(** The following lemmas express the triangle inequality only with predicates from Tarski : AC <= AB + BC, and AC = AB + BC <-> Bet A B C *)

Lemma triangle_strict_inequality_2 : forall A B C A' B' C',
Bet A' B' C' -> Cong A B A' B' -> Cong B C B' C' -> ~ Bet A B C ->
Lt A C A' C'.