reserve V for RealLinearSpace;
reserve W,W1,W2,W3 for Subspace of V;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a,a1,a2 for Real;
reserve X,Y,x,y,y1,y2 for set;

theorem Th2:
  v in W1 or v in W2 implies v in W1 + W2
proof
  assume
A1: v in W1 or v in W2;
  now
    per cases by A1;
    suppose
A2:   v in W1;
      v = v + 0.V & 0.V in W2 by RLSUB_1:17;
      hence thesis by A2,Th1;
    end;
    suppose
A3:   v in W2;
      v = 0.V + v & 0.V in W1 by RLSUB_1:17;
      hence thesis by A3,Th1;
    end;
  end;
  hence thesis;
end;
