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slightly generalize fct_prodR and some other functions in functions.v #1795

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Merged
affeldt-aist merged 1 commit into from
Dec 12, 2025
Merged

slightly generalize fct_prodR and some other functions in functions.v #1795

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8 changes: 4 additions & 4 deletions classical/functions.v
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Original file line number Diff line number Diff line change
Expand Up @@ -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.
Expand All @@ -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.

Expand All @@ -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.

Expand All @@ -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.

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