proposition: Lemma sum_O_B : forall B, Col O E B -> Sum O E E' O B B.
proof: Proof. intros. induction(eq_dec_points B O). subst B. apply sum_O_O. unfold Sum. split. repeat split; Col. assert(O <> E' /\ E <> E'). split; intro; subst E'; apply grid_ok; Col. spliter. assert(~ Par E E' O E'). intro. induction H3. apply H3. exists E'. split; Col. spliter. apply grid_ok. Col. exists O. exists B. repeat split; try(apply pj_trivial). Col. left. right. repeat split; Col. intro. subst E. apply grid_ok. Col. Qed.
imports: GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg