proposition: Lemma seg_aux8 a b: norm(#a - #b)^+2 = omd a b - omd a a + omd a b - omd b b.
proof: Proof. rewrite norm_sqr -seg_aux7 -addrA -seg_aux7 mulmxBl mxE. rewrite [(-(_*m_) )0 0]mxE ![_*m(_-_)^T]dotC !mulmxBl. rewrite mxE [X in _ + _ -X]mxE ![(-(_*m_) )0 0]mxE. by rewrite opprB [#b *m (#a)^T]dotC. 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 algC) mathcomp(zmodp) GeoCoq.Meta_theory.Models.POF_to_Tarski GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.tarski_to_gupta_inspired GeoCoq.Tarski_dev.Ch06_out_lines GeoCoq.Tarski_dev.Ch11_angles GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Meta_theory.Counter_models.Planar.independence