
theorem Th7: :: 4.13
  for L being join-commutative join-associative join-idempotent
  Huntington non empty ComplLLattStr ex c being Element of L st for a being
  Element of L holds c *' a = c & (a + a`)` = c
proof
  let L be join-commutative join-associative join-idempotent Huntington non
  empty ComplLLattStr;
  set b = the Element of L;
  take c = (b` + b)`;
  let a be Element of L;
  thus c *' a = ((b` + b) + a`)` by Th3
    .= ((a` + a) + a`)` by Th4
    .= (a + (a` + a`))` by LATTICES:def 5
    .= (a + a`)` by Def7
    .= c by Th4;
  thus thesis by Th4;
end;
