ProofBytes.byte_and.k: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 572-585 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=572&end_line=585

import Base
import lawful-words@0.1.0.0/defs.bend as D
import lawful-words@0.1.0.0/proof_u32.bend as U

def byte_and.k(+a: U32, +b: U32, +j: Nat, +k: Nat) -> {D.bit(D.byte(U32.and(a, b), j), k) == D.bit(U32.and(D.byte(a, j), D.byte(b, j)), k) : Bool}:
  +l = Nat.is_lt(k, 8n)
  +i = Nat.add(Nat.mul(8n, j), k)
  %Equal.sym(Bool, D.bit(D.byte(U32.and(a, b), j), k), Bool.and(l, D.bit(U32.and(a, b), i)), bit_byte(U32.and(a, b), j, k)) :
    {_ == D.bit(U32.and(D.byte(a, j), D.byte(b, j)), k) : Bool}
  %Equal.sym(Bool, D.bit(U32.and(a, b), i), Bool.and(D.bit(a, i), D.bit(b, i)), U.bit_and(a, b, i)) :
    {Bool.and(l, _) == D.bit(U32.and(D.byte(a, j), D.byte(b, j)), k) : Bool}
  %Equal.sym(Bool, D.bit(U32.and(D.byte(a, j), D.byte(b, j)), k), Bool.and(D.bit(D.byte(a, j), k), D.bit(D.byte(b, j), k)), U.bit_and(D.byte(a, j), D.byte(b, j), k)) :
    {Bool.and(l, Bool.and(D.bit(a, i), D.bit(b, i))) == _ : Bool}
  %Equal.sym(Bool, D.bit(D.byte(a, j), k), Bool.and(l, D.bit(a, i)), bit_byte(a, j, k)) :
    {Bool.and(l, Bool.and(D.bit(a, i), D.bit(b, i))) == Bool.and(_, D.bit(D.byte(b, j), k)) : Bool}
  %Equal.sym(Bool, D.bit(D.byte(b, j), k), Bool.and(l, D.bit(b, i)), bit_byte(b, j, k)) :
    {Bool.and(l, Bool.and(D.bit(a, i), D.bit(b, i))) == Bool.and(Bool.and(l, D.bit(a, i)), _) : Bool}
  band_dist(l, D.bit(a, i), D.bit(b, i))

Uses (14):
  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=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_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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  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=byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=band_dist
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=bit_and