ProofBytes.pack_bits: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 1099-1116 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=1099&end_line=1116

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

# Bit k (k < 8) of byte j of pack4(b0, b1, b2, b3).
law pack_bits:
  for +b0: U32
  for +b1: U32
  for +b2: U32
  for +b3: U32
  for +j: Nat
  for +k: Nat
  for +h0: {Nat.is_lt(U32.to_nat(b0), Nat.pow(2n, 8n)) == True{} : Bool}
  for +h1: {Nat.is_lt(U32.to_nat(b1), Nat.pow(2n, 8n)) == True{} : Bool}
  for +h2: {Nat.is_lt(U32.to_nat(b2), Nat.pow(2n, 8n)) == True{} : Bool}
  for +h3: {Nat.is_lt(U32.to_nat(b3), Nat.pow(2n, 8n)) == True{} : Bool}
  for +hk: {Nat.is_lt(k, 8n) == True{} : Bool}
  {D.bit(D.pack4(b0, b1, b2, b3), Nat.add(Nat.mul(8n, j), k)) ==
    Bool.or(Bool.and(Nat.is_eq(j, 0n), Bool.and(Nat.is_lt(Nat.add(Nat.mul(8n, j), k), 32n), D.bit(b0, k))),
    Bool.or(Bool.and(Nat.is_eq(j, 1n), Bool.and(Nat.is_lt(Nat.add(Nat.mul(8n, j), k), 32n), D.bit(b1, k))),
    Bool.or(Bool.and(Nat.is_eq(j, 2n), Bool.and(Nat.is_lt(Nat.add(Nat.mul(8n, j), k), 32n), D.bit(b2, k))),
            Bool.and(Nat.is_eq(j, 3n), Bool.and(Nat.is_lt(Nat.add(Nat.mul(8n, j), k), 32n), D.bit(b3, k)))))) : Bool}

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  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_eq
  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.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=bit
  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=bsel
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=bit_or