proposition: Lemma angle_construction_4 : forall A B C A' B' P, A <> B -> C <> B -> A' <> B' -> exists C', CongA A B C A' B' C' /\ Coplanar A' B' C' P.
proof: Proof. intros. destruct (col_dec A' B' P). destruct (angle_construction_3 A B C A' B') as [C']; auto. exists C'; split; Cop. destruct (col_dec A B C). destruct (angle_construction_3 A B C A' B') as [C']; auto. exists C'; split; auto. exists C'; left; split; Col. apply (col_conga_col A B C); assumption. destruct (angle_construction_1 A B C A' B' P) as [C' []]; auto. exists C'; split; Cop. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2