U32alg.adc_con_not: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 154-157 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&start_line=154&end_line=157

import Base

def adc_con_not(+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 Tuple{s, k}:
      Equal.cong(Word(p), Word(1n+p), w => WCon{s, w}, Word.adc(p, at, bt, True{}, k), Word.adc(p, at, Word.not(p, bt), False{}, k), ih(k))

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=Equal.cong
  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