
theorem Th23: :: 4.27
  for L being join-commutative join-associative Huntington non
empty ComplLLattStr, a, b being Element of L st a + b = Top L & a *' b = Bot L
  holds a` = b
proof
  let L be join-commutative join-associative Huntington non empty
  ComplLLattStr, a, b be Element of L;
  assume a + b = Top L;
  then
A1: a`` + b = Top L by Th3;
  assume
A2: a *' b = Bot L;
  b` + a` = (a` + b`)`` by Th3
    .= Top L by A2,Th9;
  hence thesis by A1,Th22;
end;
