ProofTab.gt.adc_carry: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/proof_tab.bend as ProofTab
Lines 80-96 of bend-osdev-gf@0.1.1.0/proof_tab.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&start_line=80&end_line=96

import Base

# a + b with a carry in is (a + b) + 1
def gt.adc_carry(n: Nat, a: Word(n), b: Word(n)) -> {Word.adc(n, a, b, False{}, True{}) == Word.inc(n, Word.adc(n, a, b, False{}, False{})) : Word(n)}:
  match n:
    case 0n:
      match a b:
        case WNil{} WNil{}:
          {==}
    case 1n+p:
      match a b:
        case WCon{False{}, at} WCon{False{}, bt}:
          {==}
        case WCon{True{}, +at} WCon{False{}, +bt}:
          gt.wcon2(p, False{}, False{}, Word.adc(p, at, bt, False{}, True{}), Word.inc(p, Word.adc(p, at, bt, False{}, False{})), {==}, gt.adc_carry(p, at, bt))
        case WCon{False{}, +at} WCon{True{}, +bt}:
          gt.wcon2(p, False{}, False{}, Word.adc(p, at, bt, False{}, True{}), Word.inc(p, Word.adc(p, at, bt, False{}, False{})), {==}, gt.adc_carry(p, at, bt))
        case WCon{True{}, at} WCon{True{}, bt}:
          {==}

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.adc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.inc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.wcon2