proposition: Lemma betEP a b c : reflect ([ \/ [ /\ a = b & b = c ], a = b | b = c ]) (betE a b c).
proof: Proof. by rewrite /betE; case: (a =P b)=>[->|?]; case: (b =P c)=>[->|?]=> /=; constructor; [apply Or32|apply Or32|apply Or33|]=> //; case=> [[? ?]|?|?]. 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