proposition: Lemma divf_eq1 (a b : R): b!=0 -> a/b == 1 = (a == b).
proof: Proof. move=> /negPf b_neq0. suffices: (a/b == b/b) = (a == b). by move<-; rewrite divff ?b_neq0. by rewrite -subr_eq0 -mulrBl mulf_eq0 invr_eq0 b_neq0 subr_eq0 orbF. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype choice seq) mathcomp(fintype finset finfun bigop order) mathcomp(ssralg ssrnum path generic_quotient matrix mxalgebra algC) mathcomp(zmodp) GeoCoq.Meta_theory.Models.POF_to_Tarski GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.tarski_to_gupta_inspired GeoCoq.Tarski_dev.Ch06_out_lines GeoCoq.Tarski_dev.Ch11_angles GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Meta_theory.Counter_models.Planar.independence