proposition: Lemma foldr_prop_nth : forall {T} {P: T -> Prop} d l n, foldr (fun d acc => P d /\ acc) True l -> P d -> P (nth d l n).
proof: Proof. intros T P d l n Hl Hd. revert l n Hl. induction l. intros n _. now rewrite nth_nil. intros [|n]. now intros (H,_). intros (_,H). now apply IHl. Qed.
imports: Coq(Reals Datatypes ssreflect ssrbool) mathcomp(seq) Rcomplements Hierarchy Derive RInt RInt_analysis Derive_2d Continuity ElemFct