PROOF.word.cmp_nat: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 910-925 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=910&end_line=925

import Base

def word.cmp_nat(n: Nat, a: Word(n), b: Word(n)) -> {Word.cmp(n, a, b) == Nat.cmp(Word.to_nat(n, a), Word.to_nat(n, b)) : Cmp}:
  match n:
    case 0n:
      match a b:
        case WNil{} WNil{}:
          {==}
    case 1n+ +p:
      match a b:
        case WCon{True{}, +at} WCon{True{}, +bt}:
          word.cmp_nat.h(p, True{}, True{}, at, bt, word.cmp_nat(p, at, bt))
        case WCon{True{}, +at} WCon{False{}, +bt}:
          word.cmp_nat.h(p, True{}, False{}, at, bt, word.cmp_nat(p, at, bt))
        case WCon{False{}, +at} WCon{True{}, +bt}:
          word.cmp_nat.h(p, False{}, True{}, at, bt, word.cmp_nat(p, at, bt))
        case WCon{False{}, +at} WCon{False{}, +bt}:
          word.cmp_nat.h(p, False{}, False{}, at, bt, word.cmp_nat(p, at, bt))

Uses (10):
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=word.cmp_nat.h