
theorem Th1:
  for L being antisymmetric transitive with_infima RelStr, x,y,z
  being Element of L st x <= y holds x "/\" z <= y "/\" z
proof
  let L be antisymmetric transitive with_infima RelStr;
  let x,y,z be Element of L;
A1: x"/\"z <= x by YELLOW_0:23;
A2: x"/\"z <= z by YELLOW_0:23;
  assume x <= y;
  then x"/\"z <= y by A1,ORDERS_2:3;
  hence thesis by A2,YELLOW_0:23;
end;
