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 Th20:
  for W being strict Subspace of V holds (Omega).V /\ W = W & W /\
  (Omega).V = W
proof
  let W be strict Subspace of V;
  the carrier of (Omega). V /\ W = (the carrier of V) /\ (the carrier of W
  ) & the carrier of W c= the carrier of V by Def2,RLSUB_1:def 2;
  hence (Omega).V /\ W = W by RLSUB_1:30,XBOOLE_1:28;
  hence thesis by Th14;
end;
