
theorem Th11:
  for L being complemented' join-commutative upper-bounded'
meet-commutative join-idempotent distributive distributive' lower-bounded' non
  empty LattStr holds L is join-absorbing
proof
  let L be complemented' join-commutative upper-bounded' meet-commutative
join-idempotent distributive distributive' lower-bounded' non empty LattStr;
  let x, y be Element of L;
A1: L is meet-idempotent by Th8;
A2: L is meet-absorbing by Th10;
  x "/\" (x "\/" y) = (x "/\" x) "\/" (x "/\" y) by LATTICES:def 11
    .= x "\/" (x "/\" y) by A1
    .= x by A2;
  hence thesis;
end;
