
theorem Th7:
  for L be antisymmetric transitive with_suprema RelStr for a,b,c
  be Element of L holds a <= b implies a"\/"c <= b"\/"c
proof
  let L be non empty antisymmetric transitive with_suprema RelStr;
  let a,b,c be Element of L;
A1: b <= b "\/" c by YELLOW_0:22;
A2: c <= b "\/" c by YELLOW_0:22;
  assume a <= b;
  then a <= b "\/" c by A1,YELLOW_0:def 2;
  hence thesis by A2,YELLOW_0:22;
end;
