diff --git a/classical/functions.v b/classical/functions.v index 5b84ba959..9f5b894c3 100644 --- a/classical/functions.v +++ b/classical/functions.v @@ -2666,7 +2666,7 @@ Lemma fct_sumE (I T : Type) (M : nmodType) r (P : {pred I}) (f : I -> T -> M) : \sum_(i <- r | P i) f i = fun x => \sum_(i <- r | P i) f i x. Proof. by apply/funext => ?; elim/big_rec2: _ => //= i y ? Pi <-. Qed. -Lemma fct_prodE (I : Type) (T : pointedType) (M : pzRingType) r (P : {pred I}) +Lemma fct_prodE (I T : Type) (M : pzRingType) r (P : {pred I}) (f : I -> T -> M) : \prod_(i <- r | P i) f i = fun x => \prod_(i <- r | P i) f i x. Proof. by apply/funext => ?; elim/big_rec2: _ => //= i y ? Pi <-. Qed. @@ -2689,7 +2689,7 @@ Lemma sumrfctE (T : Type) (K : nmodType) (s : seq (T -> K)) : \sum_(f <- s) f = (fun x => \sum_(f <- s) f x). Proof. exact: fct_sumE. Qed. -Lemma prodrfctE (T : pointedType) (K : pzRingType) (s : seq (T -> K)) : +Lemma prodrfctE (T : Type) (K : pzRingType) (s : seq (T -> K)) : \prod_(f <- s) f = (fun x => \prod_(f <- s) f x). Proof. exact: fct_prodE. Qed. @@ -2700,7 +2700,7 @@ Proof. by elim: n => [//|n h]; rewrite funeqE=> ?; rewrite !mulrSr h. Qed. Lemma opprfctE (T : Type) (K : zmodType) (f : T -> K) : - f = (fun x => - f x). Proof. by []. Qed. -Lemma mulrfctE (T : pointedType) (K : pzRingType) (f g : T -> K) : +Lemma mulrfctE (T : Type) (K : pzRingType) (f g : T -> K) : f * g = (fun x => f x * g x). Proof. by []. Qed. @@ -2712,7 +2712,7 @@ Proof. by []. Qed. Lemma cstE (T T': Type) (x : T) : cst x = fun _: T' => x. Proof. by []. Qed. -Lemma exprfctE (T : pointedType) (K : pzRingType) (f : T -> K) n : +Lemma exprfctE (T : Type) (K : pzRingType) (f : T -> K) n : f ^+ n = (fun x => f x ^+ n). Proof. by elim: n => [|n h]; rewrite funeqE=> ?; rewrite ?expr0 ?exprS ?h. Qed.