ProofNat.mod_mod_pow: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_nat.bend as ProofNat
Lines 1455-1461 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=1455&end_line=1461

import Base

# (a % 2^m) % 2^k = a % 2^k for k <= m.
law mod_mod_pow:
  for +a: Nat
  for +k: Nat
  for +m: Nat
  for +h: {Nat.is_le(k, m) == True{} : Bool}
  {Nat.mod(Nat.mod(a, Nat.pow(2n, m)), Nat.pow(2n, k)) == Nat.mod(a, Nat.pow(2n, k)) : Nat}

Uses (12):
  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.is_le
  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=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_sub_add
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_mod_mul
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=pow_add