proposition: Lemma FSumx_char : forall n f x Hx Hf, FSumx n f x Hx [=] Sumx (fun i Hi => f i Hi x (FSumx_pred n f Hf x Hx i Hi)).
proof: Proof. intro; induction n as [| n Hrecn]. algebra. intros; simpl in |- *. apply bin_op_wd_unfolded; algebra. cut (ext_fun_seq' (fun i Hi => f i (Nat.lt_lt_succ_r i n Hi))). intro H. eapply eq_transitive_unfolded. apply Hrecn with (Hf := H). apply Sumx_wd; intros; simpl in |- *; algebra. intros i j H H0 H' x0 y H1 H2. apply Hf with i (Nat.lt_lt_succ_r i n H0) x0; auto. Qed.
imports: CoRN.reals.CSumsReals CoRN.ftc.PartFunEquality