proposition: Lemma inner_pasch a b c p q : bet a p c -> bet b q c -> a <> p -> p <> c -> b <> q -> q <> c -> ~ (bet a b c \/ bet b c a \/ bet c a b) -> exists x, bet p x b /\ bet q x a.
proof: Proof. move=> ? ? ? ? ? ? ? . destruct (@inner_pasch' a b c p q) as [x [Hb1 Hb2]]; by rewrite -?bet_betS // /bet; exists x; rewrite Hb1 Hb2 !orbT. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype seq order) mathcomp(fintype bigop) mathcomp(ssralg ssrnum matrix) mathcomp(zmodp) GeoCoq.Axioms.tarski_axioms GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.gupta_inspired_to_tarski GeoCoq.Meta_theory.Counter_models.coplanarity GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Tarski_dev.Ch12_parallel_inter_dec