Proof with Geometry.
intros.
cases_equality A C.
apply  l2_11a_strong_strong_strong_aux...
cases_equality B D.
symmetry.
apply  l2_11a_strong_strong_strong_aux...
unfold weak_3_parallelogram in *.
DecompExAnd H X.
exists X.
intuition.
apply l2_11a_strong.
unfold weak_parallelogram.
intuition.
Qed.

Theorem l2_11b :
forall A B C D P Q : Point, parallelogram A B C D ->
S4 P A Q B = S4 P D Q C.