proposition: Lemma twice_signed_area_perm : forall A B C, twice_signed_area A B C =F= - twice_signed_area B A C.
proof: Proof. intros. unfold twice_signed_area. decompose_coordinates. unfold cross_product;simpl. field;prove_discr_for_powers_of_2. Qed.
imports: Description Ring Field Nsatz Rtauto GeoCoq.Tarski_dev.Ch16_coordinates GeoCoq.Tarski_dev.Ch15_pyth_rel GeoCoq.Tarski_dev.Annexes.midpoint_theorems