
theorem Th4: :: 4.11 revised p. 557 without idempotency
  for L being join-commutative join-associative Huntington non
  empty ComplLLattStr, a, b being Element of L holds a + a` = b + b`
proof
  let L be join-commutative join-associative Huntington non empty
  ComplLLattStr, a, b be Element of L;
  thus a + a` = (a` + b``)` + (a` + b`)` + a` by Def6
    .= (a` + b``)` + (a` + b`)` + ((a`` + b``)` + (a`` + b`)`) by Def6
    .= (a`` + b`)` + ((a`` + b``)` + ((a` + b``)` + (a` + b`)`)) by
LATTICES:def 5
    .= (a`` + b`)` + ((a` + b`)` + ((a` + b``)` + (a`` + b``)`)) by
LATTICES:def 5
    .= (a`` + b`)` + (a` + b`)` + ((a` + b``)` + (a`` + b``)`) by
LATTICES:def 5
    .= b + ((a`` + b``)` + (a` + b``)`) by Def6
    .= b + b` by Def6;
end;
