
theorem
  for L be non empty RelStr for S be non empty SubRelStr of L for x be
  Element of L for y be Element of S st x = y holds uparrow y c= uparrow x
proof
  let L be non empty RelStr;
  let S be non empty SubRelStr of L;
  let x be Element of L;
  let y be Element of S;
A1: uparrow x = uparrow {x} by WAYBEL_0:def 18;
A2: uparrow y = uparrow {y} by WAYBEL_0:def 18;
  assume x = y;
  hence thesis by A1,A2,Th12;
end;
