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;
reserve D for non empty set;
reserve d1 for Element of D;
reserve A for BinOp of D;
reserve M for Function of [:COMPLEX,D:],D;

theorem Th49:
  for W1,W2 being strict Subspace of V holds the carrier of W1 =
  the carrier of W2 implies W1 = W2
proof
  let W1,W2 be strict Subspace of V;
  assume the carrier of W1 = the carrier of W2;
  then W1 is Subspace of W2 & W2 is Subspace of W1 by Th47;
  hence thesis by Th45;
end;
