proposition: Lemma contraction_eq x y z k : k != 0 -> (contraction x y k == contraction x z k) = (y == z).
proof: Proof. move=>/eqP ?; rewrite -subr_eq -addrA subrr addr0. rewrite -subr_eq0 -scalerBr opprB addrBDB scalemx_eq0. by case: (k =P 0); rewrite // subr_eq0 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