ProofNat.go_eq: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_nat.bend as ProofNat
Lines 943-952 of lawful-words@0.1.0.0/proof_nat.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_nat.bend&start_line=943&end_line=952

import Base

# The loop of Nat.divmod keeps d * b + r + n, with b = 1 + bp and m + r = bp.
law go_eq:
  for +n: Nat
  for +m: Nat
  for +d: Nat
  for +r: Nat
  for +bp: Nat
  for +h: {Nat.add(m, r) == bp : Nat}
  {Nat.add(Nat.mul(Pair.fst(Nat, Nat, Nat.divmod.go(n, m, d, r)), 1n+bp), Pair.snd(Nat, Nat, Nat.divmod.go(n, m, d, r)))
    == Nat.add(Nat.mul(d, 1n+bp), Nat.add(r, n)) : Nat}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.divmod.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.fst
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_assoc
  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=add_succ
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_zero