ProofU32.to_nat_shln_mod.m: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_u32.bend as ProofU32
Lines 1111-1116 of lawful-words@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_u32.bend&start_line=1111&end_line=1116

import Base

law to_nat_shln_mod.m:
  for +a: U32
  for +k: Nat
  for +m: Nat
  for +hm: {Nat.pow(2n, 32n) == m : Nat}
  {Nat.mod(U32.to_nat(U32.shln(a, k)), Nat.pow(2n, k)) == 0n : Nat}

Uses (11):
  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.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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  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=shln_mod.go
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_shln.m