
theorem Th1:
  for L being non empty LattStr holds L is meet-Associative
  join-Associative meet-Absorbing join-absorbing implies L is meet-idempotent
  join-idempotent
proof
  let L be non empty LattStr;
  assume
A1: L is meet-Associative join-Associative meet-Absorbing join-absorbing;
A2: for x being Element of L holds x "\/" x = x
  proof
    let a be Element of L;
    a = a "\/" (a "/\" a) by A1;
    hence thesis by A1;
  end;
  for x being Element of L holds x "/\" x = x
  proof
    let a be Element of L;
    a = a "/\" (a "\/" a) by A1;
    hence thesis by A1;
  end;
  hence thesis by A2,ROBBINS1:def 7,SHEFFER1:def 9;
end;
