proposition: Lemma congP_aux' a b : (b - a) *m (b - a)^T = (sqr_L2_norm_2D a b)%:M.
proof: Proof. rewrite [X in X=_]mx11_scalar /sqr_L2_norm_2D !mxE. rewrite !big_ord_recr /= big_ord0 add0r !mxE -!expr2. by congr ((b 0 _ - a 0 _) ^+ 2 + (b 0 _ - a 0 _) ^+ 2)%:M; apply: val_inj. 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