theorem Th65:
  X1 is SubSpace of X0 implies for x0 being Point of X0 st x0 in
  the carrier of X1 holds g.x0 = (g|X1).x0
proof
  assume
A1: X1 is SubSpace of X0;
  let x0 be Point of X0;
  assume x0 in the carrier of X1;
  hence g.x0 = (g|(the carrier of X1)).x0 by FUNCT_1:49
    .= (g|X1).x0 by A1,Def5;
end;
