, True{})
        case True{} False{}:
          word.cmp_nat.d(ap, bp, True{}, False{})
        case False{} True{}:
          word.cmp_nat.d(ap, bp, False{}, True{})
        case False{} False{}:
          word.cmp_nat.d(ap, bp, False{}, False{})

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=Word.cmp.fin
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=nat.dbit