chore: last localEquiv -> partialEquiv renames in lemma names (#9620)

Author: grunweg

Mathlib/Geometry/Manifold/ContMDiff/Defs.lean

@@ -583,7 +583,7 @@ theorem contMDiffOn_iff_target :
         ∀ y : M',
           ContMDiffOn I 𝓘(𝕜, E') n (extChartAt I' y ∘ f) (s ∩ f ⁻¹' (extChartAt I' y).source) := by
   simp only [contMDiffOn_iff, ModelWithCorners.source_eq, chartAt_self_eq,
-    PartialHomeomorph.refl_localEquiv, PartialEquiv.refl_trans, extChartAt,
+    PartialHomeomorph.refl_partialEquiv, PartialEquiv.refl_trans, extChartAt,
     PartialHomeomorph.extend, Set.preimage_univ, Set.inter_univ, and_congr_right_iff]
   intro h
   constructor

Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean

@@ -374,9 +374,9 @@ variable (𝕜 E)
 
 /-- In the trivial model with corners, the associated `PartialEquiv` is the identity. -/
 @[simp, mfld_simps]
-theorem modelWithCornersSelf_localEquiv : 𝓘(𝕜, E).toPartialEquiv = PartialEquiv.refl E :=
+theorem modelWithCornersSelf_partialEquiv : 𝓘(𝕜, E).toPartialEquiv = PartialEquiv.refl E :=
   rfl
-#align model_with_corners_self_local_equiv modelWithCornersSelf_localEquiv
+#align model_with_corners_self_local_equiv modelWithCornersSelf_partialEquiv
 
 @[simp, mfld_simps]
 theorem modelWithCornersSelf_coe : (𝓘(𝕜, E) : E → E) = id :=

Mathlib/Geometry/Manifold/VectorBundle/FiberwiseLinear.lean

@@ -279,7 +279,7 @@ def smoothFiberwiseLinear : StructureGroupoid (B × F) where
     -/
     refine mem_iUnion.2 ⟨fun _ ↦ .refl 𝕜 F, mem_iUnion.2 ⟨univ, mem_iUnion.2 ⟨isOpen_univ, ?_⟩⟩⟩
     refine mem_iUnion.2 ⟨contMDiffOn_const, mem_iUnion.2 ⟨contMDiffOn_const, ?_, ?_⟩⟩
-    · simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_localEquiv,
+    · simp only [FiberwiseLinear.partialHomeomorph, PartialHomeomorph.refl_partialEquiv,
         PartialEquiv.refl_source, univ_prod_univ]
     · exact eqOn_refl id _
   locality' := by

Mathlib/Topology/PartialHomeomorph.lean

@@ -240,10 +240,10 @@ theorem source_preimage_target : e.source ⊆ e ⁻¹' e.target :=
 #align local_homeomorph.source_preimage_target PartialHomeomorph.source_preimage_target
 
 @[deprecated toPartialEquiv_injective]
-theorem eq_of_localEquiv_eq {e e' : PartialHomeomorph α β}
+theorem eq_of_partialEquiv_eq {e e' : PartialHomeomorph α β}
     (h : e.toPartialEquiv = e'.toPartialEquiv) : e = e' :=
   toPartialEquiv_injective h
-#align local_homeomorph.eq_of_local_equiv_eq PartialHomeomorph.eq_of_localEquiv_eq
+#align local_homeomorph.eq_of_local_equiv_eq PartialHomeomorph.eq_of_partialEquiv_eq
 
 theorem eventually_left_inverse {x} (hx : x ∈ e.source) :
     ∀ᶠ y in 𝓝 x, e.symm (e y) = y :=
@@ -773,9 +773,9 @@ protected def refl (α : Type*) [TopologicalSpace α] : PartialHomeomorph α α
 #align local_homeomorph.refl PartialHomeomorph.refl
 
 @[simp, mfld_simps]
-theorem refl_localEquiv : (PartialHomeomorph.refl α).toPartialEquiv = PartialEquiv.refl α :=
+theorem refl_partialEquiv : (PartialHomeomorph.refl α).toPartialEquiv = PartialEquiv.refl α :=
   rfl
-#align local_homeomorph.refl_local_equiv PartialHomeomorph.refl_localEquiv
+#align local_homeomorph.refl_local_equiv PartialHomeomorph.refl_partialEquiv
 
 @[simp, mfld_simps]
 theorem refl_symm : (PartialHomeomorph.refl α).symm = PartialHomeomorph.refl α :=