proposition: Lemma Least_zero alpha : Least alpha <-> alpha = zero.
proof: Proof. split. destruct alpha as [i j]; destruct i. - destruct j; [ reflexivity| ]. intro H; specialize (H (0,j)); exfalso. inversion H. inversion H0; abstract lia. abstract lia. - intro H; specialize (H (0,0)); exfalso. inversion H. inversion H0; abstract lia. - intro; subst; intro; apply zero_le. Qed.
imports: Coq(Arith Compare_dec Lia) hydras(Simple_LexProd ON_Generic ON_mult ON_Omega Compat815)