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affeldt-aist merged 1 commit into from
Dec 3, 2025
Merged

minor gen #1783

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4 changes: 4 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -63,6 +63,10 @@
- in `lebesgue_integrable.v`:
+ weaken an hypothesis of lemma `finite_measure_integrable_cst`

- in `derive.v`:
+ definition `jacobian`
+ lemmas `deriveEjacobian`, `differentiable_coord`

### Deprecated

### Removed
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12 changes: 6 additions & 6 deletions theories/derive.v
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@@ -1,4 +1,4 @@
(* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *)
(* mathcomp analysis (c) 2025 Inria and AIST. License: CeCILL-C. *)
From HB Require Import structures.
From mathcomp Require Import all_ssreflect ssralg ssrnum matrix interval poly.
From mathcomp Require Import sesquilinear.
Expand Down Expand Up @@ -174,7 +174,7 @@ Proof. by move=> ?; apply: DiffDef. Qed.

Section jacobian.

Definition jacobian n m (R : numFieldType) (f : 'rV[R]_n.+1 -> 'rV[R]_m.+1) p :=
Definition jacobian n m (R : numFieldType) (f : 'rV[R]_n -> 'rV[R]_m) p :=
lin1_mx ('d f p).

End jacobian.
Expand Down Expand Up @@ -352,7 +352,7 @@ Section DifferentialR2.
Variable R : numFieldType.
Implicit Type (V : normedModType R).

Lemma deriveEjacobian m n (f : 'rV[R]_m.+1 -> 'rV[R]_n.+1) (a v : 'rV[R]_m.+1) :
Lemma deriveEjacobian m n (f : 'rV[R]_m -> 'rV[R]_n) (a v : 'rV[R]_m) :
differentiable f a -> 'D_ v f a = v *m jacobian f a.
Proof. by move=> /deriveE->; rewrite /jacobian mul_rV_lin1. Qed.

Expand Down Expand Up @@ -684,10 +684,10 @@ apply: DiffDef; first exact/linear_differentiable/scalel_continuous.
by rewrite diff_lin //; apply: scalel_continuous.
Qed.

Lemma differentiable_coord m n (M : 'M[R]_(m.+1, n.+1)) i j :
differentiable (fun N : 'M[R]_(m.+1, n.+1) => N i j : R ) M.
Lemma differentiable_coord m n (M : 'M[R]_(m, n)) i j :
differentiable (fun N : 'M[R]_(m, n) => N i j : R ) M.
Proof.
have @f : {linear 'M[R]_(m.+1, n.+1) -> R}.
have @f : {linear 'M[R]_(m, n) -> R}.
by exists (fun N : 'M[R]_(_, _) => N i j); do 2![eexists]; do ?[constructor];
rewrite ?mxE// => ? *; rewrite ?mxE//; move=> ?; rewrite !mxE.
rewrite (_ : (fun _ => _) = f) //; exact/linear_differentiable/coord_continuous.
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