proposition: Lemma segment_construction_0 : forall A B A', exists B', Cong A' B' A B.
proof: Proof. intros. induction (eq_dec_points A B). exists A'. subst B. apply cong_trivial_identity. assert(exists X : Tpoint, A' <> X). apply another_point. ex_and H0 X. assert(HH:=segment_construction_3 A' X A B H1 H). ex_and HH B'. exists B'. assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2