reserve T for non empty Abelian
  add-associative right_zeroed right_complementable RLSStruct,
  X,Y,Z,B,C,B1,B2 for Subset of T,
  x,y,p for Point of T;
reserve t,s,r1 for Real;
reserve n for Element of NAT;
reserve X,Y,B1,B2 for Subset of TOP-REAL n;
reserve x,y for Point of TOP-REAL n;

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;
