ProofWord.moddbl: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 106-112 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=106&end_line=112

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

# (b + 2x) % 2q = b + 2 (x % q).
law moddbl:
  for +b: Bool
  for +x: Nat
  for +q: Nat
  for +hq: {Nat.is_lt(0n, q) == True{} : Bool}
  {Nat.mod(Nat.add(N.bn(b), Nat.double(x)), Nat.double(q)) == Nat.add(N.bn(b), Nat.double(Nat.mod(x, q))) : Nat}

Uses (17):
  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.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=div_mod
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_mul_add
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_dbl_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=lt_dbl_bit