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fix(Geometry/Manifold/VectorBundle/Hom): fix typo in doc-string (#41025)
Discovered while working on #36036.
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  • Mathlib/Geometry/Manifold/VectorBundle

Mathlib/Geometry/Manifold/VectorBundle/Hom.lean

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@@ -360,7 +360,7 @@ section TwoVariables
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variable [∀ x, IsTopologicalAddGroup (E₃ x)] [∀ x, ContinuousSMul 𝕜 (E₃ x)]
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{ψ : ∀ x, (E₁ (b x) →L[𝕜] E₂ (b x) →L[𝕜] E₃ (b x))} {w : ∀ x, E₂ (b x)}
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/-- Consider `C^n` maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider `C^n` maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is `C^n`.
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@@ -373,7 +373,7 @@ lemma ContMDiffWithinAt.clm_bundle_apply₂
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CMDiffAt[s] n (fun m ↦ TotalSpace.mk' F₃ (b m) (ψ m (v m) (w m))) x :=
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hψ.clm_bundle_apply hv |>.clm_bundle_apply hw
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/-- Consider `C^n` maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider `C^n` maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is `C^n`.
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@@ -386,7 +386,7 @@ lemma ContMDiffAt.clm_bundle_apply₂
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CMDiffAt n (fun m ↦ TotalSpace.mk' F₃ (b m) (ψ m (v m) (w m))) x :=
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ContMDiffWithinAt.clm_bundle_apply₂ hψ hv hw
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/-- Consider `C^n` maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider `C^n` maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is `C^n`.
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@@ -399,7 +399,7 @@ lemma ContMDiffOn.clm_bundle_apply₂
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CMDiff[s] n (fun m ↦ TotalSpace.mk' F₃ (b m) (ψ m (v m) (w m))) :=
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fun x hx ↦ (hψ x hx).clm_bundle_apply₂ (hv x hx) (hw x hx)
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/-- Consider `C^n` maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider `C^n` maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is `C^n`. -/
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lemma ContMDiff.clm_bundle_apply₂
@@ -417,7 +417,7 @@ section TwoVariables'
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variable [∀ x, IsTopologicalAddGroup (E₃ x)] [∀ x, ContinuousSMul 𝕜 (E₃ x)]
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{ψ : ∀ x, (E₁ (b x) →L[𝕜] E₂ (b x) →L[𝕜] E₃ (b x))} {w : ∀ x, E₂ (b x)}
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/-- Consider differentiable maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider differentiable maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is differentiable.
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@@ -430,7 +430,7 @@ lemma MDifferentiableWithinAt.clm_bundle_apply₂
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MDiffAt[s] (fun m ↦ TotalSpace.mk' F₃ (b m) (ψ m (v m) (w m))) x :=
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hψ.clm_bundle_apply hv |>.clm_bundle_apply hw
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/-- Consider differentiable maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider differentiable maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is differentiable.
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@@ -443,7 +443,7 @@ lemma MDifferentiableAt.clm_bundle_apply₂
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MDiffAt (fun m ↦ TotalSpace.mk' F₃ (b m) (ψ m (v m) (w m))) x :=
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MDifferentiableWithinAt.clm_bundle_apply₂ hψ hv hw
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/-- Consider differentiable maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider differentiable maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is differentiable.
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@@ -456,7 +456,7 @@ lemma MDifferentiableOn.clm_bundle_apply₂
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MDiff[s] (fun m ↦ TotalSpace.mk' F₃ (b m) (ψ m (v m) (w m))) :=
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fun x hx ↦ (hψ x hx).clm_bundle_apply₂ (hv x hx) (hw x hx)
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/-- Consider differentiable maps `v : M → E₁` and `v : M → E₂` to vector bundles, over a base map
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/-- Consider differentiable maps `v : M → E₁` and `w : M → E₂` to vector bundles, over a base map
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`b : M → B`, and bilinear maps `ψ m : E₁ (b m) → E₂ (b m) → E₃ (b m)` depending smoothly on `m`.
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One can apply `ψ m` to `v m` and `w m`, and the resulting map is differentiable. -/
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lemma MDifferentiable.clm_bundle_apply₂

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