
theorem Th14:
  for X being non empty set, T being non empty RelStr
  for f,g being Element of T|^X holds
  f <= g iff for x being Element of X holds f.x <= g.x
proof
  let X be non empty set, T be non empty RelStr;
  let f,g be Element of T|^X;
  reconsider a = f, b = g as Element of product (X --> T) by YELLOW_1:def 5;
A1: T|^X = product (X --> T) by YELLOW_1:def 5;
  hereby
    assume
A2: f <= g;
    let x be Element of X;
    (X --> T).x = T;
    hence f.x <= g.x by A1,A2,WAYBEL_3:28;
  end;
  assume for x being Element of X holds f.x <= g.x;
  then for x be Element of X holds a.x <= b.x;
  hence thesis by A1,WAYBEL_3:28;
end;
