
theorem
  for L be antisymmetric transitive with_infima with_suprema RelStr for
  a,b,c be Element of L holds a <= c implies a \ b <= c
proof
  let L be antisymmetric transitive with_infima with_suprema RelStr;
  let a,b,c be Element of L;
A1: a "/\" 'not' b <= a by YELLOW_0:23;
  assume a <= c;
  hence thesis by A1,YELLOW_0:def 2;
end;
