theorem Th75:
  X1 is SubSpace of X0 implies for x0 being Point of X0, x1 being
  Point of X1 st x0 = x1 holds f|X0 is_continuous_at x0 implies f|X1
  is_continuous_at x1
proof
  assume
A1: X1 is SubSpace of X0;
  let x0 be Point of X0, x1 be Point of X1;
  assume
A2: x0 = x1;
  assume f|X0 is_continuous_at x0;
  then (f|X0)|X1 is_continuous_at x1 by A1,A2,Th74;
  hence thesis by A1,Th71;
end;
