ProofWord.cmp_dbl: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 164-169 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=164&end_line=169

import Base
import lawful-words@0.1.0.0/proof_nat.bend as N

law cmp_dbl:
  for +x: Nat
  for +y: Nat
  for +a: Bool
  for +b: Bool
  {Word.cmp.fin(a, b, Nat.cmp(x, y)) == Nat.cmp(Nat.add(N.bn(a), Nat.double(x)), Nat.add(N.bn(b), Nat.double(y))) : Cmp}

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=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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp.fin
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=bn