proposition: Lemma congP_aux a b c d : cong a b c d = (sqr_L2_norm_2D a b == sqr_L2_norm_2D c d).
proof: Proof. rewrite /cong !congP_aux' /sqr_L2_norm_2D; apply /eqP/eqP=> [|->] //. move=>/matrixP /(_ 0 0) /eqP. by rewrite !mxE /= !mulr1n; apply /eqP. 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