proposition: Lemma extension_to_3d__upper_dim_3 : forall {Tm: Tarski_neutral_dimensionless} {Tm2 : Tarski_neutral_dimensionless_with_decidable_point_equality Tm} {M : Tarski_3D Tm2} (f : @Tpoint Tn -> @Tpoint Tm), extension f -> @upper_dim_3_axiom Tn.
proof: Proof. intros Tm Tm2 M f fext A B C P Q R; intros. apply (extension_reverse_col f); trivial. unfold extension, inj, pres_cong in fext; spliter. unfold Col; apply upper_dim_3 with (f P) (f Q) (f R); auto. Qed.
imports: GeoCoq.Axioms.continuity_axioms GeoCoq.Meta_theory.Dimension_axioms.upper_dim_2 GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Continuity.grad