
theorem Th5: :: 4.12
  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 = a` + a + a by Th4
    .= a` + (a + a) by LATTICES:def 5
    .= a` + a by Def7
    .= c by Th4;
  thus thesis by Th4;
end;
