
theorem Th12:
  for S being non empty RelStr for T,T1 being non empty RelStr st
T is full SubRelStr of T1 for f being Function of S, T for f1 being Function of
  S, T1 holds f1 is monotone & f=f1 implies f is monotone
proof
  let S be non empty RelStr;
  let T,T1 be non empty RelStr;
  assume
A1: T is full SubRelStr of T1;
  let f be Function of S, T;
  let f1 be Function of S, T1;
  assume that
A2: f1 is monotone and
A3: f=f1;
  thus f is monotone
  proof
    let x,y be Element of S;
    assume x <= y;
    then f1.x <= f1.y by A2;
    hence thesis by A1,A3,YELLOW_0:60;
  end;
end;
