ProofWord.split_step: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 1110-1117 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=1110&end_line=1117

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

# y + 2r = 2a + (y + 2b) when r = a + b.
law split_step:
  for +y: Bool
  for +a: Nat
  for +b: Nat
  for +r: Nat
  for +ih: {r == Nat.add(a, b) : Nat}
  {Nat.add(N.bn(y), Nat.double(r)) == Nat.add(Nat.double(a), Nat.add(N.bn(y), Nat.double(b))) : Nat}

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=Equal.sym
  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.double
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_left_comm
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=bn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=dbl_dist