
theorem Th10:
  for L being complemented' join-commutative meet-commutative
  join-idempotent distributive upper-bounded' distributive' non empty LattStr
  holds L is meet-absorbing
proof
  let L be complemented' join-commutative meet-commutative join-idempotent
  distributive upper-bounded' distributive' non empty LattStr;
  let y, x be Element of L;
  x "\/" (x "/\" y) = (Top' L "/\" x) "\/" (x "/\" y) by Def2
    .= x "/\" (Top' L "\/" y) by LATTICES:def 11
    .= x "/\" Top' L by Th4
    .= x by Def2;
  hence thesis;
end;
