
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 downarrow y c= downarrow 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: downarrow x = downarrow {x} by WAYBEL_0:def 17;
A2: downarrow y = downarrow {y} by WAYBEL_0:def 17;
  assume x = y;
  hence thesis by A1,A2,Th11;
end;
