proposition: Lemma sumx_const : forall n (x : R), Sumx (fun i (_ : i < n) => x) [=] nring n[*]x.
proof: Proof. intros n x; induction n as [| n Hrecn]. simpl in |- *; algebra. simpl in |- *. astepr (nring n[*]x[+][1][*]x). Step_final (nring n[*]x[+]x). 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)