(** * Group IV Congruence *)

(** The cong predicate of Hilbert is the same as the one of Tarski: *)

Definition outH := fun P A B => Between_H P A B \/ Between_H P B A \/ (P <> A /\ A = B).

Lemma axiom_hcong_1_existence : forall A B A' P l, A <> B -> A' <> P -> IncidentL A' l -> IncidentL P l -> exists B', IncidentL B' l /\ outH A' P B' /\ Cong A' B' A B.