ProofBytes.pack4_bytes.k: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 1330-1336 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=1330&end_line=1336

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

def pack4_bytes.k(+w: U32, +k: Nat) -> {D.bit(D.pack4(D.byte(w, 0n), D.byte(w, 1n), D.byte(w, 2n), D.byte(w, 3n)), k) == D.bit(w, k) : Bool}:
  +j = Nat.div(k, 8n)
  +r = Nat.mod(k, 8n)
  %Equal.trans(Nat, Nat.add(Nat.mul(8n, j), r), Nat.add(Nat.mul(j, 8n), r), k,
      Equal.cong(Nat, Nat, t => Nat.add(t, r), Nat.mul(8n, j), Nat.mul(j, 8n), N.mul_comm(8n, j)), N.div_mod(k, 8n)) :
    {D.bit(D.pack4(D.byte(w, 0n), D.byte(w, 1n), D.byte(w, 2n), D.byte(w, 3n)), _) == D.bit(w, _) : Bool}
  pack4_bytes.go(w, j, r, N.mod_lt(k, 8n, {==}), Nat.is_lt(j, 4n), {==})

Uses (17):
  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.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.div
  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=U32
  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/defs.bend&name=pack4
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=pack4_bytes.go
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=div_mod
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_comm