proposition: Lemma vector2_eq a b : a == b = (a 0 0 == b 0 0) && (a 0 1 == b 0 1).
proof: Proof. apply /eqP/andP=> [->|[/eqP eq0 /eqP eq1]]; rewrite ?eqxx //. apply /rowP=> j; case: j => [] [|[|//]] p. by rewrite (@ord_inj _ (Ordinal p) 0). by rewrite (@ord_inj _ (Ordinal p) 1). 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