proposition: Lemma cong_perp_aux2 (a p q : 'rV[R]_2) (m := (1 / (1 + 1)) *: (p + q)) i : (m 0 i - a 0 i) + (m 0 i - p 0 i) = q 0 i - a 0 i.
proof: Proof. rewrite addrAC addrA /m !mxE -mulrDl addf_divrr ?divff ?add11_neq0 //. by rewrite mul1r -addrA addrACA subrr add0r. 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