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 Th11:
  (Omega).V + W = the RLSStruct of V & W + (Omega).V = the RLSStruct of V
proof
  the carrier of W c= the carrier of V by RLSUB_1:def 2;
  then W + (Omega).V = the RLSStruct of V by Lm3;
  hence thesis by Lm1;
end;
