proposition: Lemma twice_signed_area_ABA : forall A B, twice_signed_area A B A =F= 0.
proof: Proof. intros. unfold twice_signed_area, cross_product. decompose_coordinates;simpl. ring. Qed.
imports: Description Ring Field Nsatz Rtauto GeoCoq.Tarski_dev.Ch16_coordinates GeoCoq.Tarski_dev.Ch15_pyth_rel GeoCoq.Tarski_dev.Annexes.midpoint_theorems