ProofBytes.band_perm: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 29-36 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=29&end_line=36

import Base

# and(a, and(b, and(c, d))) = and(b, and(a, d)) when a implies c.
law band_perm:
  for +a: Bool
  for +b: Bool
  for +c: Bool
  for +d: Bool
  for imp: {a == True{} : Bool} -> {c == True{} : Bool}
  {Bool.and(a, Bool.and(b, Bool.and(c, d))) == Bool.and(b, Bool.and(a, d)) : Bool}

Uses (4):
  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=lawful-words@0.1.0.0/proof_nat.bend&name=and_false_r