proposition: Lemma bet_trans a b c d : bet a b c = bet (a + d) (b + d) (c + d).
proof: Proof. rewrite ![_ + d]addrC /bet /betE /betS !add2r_eq ![d + _]addrC !addrDBD. suffices: betR a b c = betR (a + d) (b + d) (c + d) by move ->. by rewrite /betR !addrDBD. 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