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;
