theorem
  2(.)X c= X (+) X
proof
  let x be object;
  assume x in 2(.)X;
  then consider z being Point of TOP-REAL n such that
A1: x=2*z and
A2: z in X;
  x = (1+1)*z by A1
    .= 1*z+1*z by RLVECT_1:def 6
    .= z + 1*z by RLVECT_1:def 8
    .= z + z by RLVECT_1:def 8;
  hence thesis by A2;
end;
