analysis.analytic.uniqueness ⟷ Mathlib.Analysis.Analytic.Uniqueness

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -60,7 +60,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
     by
     have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy
     have := hp.change_origin (A.trans_le ENNReal.half_le_self)
-    simp only [add_sub_cancel'_right] at this
+    simp only [add_sub_cancel] at this
     apply this.mono (ENNReal.half_pos hp.r_pos.ne')
     apply ENNReal.le_sub_of_add_le_left ENNReal.coe_ne_top
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -58,9 +58,9 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   let q := p.change_origin (y - x)
   have has_series : HasFPowerSeriesOnBall f q y (r / 2) :=
     by
-    have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy 
+    have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy
     have := hp.change_origin (A.trans_le ENNReal.half_le_self)
-    simp only [add_sub_cancel'_right] at this 
+    simp only [add_sub_cancel'_right] at this
     apply this.mono (ENNReal.half_pos hp.r_pos.ne')
     apply ENNReal.le_sub_of_add_le_left ENNReal.coe_ne_top
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,9 +3,9 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Analysis.Analytic.Linear
-import Mathbin.Analysis.Analytic.Composition
-import Mathbin.Analysis.NormedSpace.Completion
+import Analysis.Analytic.Linear
+import Analysis.Analytic.Composition
+import Analysis.NormedSpace.Completion
 
 #align_import analysis.analytic.uniqueness from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.analytic.uniqueness
-! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Analytic.Linear
 import Mathbin.Analysis.Analytic.Composition
 import Mathbin.Analysis.NormedSpace.Completion
 
+#align_import analysis.analytic.uniqueness from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
+
 /-!
 # Uniqueness principle for analytic functions
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf9bbbcf0c1c1ead18280b0d010e417b10abb1b6

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.analytic.uniqueness
-! leanprover-community/mathlib commit a3209ddf94136d36e5e5c624b10b2a347cc9d090
+! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.Completion
 /-!
 # Uniqueness principle for analytic functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We show that two analytic functions which coincide around a point coincide on whole connected sets,
 in `analytic_on.eq_on_of_preconnected_of_eventually_eq`.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

@@ -29,6 +29,7 @@ open scoped Topology ENNReal
 
 namespace AnalyticOn
 
+#print AnalyticOn.eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux /-
 /-- If an analytic function vanishes around a point, then it is uniformly zero along
 a connected set. Superseded by `eq_on_zero_of_preconnected_of_locally_zero` which does not assume
 completeness of the target space. -/
@@ -75,7 +76,9 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
     exact this.apply_eq_zero n _
   exact HasSum.unique A B
 #align analytic_on.eq_on_zero_of_preconnected_of_eventually_eq_zero_aux AnalyticOn.eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux
+-/
 
+#print AnalyticOn.eqOn_zero_of_preconnected_of_eventuallyEq_zero /-
 /-- The *identity principle* for analytic functions: If an analytic function vanishes in a whole
 neighborhood of a point `z₀`, then it is uniformly zero along a connected set. For a one-dimensional
 version assuming only that the function vanishes at some points arbitrarily close to `z₀`, see
@@ -95,7 +98,9 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero {f : E → F} {U : Set E}
   have : e (f z) = e 0 := by simpa only using A hz
   exact UniformSpace.Completion.coe_injective F this
 #align analytic_on.eq_on_zero_of_preconnected_of_eventually_eq_zero AnalyticOn.eqOn_zero_of_preconnected_of_eventuallyEq_zero
+-/
 
+#print AnalyticOn.eqOn_of_preconnected_of_eventuallyEq /-
 /-- The *identity principle* for analytic functions: If two analytic functions coincide in a whole
 neighborhood of a point `z₀`, then they coincide globally along a connected set.
 For a one-dimensional version assuming only that the functions coincide at some points
@@ -107,7 +112,9 @@ theorem eqOn_of_preconnected_of_eventuallyEq {f g : E → F} {U : Set E} (hf : A
   simpa [sub_eq_zero] using fun z hz =>
     (hf.sub hg).eqOn_zero_of_preconnected_of_eventuallyEq_zero hU h₀ hfg' hz
 #align analytic_on.eq_on_of_preconnected_of_eventually_eq AnalyticOn.eqOn_of_preconnected_of_eventuallyEq
+-/
 
+#print AnalyticOn.eq_of_eventuallyEq /-
 /-- The *identity principle* for analytic functions: If two analytic functions on a normed space
 coincide in a neighborhood of a point `z₀`, then they coincide everywhere.
 For a one-dimensional version assuming only that the functions coincide at some points
@@ -117,6 +124,7 @@ theorem eq_of_eventuallyEq {f g : E → F} [PreconnectedSpace E] (hf : AnalyticO
   funext fun x =>
     eqOn_of_preconnected_of_eventuallyEq hf hg isPreconnected_univ (mem_univ z₀) hfg (mem_univ x)
 #align analytic_on.eq_of_eventually_eq AnalyticOn.eq_of_eventuallyEq
+-/
 
 end AnalyticOn
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.analytic.uniqueness
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit a3209ddf94136d36e5e5c624b10b2a347cc9d090
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -96,7 +96,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero {f : E → F} {U : Set E}
   exact UniformSpace.Completion.coe_injective F this
 #align analytic_on.eq_on_zero_of_preconnected_of_eventually_eq_zero AnalyticOn.eqOn_zero_of_preconnected_of_eventuallyEq_zero
 
-/-- The *identity principle* for analytic functions: If two analytic function coincide in a whole
+/-- The *identity principle* for analytic functions: If two analytic functions coincide in a whole
 neighborhood of a point `z₀`, then they coincide globally along a connected set.
 For a one-dimensional version assuming only that the functions coincide at some points
 arbitrarily close to `z₀`, see `eq_on_of_preconnected_of_frequently_eq`. -/
@@ -108,5 +108,15 @@ theorem eqOn_of_preconnected_of_eventuallyEq {f g : E → F} {U : Set E} (hf : A
     (hf.sub hg).eqOn_zero_of_preconnected_of_eventuallyEq_zero hU h₀ hfg' hz
 #align analytic_on.eq_on_of_preconnected_of_eventually_eq AnalyticOn.eqOn_of_preconnected_of_eventuallyEq
 
+/-- The *identity principle* for analytic functions: If two analytic functions on a normed space
+coincide in a neighborhood of a point `z₀`, then they coincide everywhere.
+For a one-dimensional version assuming only that the functions coincide at some points
+arbitrarily close to `z₀`, see `eq_of_frequently_eq`. -/
+theorem eq_of_eventuallyEq {f g : E → F} [PreconnectedSpace E] (hf : AnalyticOn 𝕜 f univ)
+    (hg : AnalyticOn 𝕜 g univ) {z₀ : E} (hfg : f =ᶠ[𝓝 z₀] g) : f = g :=
+  funext fun x =>
+    eqOn_of_preconnected_of_eventuallyEq hf hg isPreconnected_univ (mem_univ z₀) hfg (mem_univ x)
+#align analytic_on.eq_of_eventually_eq AnalyticOn.eq_of_eventuallyEq
+
 end AnalyticOn
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -39,7 +39,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   /- Let `u` be the set of points around which `f` vanishes. It is clearly open. We have to show
     that its limit points in `U` still belong to it, from which the inclusion `U ⊆ u` will follow
     by connectedness. -/
-  let u := { x | f =ᶠ[𝓝 x] 0 }
+  let u := {x | f =ᶠ[𝓝 x] 0}
   suffices main : closure u ∩ U ⊆ u
   · have Uu : U ⊆ u :=
       hU.subset_of_closure_inter_subset isOpen_setOf_eventually_nhds ⟨z₀, h₀, hfz₀⟩ main
@@ -65,7 +65,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)
     exact ENNReal.add_halves _
   have M : EMetric.ball y (r / 2) ∈ 𝓝 x := emetric.is_open_ball.mem_nhds hxy
-  filter_upwards [M]with z hz
+  filter_upwards [M] with z hz
   have A : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) (f z) := has_series.has_sum_sub hz
   have B : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) 0 :=
     by
@@ -89,7 +89,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero {f : E → F} {U : Set E}
   have A : eq_on (e ∘ f) 0 U :=
     by
     apply eq_on_zero_of_preconnected_of_eventually_eq_zero_aux this hU h₀
-    filter_upwards [hfz₀]with x hx
+    filter_upwards [hfz₀] with x hx
     simp only [hx, Function.comp_apply, Pi.zero_apply, map_zero]
   intro z hz
   have : e (f z) = e 0 := by simpa only using A hz

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -55,7 +55,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   obtain ⟨y, yu, hxy⟩ : ∃ y ∈ u, edist x y < r / 2
   exact EMetric.mem_closure_iff.1 xu (r / 2) (ENNReal.half_pos hp.r_pos.ne')
   let q := p.change_origin (y - x)
-  have has_series : HasFpowerSeriesOnBall f q y (r / 2) :=
+  have has_series : HasFPowerSeriesOnBall f q y (r / 2) :=
     by
     have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy 
     have := hp.change_origin (A.trans_le ENNReal.half_le_self)
@@ -69,7 +69,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   have A : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) (f z) := has_series.has_sum_sub hz
   have B : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) 0 :=
     by
-    have : HasFpowerSeriesAt 0 q y := has_series.has_fpower_series_at.congr yu
+    have : HasFPowerSeriesAt 0 q y := has_series.has_fpower_series_at.congr yu
     convert hasSum_zero
     ext n
     exact this.apply_eq_zero n _

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -57,9 +57,9 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   let q := p.change_origin (y - x)
   have has_series : HasFpowerSeriesOnBall f q y (r / 2) :=
     by
-    have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy
+    have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy 
     have := hp.change_origin (A.trans_le ENNReal.half_le_self)
-    simp only [add_sub_cancel'_right] at this
+    simp only [add_sub_cancel'_right] at this 
     apply this.mono (ENNReal.half_pos hp.r_pos.ne')
     apply ENNReal.le_sub_of_add_le_left ENNReal.coe_ne_top
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -25,7 +25,7 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddC
 
 open Set
 
-open Topology ENNReal
+open scoped Topology ENNReal
 
 namespace AnalyticOn
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -53,7 +53,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   rintro x ⟨xu, xU⟩
   rcases hf x xU with ⟨p, r, hp⟩
   obtain ⟨y, yu, hxy⟩ : ∃ y ∈ u, edist x y < r / 2
-  exact Emetric.mem_closure_iff.1 xu (r / 2) (ENNReal.half_pos hp.r_pos.ne')
+  exact EMetric.mem_closure_iff.1 xu (r / 2) (ENNReal.half_pos hp.r_pos.ne')
   let q := p.change_origin (y - x)
   have has_series : HasFpowerSeriesOnBall f q y (r / 2) :=
     by
@@ -64,7 +64,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
     apply ENNReal.le_sub_of_add_le_left ENNReal.coe_ne_top
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)
     exact ENNReal.add_halves _
-  have M : Emetric.ball y (r / 2) ∈ 𝓝 x := emetric.is_open_ball.mem_nhds hxy
+  have M : EMetric.ball y (r / 2) ∈ 𝓝 x := emetric.is_open_ball.mem_nhds hxy
   filter_upwards [M]with z hz
   have A : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) (f z) := has_series.has_sum_sub hz
   have B : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) 0 :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -25,7 +25,7 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddC
 
 open Set
 
-open Topology Ennreal
+open Topology ENNReal
 
 namespace AnalyticOn
 
@@ -53,17 +53,17 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   rintro x ⟨xu, xU⟩
   rcases hf x xU with ⟨p, r, hp⟩
   obtain ⟨y, yu, hxy⟩ : ∃ y ∈ u, edist x y < r / 2
-  exact Emetric.mem_closure_iff.1 xu (r / 2) (Ennreal.half_pos hp.r_pos.ne')
+  exact Emetric.mem_closure_iff.1 xu (r / 2) (ENNReal.half_pos hp.r_pos.ne')
   let q := p.change_origin (y - x)
   have has_series : HasFpowerSeriesOnBall f q y (r / 2) :=
     by
     have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy
-    have := hp.change_origin (A.trans_le Ennreal.half_le_self)
+    have := hp.change_origin (A.trans_le ENNReal.half_le_self)
     simp only [add_sub_cancel'_right] at this
-    apply this.mono (Ennreal.half_pos hp.r_pos.ne')
-    apply Ennreal.le_sub_of_add_le_left Ennreal.coe_ne_top
+    apply this.mono (ENNReal.half_pos hp.r_pos.ne')
+    apply ENNReal.le_sub_of_add_le_left ENNReal.coe_ne_top
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)
-    exact Ennreal.add_halves _
+    exact ENNReal.add_halves _
   have M : Emetric.ball y (r / 2) ∈ 𝓝 x := emetric.is_open_ball.mem_nhds hxy
   filter_upwards [M]with z hz
   have A : HasSum (fun n : ℕ => q n fun i : Fin n => z - y) (f z) := has_series.has_sum_sub hz

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -54,7 +54,7 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
   have has_series : HasFPowerSeriesOnBall f q y (r / 2) := by
     have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy
     have := hp.changeOrigin (A.trans_le ENNReal.half_le_self)
-    simp only [add_sub_cancel'_right] at this
+    simp only [add_sub_cancel] at this
     apply this.mono (ENNReal.half_pos hp.r_pos.ne')
     apply ENNReal.le_sub_of_add_le_left ENNReal.coe_ne_top
     apply (add_le_add A.le (le_refl (r / 2))).trans (le_of_eq _)

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -48,8 +48,8 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
     it follows that `f` vanishes on a neighborhood of `x`, proving the claim. -/
   rintro x ⟨xu, xU⟩
   rcases hf x xU with ⟨p, r, hp⟩
-  obtain ⟨y, yu, hxy⟩ : ∃ y ∈ u, edist x y < r / 2
-  exact EMetric.mem_closure_iff.1 xu (r / 2) (ENNReal.half_pos hp.r_pos.ne')
+  obtain ⟨y, yu, hxy⟩ : ∃ y ∈ u, edist x y < r / 2 :=
+    EMetric.mem_closure_iff.1 xu (r / 2) (ENNReal.half_pos hp.r_pos.ne')
   let q := p.changeOrigin (y - x)
   have has_series : HasFPowerSeriesOnBall f q y (r / 2) := by
     have A : (‖y - x‖₊ : ℝ≥0∞) < r / 2 := by rwa [edist_comm, edist_eq_coe_nnnorm_sub] at hxy

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -36,8 +36,8 @@ theorem eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux [CompleteSpace F] {f
     that its limit points in `U` still belong to it, from which the inclusion `U ⊆ u` will follow
     by connectedness. -/
   let u := {x | f =ᶠ[𝓝 x] 0}
-  suffices main : closure u ∩ U ⊆ u
-  · have Uu : U ⊆ u :=
+  suffices main : closure u ∩ U ⊆ u by
+    have Uu : U ⊆ u :=
       hU.subset_of_closure_inter_subset isOpen_setOf_eventually_nhds ⟨z₀, h₀, hfz₀⟩ main
     intro z hz
     simpa using mem_of_mem_nhds (Uu hz)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -17,8 +17,8 @@ in `AnalyticOn.eqOn_of_preconnected_of_eventuallyEq`.
 -/
 
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
-  [NormedSpace 𝕜 E] {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {E : Type*} [NormedAddCommGroup E]
+  [NormedSpace 𝕜 E] {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 open Set
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.analytic.uniqueness
-! leanprover-community/mathlib commit a3209ddf94136d36e5e5c624b10b2a347cc9d090
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Analytic.Linear
 import Mathlib.Analysis.Analytic.Composition
 import Mathlib.Analysis.NormedSpace.Completion
 
+#align_import analysis.analytic.uniqueness from "leanprover-community/mathlib"@"a3209ddf94136d36e5e5c624b10b2a347cc9d090"
+
 /-!
 # Uniqueness principle for analytic functions