
theorem
  for L be antisymmetric transitive with_infima RelStr st L is
  distributive for a,b,c be Element of L holds (a "/\" b) "\/" (a "/\" c) = a
  implies a <= b "\/" c
proof
  let L be antisymmetric transitive with_infima RelStr such that
A1: L is distributive;
  let a,b,c be Element of L;
  assume (a "/\" b) "\/" (a "/\" c) = a;
  then (b "\/" c) "/\" a = a by A1,WAYBEL_1:def 3;
  hence thesis by YELLOW_0:23;
end;
