reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;
reserve V1,V2,V3 for Subset of V;
reserve W,W1,W2 for Subspace of V;
reserve x for set;
reserve w,w1,w2 for VECTOR of W;

theorem
  x in W1 & W1 is Subspace of W2 implies x in W2
proof
  assume x in W1 & W1 is Subspace of W2;
  then x in the carrier of W1 & the carrier of W1 c= the carrier of W2 by Def8;
  hence thesis;
end;
