
theorem :: 4.35
  for L being join-commutative join-associative Huntington non empty
ComplLLattStr, a, b, c being Element of L holds a + (b *' c) = (a + b) *' (a +
  c)
proof
  let L be join-commutative join-associative Huntington non empty
  ComplLLattStr, a, b, c be Element of L;
  thus a + (b *' c) = (a` *' (b` + c`)``)` by Th17
    .= (a` *' (b` + c`))` by Th3
    .= ((a` *' b`) + (a` *' c`))` by Th30
    .= ((a` *' b`)` *' (a` *' c`)`)`` by Th17
    .= (a` *' b`)` *' (a` *' c`)` by Th3
    .= (a + b) *' (a` *' c`)` by Th17
    .= (a + b) *' (a + c) by Th17;
end;
