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Oct 24, 2025
Merged

Remove MC2.4 deprecations and cleanup mathcomp_extra.v #1736

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45fc1a7
Remove MC2.4 deprecations and cleanup mathcomp_extra.v
pi8027 Oct 21, 2025
5a5d2ae
fix comment
affeldt-aist Oct 23, 2025
52c22bf
fix
affeldt-aist Oct 23, 2025
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1 change: 1 addition & 0 deletions classical/fsbigop.v
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Expand Up @@ -316,6 +316,7 @@ Proof.
move=> finF; elim/Peq : R => R in zero times plus a F finF *.
have [->|a0] := eqVneq a zero.
by rewrite Monoid.mul0m fsbig1//; move=> i _; rewrite Monoid.mul0m.
#[warning="deprecated"] (* FIXME *)
rewrite big_distrr [RHS](full_fsbigID (F @^-1` [set zero])); last first.
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I didn't manage to get rid of full_fsbigID here.

apply: sub_finite_set finF => x /= [Px aFN0].
by split=> //; apply: contra_not aFN0 => ->; rewrite Monoid.simpm.
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52 changes: 33 additions & 19 deletions classical/functions.v
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Expand Up @@ -2598,8 +2598,8 @@ HB.instance Definition _ :=

End fct_zmodType.

Section fct_ringType.
Variables (T : pointedType) (M : ringType).
Section fct_pzRingType.
Variables (T : Type) (M : pzRingType).
Implicit Types f g h : T -> M.

Let mulrA : associative (fun f g => f \* g).
Expand All @@ -2617,24 +2617,38 @@ Proof. by move=> f g h; rewrite funeqE=> x/=; rewrite mulrDl. Qed.
Let mulrDr : right_distributive (fun f g => f \* g) +%R.
Proof. by move=> f g h; rewrite funeqE=> x/=; rewrite mulrDr. Qed.

HB.instance Definition _ := @GRing.Zmodule_isPzRing.Build (T -> M) (cst 1)
(fun f g => f \* g) mulrA mul1r mulr1 mulrDl mulrDr.

End fct_pzRingType.

Section fct_nzRingType.
Variables (T : pointedType) (M : nzRingType).

Let oner_neq0 : cst 1 != 0 :> (T -> M).
Proof. by apply/eqP; rewrite funeqE => /(_ point) /eqP; rewrite oner_eq0. Qed.

HB.instance Definition _ := @GRing.Zmodule_isRing.Build (T -> M) (cst 1)
(fun f g => f \* g) mulrA mul1r mulr1 mulrDl mulrDr oner_neq0.
HB.instance Definition _ :=
@GRing.PzSemiRing_isNonZero.Build (T -> M) oner_neq0.

End fct_ringType.
End fct_nzRingType.

Program Definition fct_comRingType (T : pointedType) (M : comRingType) :=
GRing.Ring_hasCommutativeMul.Build (T -> M) _.
Next Obligation.
by move=> T M f g; rewrite funeqE => x; rewrite /GRing.mul/= mulrC.
Qed.
HB.instance Definition _ (T : pointedType) (M : comRingType) :=
fct_comRingType T M.
Section fct_comPzRingType.
Variables (T : Type) (M : comPzRingType).

Let mulrC : commutative (@GRing.mul (T -> M)).
Proof. by move=> f g; rewrite funeqE => x; rewrite /GRing.mul/= mulrC. Qed.

HB.instance Definition _ :=
GRing.PzRing_hasCommutativeMul.Build (T -> M) mulrC.

End fct_comPzRingType.

HB.instance Definition _ (T : pointedType) (M : comNzRingType) :=
GRing.ComPzRing.on (T -> M).

Section fct_lmod.
Variables (U : Type) (R : ringType) (V : lmodType R).
Variables (U : Type) (R : pzRingType) (V : lmodType R).
Program Definition fct_lmodMixin := @GRing.Zmodule_isLmodule.Build R (U -> V)
(fun k f => k \*: f) _ _ _ _.
Next Obligation. by move=> k f v; rewrite funeqE=> x; exact: scalerA. Qed.
Expand All @@ -2652,12 +2666,12 @@ 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 : ringType) r (P : {pred I})
Lemma fct_prodE (I : Type) (T : pointedType) (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.

Lemma mul_funC (T : Type) {R : comSemiRingType} (f : T -> R) (r : R) :
Lemma mul_funC (T : Type) {R : comPzSemiRingType} (f : T -> R) (r : R) :
r \*o f = r \o* f.
Proof. by apply/funext => x/=; rewrite mulrC. Qed.

Expand All @@ -2675,7 +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 : ringType) (s : seq (T -> K)) :
Lemma prodrfctE (T : pointedType) (K : pzRingType) (s : seq (T -> K)) :
\prod_(f <- s) f = (fun x => \prod_(f <- s) f x).
Proof. exact: fct_prodE. Qed.

Expand All @@ -2686,19 +2700,19 @@ 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 : ringType) (f g : T -> K) :
Lemma mulrfctE (T : pointedType) (K : pzRingType) (f g : T -> K) :
f * g = (fun x => f x * g x).
Proof. by []. Qed.

Lemma scalrfctE (T : Type) (K : ringType) (L : lmodType K)
Lemma scalrfctE (T : Type) (K : pzRingType) (L : lmodType K)
k (f : T -> L) :
k *: f = (fun x : T => k *: f x).
Proof. by []. Qed.

Lemma cstE (T T': Type) (x : T) : cst x = fun _: T' => x.
Proof. by []. Qed.

Lemma exprfctE (T : pointedType) (K : ringType) (f : T -> K) n :
Lemma exprfctE (T : pointedType) (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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