theorem Th68:
  X1 is SubSpace of X0 implies for A being Subset of X0 st A c=
  the carrier of X1 holds g.:A = (g|X1).:A
proof
  assume
A1: X1 is SubSpace of X0;
  let A be Subset of X0;
  assume A c= the carrier of X1;
  hence g.:A = (g|(the carrier of X1)).:A by FUNCT_2:97
    .= (g|X1).:A by A1,Def5;
end;
