proposition: Lemma seg_aux7 a b c d: (# a *m (# b)^T) 0 0 - (# c *m (# d)^T) 0 0 = omd c d - omd a b.
proof: Proof. apply /eqP. rewrite eq_sym /omd/omd_v opprB addrA addrC !addrA. by rewrite [-1+1]addrC subrr sub0r addrC. 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