proposition: Lemma cr_Product_0 (z: R) (zE: z [=] [0]): forall l, In z l -> cr_Product l [=] [0].
proof: Proof. Proof with auto. induction l. simpl. intuition. intros [?|?]; simpl. subst. rewrite zE. apply cring_mult_zero_op. rewrite IHl... apply cring_mult_zero. 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)