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 Th29:
  W1 is strict Subspace of W3 implies W1 + (W2 /\ W3) = (W1 + W2) /\ W3
proof
  assume
A1: W1 is strict Subspace of W3;
  thus (W1 + W2) /\ W3 = W3 /\ (W1 + W2) by Th14
    .= (W1 /\ W3) + (W3 /\ W2) by A1,Lm9,RLSUB_1:30
    .= W1 + (W3 /\ W2) by A1,Th17
    .= W1 + (W2 /\ W3) by Th14;
end;
