
theorem Th2:
  for L being antisymmetric transitive with_suprema RelStr, x,y,z
  being Element of L st x <= y holds x "\/" z <= y "\/" z
proof
  let L be antisymmetric transitive with_suprema RelStr;
  let x,y,z be Element of L;
A1: y <= y"\/"z by YELLOW_0:22;
A2: z <= y"\/"z by YELLOW_0:22;
  assume x <= y;
  then x <= y"\/"z by A1,ORDERS_2:3;
  hence thesis by A2,YELLOW_0:22;
end;
