proposition: Lemma bet_opp a b c : bet a b c = bet (-a) (-b) (-c).
proof: Proof. rewrite /bet /betE /betS !eqr_opp; apply orb_id2l => _. rewrite -eqr_opp opprB opprK -scalerN opprB ![a + _]addrC. suffices: betR a b c = betR (-a) (-b) (-c) by move ->. by rewrite /betR !opprK ![_ +a]addrC -![a + _]opprB ratioNN. 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