proposition: Lemma square_minus : forall x y : R, (x[-]y) [^]2 [=] x[^]2[+]y[^]2[-]Two[*]x[*]y.
proof: Proof. intros x y. unfold cg_minus in |- *. eapply eq_transitive_unfolded. apply square_plus. algebra. Qed.
imports: CoRN.tactics.CornTac CoRN.algebra.CSums CoRN.algebra.CAbMonoids Coq.Sorting.Permutation CoRN.util.SetoidPermutation Coq.Setoids.Setoid Coq.Classes.Morphisms Coq(Lia)