
theorem Th11:
  for K be add-associative right_zeroed right_complementable
associative Abelian well-unital distributive non empty doubleLoopStr for V be
VectSp of K for V1 be Subspace of V, W1 be Subspace of V1, v be Vector of V st
  v in W1 holds v is Vector of V1
proof
  let K be add-associative right_zeroed right_complementable associative
  Abelian well-unital distributive non empty doubleLoopStr, V be VectSp of K;
  let V1 be Subspace of V, W1 be Subspace of V1, v be Vector of V;
  assume v in W1;
  then the carrier of W1 c= the carrier of V1 & v in the carrier of W1 by
VECTSP_4:def 2;
  hence thesis;
end;
