Proof with Geometry.
intros.
replace (S4 P D A C) with (S P D C - S A D C)...
apply l2_12a...
Qed.

(* Specifications: *)
Theorem l2_12b_strong_3 :
forall A B C D P : Point, weak_3_parallelogram A B C D ->
S P A B = S4 P D A C.