theorem Th83:
  X1 is SubSpace of X0 & X2 is SubSpace of X1 implies for g being
  Function of X0,Y holds g|X1 is continuous Function of X1,Y implies g|X2 is
  continuous Function of X2,Y
proof
  assume
A1: X1 is SubSpace of X0;
  assume
A2: X2 is SubSpace of X1;
  let g be Function of X0,Y;
  assume g|X1 is continuous Function of X1,Y;
  then (g|X1)|X2 is continuous Function of X2,Y by A2,Th82;
  hence thesis by A1,A2,Th72;
end;
