ProofWord.adc_t.con: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 455-462 of lawful-words@0.1.0.0/proof_word.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_word.bend&start_line=455&end_line=462

import Base

# Subtraction is addition of the complement with carry in.
def adc_t.con(-p: Nat, at: Word(p), bt: Word(p), sk: Bool & Bool,
  ih: @k: Bool -> {Word.adc(p, at, bt, True{}, k) == Word.adc(p, at, Word.not(p, bt), False{}, k) : Word(p)}) ->
  {Word.adc.con(p, at, bt, True{}, sk) == Word.adc.con(p, at, Word.not(p, bt), False{}, sk) : Word(1n+p)}:
  match sk:
    case (s, k):
      %ih(k) : {WCon{s, Word.adc(p, at, bt, True{}, k)} == WCon{s, _} : Word(1n+p)}
      {==}

Uses (9):
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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.adc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.adc.con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.not