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 Th7:
  W1 is Subspace of W1 + W2 & W2 is Subspace of W1 + W2
proof
  the carrier of W1 c= the carrier of W1 + W2 by Lm2;
  hence W1 is Subspace of W1 + W2 by RLSUB_1:28;
  the carrier of W2 c= the carrier of W2 + W1 by Lm2;
  then the carrier of W2 c= the carrier of W1 + W2 by Lm1;
  hence thesis by RLSUB_1:28;
end;
