reserve n for Element of NAT,
  a, b for Real;

theorem
  a <= b implies for x, y being Point of Closed-Interval-TSpace(a,b), P,
  Q being Path of x,y holds P, Q are_homotopic
proof
  assume
A1: a <= b;
  let x, y be Point of Closed-Interval-TSpace(a,b), P, Q be Path of x,y;
  Closed-Interval-TSpace(a,b) is interval by A1,Th9;
  hence thesis by Th12;
end;
