ProofBytes.pk.m: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 1496-1510 of lawful-words@0.1.0.0/proof_bytes.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&start_line=1496&end_line=1510

import Base
import lawful-words@0.1.0.0/defs.bend as D

law pk.m:
  for +b0: U32
  for +b1: U32
  for +b2: U32
  for +b3: U32
  for +a: Nat
  for +m: Nat
  for +ha: {Nat.pow(2n, 8n) == a : Nat}
  for +hm: {Nat.pow(2n, 32n) == m : Nat}
  for +h0: {Nat.is_lt(U32.to_nat(b0), a) == True{} : Bool}
  for +h1: {Nat.is_lt(U32.to_nat(b1), a) == True{} : Bool}
  for +h2: {Nat.is_lt(U32.to_nat(b2), a) == True{} : Bool}
  for +h3: {Nat.is_lt(U32.to_nat(b3), a) == True{} : Bool}
  {U32.to_nat(D.pack4(b0, b1, b2, b3)) == Nat.add(U32.to_nat(b0), Nat.add(Nat.mul(U32.to_nat(b1), a),
    Nat.add(Nat.mul(U32.to_nat(b2), Nat.mul(a, a)), Nat.mul(U32.to_nat(b3), Nat.mul(Nat.mul(a, a), a))))) : Nat}

Uses (32):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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.is_le
  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=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.or
  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/defs.bend&name=pack4
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=le_mul_pos
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=lt_mul_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=or_comm
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=p16
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=p24
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=p32
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=shv
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_add_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_comm
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_mod
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=pow_pos
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_or_split