
theorem Th8:
  for L being complemented' join-commutative meet-commutative
  distributive upper-bounded' lower-bounded' distributive' non empty LattStr
  holds L is meet-idempotent
proof
  let L be complemented' join-commutative meet-commutative distributive
  upper-bounded' lower-bounded' distributive' non empty LattStr;
  now
    let x be Element of L;
    thus x "/\" x = (x "/\" x) "\/" Bot' L by Def4
      .= (x "/\" x) "\/" (x "/\" x`# ) by Th3
      .= x "/\" (x "\/" x`# ) by LATTICES:def 11
      .= x "/\" Top' L by Th2
      .= x by Def2;
  end;
  hence thesis;
end;
