
theorem Th3: :: see yellow14:9
  for X,Y being non empty TopSpace for a,b being Element of
oContMaps(X,Y) for f,g being Function of X, Omega Y st a = f & b = g holds a <=
  b iff f <= g
proof
  let X,Y be non empty TopSpace;
  let a,b be Element of oContMaps(X,Y);
A1: oContMaps(X,Y) is full SubRelStr of (Omega Y)|^the carrier of X by
WAYBEL24:def 3;
  then reconsider x = a, y = b as Element of (Omega Y)|^the carrier of X by
YELLOW_0:58;
A2: a <= b iff x <= y by A1,YELLOW_0:59,60;
  let f,g be Function of X, Omega Y;
  assume a = f & b = g;
  hence thesis by A2,WAYBEL10:11;
end;
