LAWS.to_nat_and_mask: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/LAWS.bend as LAWS
Lines 251-260 of lawful-words@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/LAWS.bend&start_line=251&end_line=260

import Base

# And with a mask of the low k bits takes the number modulo 2^k. The mask is
# any word standing for 2^k - 1, so a literal such as 255 or 3 qualifies. No
# word stands for 2^k - 1 when k > 32, so in practice k <= 32 (k = 32 is the
# all-ones word).
law to_nat_and_mask:
  for a: U32
  for m: U32
  for k: Nat
  for h: {U32.to_nat(m) == Nat.sub(Nat.pow(2n, k), 1n) : Nat}
  {U32.to_nat(U32.and(a, m)) == Nat.mod(U32.to_nat(a), Nat.pow(2n, k)) : Nat}

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_and_mask