proposition: Lemma bet_betS a b c : a <> b -> b <> c -> bet a b c = betS a b c.
proof: Proof. rewrite /bet /betE. case: (a =P b)=>[-> /eqP|? ?]; first by rewrite eqxx. case: (b =P c)=> [-> /eqP|? ?]; by rewrite ?eqxx andFb !orFb. 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