
theorem Th17:
  for K be add-associative right_zeroed right_complementable
  associative Abelian well-unital distributive non empty doubleLoopStr, V be
VectSp of K for v be Vector of V, W1,W2 be Subspace of V ex v1,v2 be Vector of
  V st v |-- (W1,W2) = [v1,v2]
proof
  let K be add-associative right_zeroed right_complementable associative
  Abelian well-unital distributive non empty doubleLoopStr, V be VectSp of K;
  let v be Vector of V, W1,W2 be Subspace of V;
  take (v |-- (W1,W2))`1,(v |-- (W1,W2))`2;
  thus thesis by MCART_1:21;
end;
