proposition: Lemma congP_aux' (a b : 'rV[R]_1) : (b - a) *m (b - a)^T = (sqr_L2_norm_1D a b)%:M.
proof: Proof. rewrite [X in X=_]mx11_scalar /sqr_L2_norm_1D !mxE. rewrite !big_ord_recr /= big_ord0 add0r !mxE -!expr2. by congr ((b 0 _ - a 0 _) ^+ 2)%:M; apply: val_inj. 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) mathcomp(zmodp) GeoCoq.Meta_theory.Models.POF_to_Tarski GeoCoq.Meta_theory.Counter_models.Planar.independence