unfold PythRel in H.
spliter.
induction H0.
spliter.
induction H1.
auto.
apply opp_midpoint in H1.
unfold Midpoint in H1.
spliter.
apply cong_symmetry in H2.
apply cong_identity in H2.
auto.
ex_and H0 B'.
apply perp_distinct in H0.
tauto.
Qed.

(* Specifications: *)
Lemma Pyth_f : forall A B, Col O E A -> Col O E B -> {C | PythRel O E E' A B C /\ (Ps O E C \/ C = O)}.
Definition inv O E E' A MA :=
(A <> O /\ Prod O E E' MA A E) \/ (A = O /\ MA = O).