analysis.calculus.tangent_cone ⟷ Mathlib.Analysis.Calculus.TangentCone

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

@@ -221,8 +221,8 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print mapsTo_tangentCone_pi /-
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}

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

@@ -131,7 +131,7 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   have A : tendsto (fun n => ‖c n‖⁻¹) l (𝓝 0) := tendsto_inv_at_top_zero.comp hc
   have B : tendsto (fun n => ‖c n • d n‖) l (𝓝 ‖y‖) := (continuous_norm.tendsto _).comp hd
   have C : tendsto (fun n => ‖c n‖⁻¹ * ‖c n • d n‖) l (𝓝 (0 * ‖y‖)) := A.mul B
-  rw [MulZeroClass.zero_mul] at C 
+  rw [MulZeroClass.zero_mul] at C
   have : ∀ᶠ n in l, ‖c n‖⁻¹ * ‖c n • d n‖ = ‖d n‖ :=
     by
     apply (eventually_ne_of_tendsto_norm_atTop hc 0).mono fun n hn => _
@@ -416,7 +416,7 @@ theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 
   have : _ ≤ Submodule.span 𝕜 (tangentConeAt 𝕜 (s ×ˢ t) (x, y)) :=
     Submodule.span_mono
       (union_subset (subset_tangentCone_prod_left ht.2) (subset_tangentCone_prod_right hs.2))
-  rw [LinearMap.span_inl_union_inr, SetLike.le_def] at this 
+  rw [LinearMap.span_inl_union_inr, SetLike.le_def] at this
   exact (hs.1.Prod ht.1).mono this
 #align unique_diff_within_at.prod UniqueDiffWithinAt.prod
 -/

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

@@ -191,7 +191,7 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
     simp [hn, (hd' n).1]
   · apply tendsto.prod_mk_nhds hy _
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
-    exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
+    exact tendsto_pow_atTop_nhds_zero_of_lt_one one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_left subset_tangentCone_prod_left
 -/
 
@@ -217,7 +217,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
     simp [hn, (hd' n).1]
   · apply tendsto.prod_mk_nhds _ hy
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
-    exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
+    exact tendsto_pow_atTop_nhds_zero_of_lt_one one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 -/
 
@@ -248,7 +248,7 @@ theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
     · simp [hy]
     · suffices tendsto (fun n => c n • d' n j) at_top (𝓝 0) by simpa [hj]
       refine' squeeze_zero_norm (fun n => (hcd' n j hj).le) _
-      exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
+      exact tendsto_pow_atTop_nhds_zero_of_lt_one one_half_pos.le one_half_lt_one
 #align maps_to_tangent_cone_pi mapsTo_tangentCone_pi
 -/
 

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

@@ -426,6 +426,12 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
   classical
+  simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h ⊢
+  refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
+  norm_cast
+  simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←
+    maps_to']
+  exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
 -/
 
@@ -433,7 +439,11 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
 theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
-    UniqueDiffWithinAt 𝕜 (Set.pi I s) x := by classical
+    UniqueDiffWithinAt 𝕜 (Set.pi I s) x := by
+  classical
+  rw [← Set.univ_pi_piecewise_univ]
+  refine' UniqueDiffWithinAt.univ_pi _ _ _ _ fun i => _
+  by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
 #align unique_diff_within_at.pi UniqueDiffWithinAt.pi
 -/
 

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

@@ -426,12 +426,6 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
   classical
-  simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h ⊢
-  refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
-  norm_cast
-  simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←
-    maps_to']
-  exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
 -/
 
@@ -439,11 +433,7 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
 theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
-    UniqueDiffWithinAt 𝕜 (Set.pi I s) x := by
-  classical
-  rw [← Set.univ_pi_piecewise_univ]
-  refine' UniqueDiffWithinAt.univ_pi _ _ _ _ fun i => _
-  by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
+    UniqueDiffWithinAt 𝕜 (Set.pi I s) x := by classical
 #align unique_diff_within_at.pi UniqueDiffWithinAt.pi
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Analysis.Convex.Topology
-import Mathbin.Analysis.NormedSpace.Basic
-import Mathbin.Analysis.SpecificLimits.Basic
+import Analysis.Convex.Topology
+import Analysis.NormedSpace.Basic
+import Analysis.SpecificLimits.Basic
 
 #align_import analysis.calculus.tangent_cone from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
 
@@ -221,8 +221,8 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print mapsTo_tangentCone_pi /-
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 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.calculus.tangent_cone
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Topology
 import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.Analysis.SpecificLimits.Basic
 
+#align_import analysis.calculus.tangent_cone from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 # Tangent cone
 
@@ -224,8 +221,8 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print mapsTo_tangentCone_pi /-
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -124,6 +124,7 @@ theorem tangentCone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeA
 #align tangent_cone_mono tangentCone_mono
 -/
 
+#print tangentConeAt.lim_zero /-
 /-- Auxiliary lemma ensuring that, under the assumptions defining the tangent cone,
 the sequence `d` tends to 0 at infinity. -/
 theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {d : α → E}
@@ -143,7 +144,9 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   rw [tendsto_zero_iff_norm_tendsto_zero]
   exact D
 #align tangent_cone_at.lim_zero tangentConeAt.lim_zero
+-/
 
+#print tangentCone_mono_nhds /-
 theorem tangentCone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x :=
   by
   rintro y ⟨c, d, ds, ctop, clim⟩
@@ -153,6 +156,7 @@ theorem tangentCone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) : tangentConeAt 𝕜
   refine' (tendsto_inf.2 ⟨_, tendsto_principal.2 ds⟩).mono_right h
   simpa only [add_zero] using tendsto_const_nhds.add (tangentConeAt.lim_zero at_top Ctop clim)
 #align tangent_cone_mono_nhds tangentCone_mono_nhds
+-/
 
 #print tangentCone_congr /-
 /-- Tangent cone of `s` at `x` depends only on `𝓝[s] x`. -/
@@ -161,13 +165,16 @@ theorem tangentCone_congr (h : 𝓝[s] x = 𝓝[t] x) : tangentConeAt 𝕜 s x =
 #align tangent_cone_congr tangentCone_congr
 -/
 
+#print tangentCone_inter_nhds /-
 /-- Intersecting with a neighborhood of the point does not change the tangent cone. -/
 theorem tangentCone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t) x = tangentConeAt 𝕜 s x :=
   tangentCone_congr (nhdsWithin_restrict' _ ht).symm
 #align tangent_cone_inter_nhds tangentCone_inter_nhds
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print subset_tangentCone_prod_left /-
 /-- The tangent cone of a product contains the tangent cone of its left factor. -/
 theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t) :
     LinearMap.inl 𝕜 E F '' tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 (s ×ˢ t) (x, y) :=
@@ -189,9 +196,11 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_left subset_tangentCone_prod_left
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print subset_tangentCone_prod_right /-
 /-- The tangent cone of a product contains the tangent cone of its right factor. -/
 theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s) :
     LinearMap.inr 𝕜 E F '' tangentConeAt 𝕜 t y ⊆ tangentConeAt 𝕜 (s ×ˢ t) (x, y) :=
@@ -213,9 +222,11 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+#print mapsTo_tangentCone_pi /-
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] {s : ∀ i, Set (E i)} {x : ∀ i, E i}
@@ -242,7 +253,9 @@ theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
       refine' squeeze_zero_norm (fun n => (hcd' n j hj).le) _
       exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align maps_to_tangent_cone_pi mapsTo_tangentCone_pi
+-/
 
+#print mem_tangentCone_of_openSegment_subset /-
 /-- If a subset of a real vector space contains an open segment, then the direction of this
 segment belongs to the tangent cone at its endpoints. -/
 theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSegment ℝ x y ⊆ s) :
@@ -271,13 +284,16 @@ theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSeg
     rw [this]
     apply tendsto_const_nhds
 #align mem_tangent_cone_of_open_segment_subset mem_tangentCone_of_openSegment_subset
+-/
 
+#print mem_tangentCone_of_segment_subset /-
 /-- If a subset of a real vector space contains a segment, then the direction of this
 segment belongs to the tangent cone at its endpoints. -/
 theorem mem_tangentCone_of_segment_subset {s : Set G} {x y : G} (h : segment ℝ x y ⊆ s) :
     y - x ∈ tangentConeAt ℝ s x :=
   mem_tangentCone_of_openSegment_subset ((openSegment_subset_segment ℝ x y).trans h)
 #align mem_tangent_cone_of_segment_subset mem_tangentCone_of_segment_subset
+-/
 
 end TangentCone
 
@@ -297,16 +313,23 @@ theorem UniqueDiffOn.uniqueDiffWithinAt {s : Set E} {x} (hs : UniqueDiffOn 𝕜
 #align unique_diff_on.unique_diff_within_at UniqueDiffOn.uniqueDiffWithinAt
 -/
 
+#print uniqueDiffWithinAt_univ /-
 theorem uniqueDiffWithinAt_univ : UniqueDiffWithinAt 𝕜 univ x := by
   rw [uniqueDiffWithinAt_iff, tangentCone_univ]; simp
 #align unique_diff_within_at_univ uniqueDiffWithinAt_univ
+-/
 
+#print uniqueDiffOn_univ /-
 theorem uniqueDiffOn_univ : UniqueDiffOn 𝕜 (univ : Set E) := fun x hx => uniqueDiffWithinAt_univ
 #align unique_diff_on_univ uniqueDiffOn_univ
+-/
 
+#print uniqueDiffOn_empty /-
 theorem uniqueDiffOn_empty : UniqueDiffOn 𝕜 (∅ : Set E) := fun x hx => hx.elim
 #align unique_diff_on_empty uniqueDiffOn_empty
+-/
 
+#print UniqueDiffWithinAt.mono_nhds /-
 theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 𝓝[s] x ≤ 𝓝[t] x) :
     UniqueDiffWithinAt 𝕜 t x :=
   by
@@ -314,11 +337,14 @@ theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 
   rw [mem_closure_iff_nhdsWithin_neBot] at h ⊢
   exact ⟨h.1.mono <| Submodule.span_mono <| tangentCone_mono_nhds st, h.2.mono st⟩
 #align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhds
+-/
 
+#print UniqueDiffWithinAt.mono /-
 theorem UniqueDiffWithinAt.mono (h : UniqueDiffWithinAt 𝕜 s x) (st : s ⊆ t) :
     UniqueDiffWithinAt 𝕜 t x :=
   h.mono_nhds <| nhdsWithin_mono _ st
 #align unique_diff_within_at.mono UniqueDiffWithinAt.mono
+-/
 
 #print uniqueDiffWithinAt_congr /-
 theorem uniqueDiffWithinAt_congr (st : 𝓝[s] x = 𝓝[t] x) :
@@ -327,25 +353,33 @@ theorem uniqueDiffWithinAt_congr (st : 𝓝[s] x = 𝓝[t] x) :
 #align unique_diff_within_at_congr uniqueDiffWithinAt_congr
 -/
 
+#print uniqueDiffWithinAt_inter /-
 theorem uniqueDiffWithinAt_inter (ht : t ∈ 𝓝 x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x ↔ UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_congr <| (nhdsWithin_restrict' _ ht).symm
 #align unique_diff_within_at_inter uniqueDiffWithinAt_inter
+-/
 
+#print UniqueDiffWithinAt.inter /-
 theorem UniqueDiffWithinAt.inter (hs : UniqueDiffWithinAt 𝕜 s x) (ht : t ∈ 𝓝 x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x :=
   (uniqueDiffWithinAt_inter ht).2 hs
 #align unique_diff_within_at.inter UniqueDiffWithinAt.inter
+-/
 
+#print uniqueDiffWithinAt_inter' /-
 theorem uniqueDiffWithinAt_inter' (ht : t ∈ 𝓝[s] x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x ↔ UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_congr <| (nhdsWithin_restrict'' _ ht).symm
 #align unique_diff_within_at_inter' uniqueDiffWithinAt_inter'
+-/
 
+#print UniqueDiffWithinAt.inter' /-
 theorem UniqueDiffWithinAt.inter' (hs : UniqueDiffWithinAt 𝕜 s x) (ht : t ∈ 𝓝[s] x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x :=
   (uniqueDiffWithinAt_inter' ht).2 hs
 #align unique_diff_within_at.inter' UniqueDiffWithinAt.inter'
+-/
 
 #print uniqueDiffWithinAt_of_mem_nhds /-
 theorem uniqueDiffWithinAt_of_mem_nhds (h : s ∈ 𝓝 x) : UniqueDiffWithinAt 𝕜 s x := by
@@ -359,9 +393,11 @@ theorem IsOpen.uniqueDiffWithinAt (hs : IsOpen s) (xs : x ∈ s) : UniqueDiffWit
 #align is_open.unique_diff_within_at IsOpen.uniqueDiffWithinAt
 -/
 
+#print UniqueDiffOn.inter /-
 theorem UniqueDiffOn.inter (hs : UniqueDiffOn 𝕜 s) (ht : IsOpen t) : UniqueDiffOn 𝕜 (s ∩ t) :=
   fun x hx => (hs x hx.1).inter (IsOpen.mem_nhds ht hx.2)
 #align unique_diff_on.inter UniqueDiffOn.inter
+-/
 
 #print IsOpen.uniqueDiffOn /-
 theorem IsOpen.uniqueDiffOn (hs : IsOpen s) : UniqueDiffOn 𝕜 s := fun x hx =>
@@ -371,6 +407,7 @@ theorem IsOpen.uniqueDiffOn (hs : IsOpen s) : UniqueDiffOn 𝕜 s := fun x hx =>
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UniqueDiffWithinAt.prod /-
 /-- The product of two sets of unique differentiability at points `x` and `y` has unique
 differentiability at `(x, y)`. -/
 theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 𝕜 s x)
@@ -385,7 +422,9 @@ theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 
   rw [LinearMap.span_inl_union_inr, SetLike.le_def] at this 
   exact (hs.1.Prod ht.1).mono this
 #align unique_diff_within_at.prod UniqueDiffWithinAt.prod
+-/
 
+#print UniqueDiffWithinAt.univ_pi /-
 theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
@@ -397,7 +436,9 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     maps_to']
   exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
+-/
 
+#print UniqueDiffWithinAt.pi /-
 theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
@@ -407,13 +448,17 @@ theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
   refine' UniqueDiffWithinAt.univ_pi _ _ _ _ fun i => _
   by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
 #align unique_diff_within_at.pi UniqueDiffWithinAt.pi
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UniqueDiffOn.prod /-
 /-- The product of two sets of unique differentiability is a set of unique differentiability. -/
 theorem UniqueDiffOn.prod {t : Set F} (hs : UniqueDiffOn 𝕜 s) (ht : UniqueDiffOn 𝕜 t) :
     UniqueDiffOn 𝕜 (s ×ˢ t) := fun ⟨x, y⟩ h => UniqueDiffWithinAt.prod (hs x h.1) (ht y h.2)
 #align unique_diff_on.prod UniqueDiffOn.prod
+-/
 
+#print UniqueDiffOn.pi /-
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
 theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, NormedAddCommGroup (E i)]
@@ -421,7 +466,9 @@ theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, No
     (h : ∀ i ∈ I, UniqueDiffOn 𝕜 (s i)) : UniqueDiffOn 𝕜 (Set.pi I s) := fun x hx =>
   UniqueDiffWithinAt.pi _ _ _ _ _ fun i hi => h i hi (x i) (hx i hi)
 #align unique_diff_on.pi UniqueDiffOn.pi
+-/
 
+#print UniqueDiffOn.univ_pi /-
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
 theorem UniqueDiffOn.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
@@ -429,6 +476,7 @@ theorem UniqueDiffOn.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     (h : ∀ i, UniqueDiffOn 𝕜 (s i)) : UniqueDiffOn 𝕜 (Set.pi univ s) :=
   UniqueDiffOn.pi _ _ _ _ fun i _ => h i
 #align unique_diff_on.univ_pi UniqueDiffOn.univ_pi
+-/
 
 #print uniqueDiffWithinAt_convex /-
 /-- In a real vector space, a convex set with nonempty interior is a set of unique
@@ -483,9 +531,11 @@ theorem uniqueDiffOn_Iio (a : ℝ) : UniqueDiffOn ℝ (Iio a) :=
 #align unique_diff_on_Iio uniqueDiffOn_Iio
 -/
 
+#print uniqueDiffOn_Icc /-
 theorem uniqueDiffOn_Icc {a b : ℝ} (hab : a < b) : UniqueDiffOn ℝ (Icc a b) :=
   uniqueDiffOn_convex (convex_Icc a b) <| by simp only [interior_Icc, nonempty_Ioo, hab]
 #align unique_diff_on_Icc uniqueDiffOn_Icc
+-/
 
 #print uniqueDiffOn_Ico /-
 theorem uniqueDiffOn_Ico (a b : ℝ) : UniqueDiffOn ℝ (Ico a b) :=
@@ -509,10 +559,12 @@ theorem uniqueDiffOn_Ioo (a b : ℝ) : UniqueDiffOn ℝ (Ioo a b) :=
 #align unique_diff_on_Ioo uniqueDiffOn_Ioo
 -/
 
+#print uniqueDiffOn_Icc_zero_one /-
 /-- The real interval `[0, 1]` is a set of unique differentiability. -/
 theorem uniqueDiffOn_Icc_zero_one : UniqueDiffOn ℝ (Icc (0 : ℝ) 1) :=
   uniqueDiffOn_Icc zero_lt_one
 #align unique_diff_on_Icc_zero_one uniqueDiffOn_Icc_zero_one
+-/
 
 #print uniqueDiffWithinAt_Ioo /-
 theorem uniqueDiffWithinAt_Ioo {a b t : ℝ} (ht : t ∈ Set.Ioo a b) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -214,8 +214,8 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] {s : ∀ i, Set (E i)} {x : ∀ i, E i}

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

@@ -52,10 +52,10 @@ variable {E : Type _} [AddCommMonoid E] [Module 𝕜 E] [TopologicalSpace E]
 #print tangentConeAt /-
 /-- The set of all tangent directions to the set `s` at the point `x`. -/
 def tangentConeAt (s : Set E) (x : E) : Set E :=
-  { y : E |
+  {y : E |
     ∃ (c : ℕ → 𝕜) (d : ℕ → E),
       (∀ᶠ n in atTop, x + d n ∈ s) ∧
-        Tendsto (fun n => ‖c n‖) atTop atTop ∧ Tendsto (fun n => c n • d n) atTop (𝓝 y) }
+        Tendsto (fun n => ‖c n‖) atTop atTop ∧ Tendsto (fun n => c n • d n) atTop (𝓝 y)}
 #align tangent_cone_at tangentConeAt
 -/
 
@@ -183,7 +183,7 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
   choose d' hd' using this
   refine' ⟨c, fun n => (d n, d' n), _, hc, _⟩
   show ∀ᶠ n in at_top, (x, y) + (d n, d' n) ∈ s ×ˢ t
-  · filter_upwards [hd]with n hn
+  · filter_upwards [hd] with n hn
     simp [hn, (hd' n).1]
   · apply tendsto.prod_mk_nhds hy _
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
@@ -207,7 +207,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
   choose d' hd' using this
   refine' ⟨c, fun n => (d' n, d n), _, hc, _⟩
   show ∀ᶠ n in at_top, (x, y) + (d' n, d n) ∈ s ×ˢ t
-  · filter_upwards [hd]with n hn
+  · filter_upwards [hd] with n hn
     simp [hn, (hd' n).1]
   · apply tendsto.prod_mk_nhds _ hy
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
@@ -390,12 +390,12 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
   classical
-    simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h ⊢
-    refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
-    norm_cast
-    simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←
-      maps_to']
-    exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
+  simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h ⊢
+  refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
+  norm_cast
+  simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←
+    maps_to']
+  exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
 
 theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
@@ -403,9 +403,9 @@ theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
     UniqueDiffWithinAt 𝕜 (Set.pi I s) x := by
   classical
-    rw [← Set.univ_pi_piecewise_univ]
-    refine' UniqueDiffWithinAt.univ_pi _ _ _ _ fun i => _
-    by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
+  rw [← Set.univ_pi_piecewise_univ]
+  refine' UniqueDiffWithinAt.univ_pi _ _ _ _ fun i => _
+  by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
 #align unique_diff_within_at.pi UniqueDiffWithinAt.pi
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

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

@@ -53,7 +53,7 @@ variable {E : Type _} [AddCommMonoid E] [Module 𝕜 E] [TopologicalSpace E]
 /-- The set of all tangent directions to the set `s` at the point `x`. -/
 def tangentConeAt (s : Set E) (x : E) : Set E :=
   { y : E |
-    ∃ (c : ℕ → 𝕜)(d : ℕ → E),
+    ∃ (c : ℕ → 𝕜) (d : ℕ → E),
       (∀ᶠ n in atTop, x + d n ∈ s) ∧
         Tendsto (fun n => ‖c n‖) atTop atTop ∧ Tendsto (fun n => c n • d n) atTop (𝓝 y) }
 #align tangent_cone_at tangentConeAt
@@ -133,7 +133,7 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   have A : tendsto (fun n => ‖c n‖⁻¹) l (𝓝 0) := tendsto_inv_at_top_zero.comp hc
   have B : tendsto (fun n => ‖c n • d n‖) l (𝓝 ‖y‖) := (continuous_norm.tendsto _).comp hd
   have C : tendsto (fun n => ‖c n‖⁻¹ * ‖c n • d n‖) l (𝓝 (0 * ‖y‖)) := A.mul B
-  rw [MulZeroClass.zero_mul] at C
+  rw [MulZeroClass.zero_mul] at C 
   have : ∀ᶠ n in l, ‖c n‖⁻¹ * ‖c n • d n‖ = ‖d n‖ :=
     by
     apply (eventually_ne_of_tendsto_norm_atTop hc 0).mono fun n hn => _
@@ -311,7 +311,7 @@ theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 
     UniqueDiffWithinAt 𝕜 t x :=
   by
   simp only [uniqueDiffWithinAt_iff] at *
-  rw [mem_closure_iff_nhdsWithin_neBot] at h⊢
+  rw [mem_closure_iff_nhdsWithin_neBot] at h ⊢
   exact ⟨h.1.mono <| Submodule.span_mono <| tangentCone_mono_nhds st, h.2.mono st⟩
 #align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhds
 
@@ -376,13 +376,13 @@ differentiability at `(x, y)`. -/
 theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 𝕜 s x)
     (ht : UniqueDiffWithinAt 𝕜 t y) : UniqueDiffWithinAt 𝕜 (s ×ˢ t) (x, y) :=
   by
-  rw [uniqueDiffWithinAt_iff] at hs ht⊢
+  rw [uniqueDiffWithinAt_iff] at hs ht ⊢
   rw [closure_prod_eq]
   refine' ⟨_, hs.2, ht.2⟩
   have : _ ≤ Submodule.span 𝕜 (tangentConeAt 𝕜 (s ×ˢ t) (x, y)) :=
     Submodule.span_mono
       (union_subset (subset_tangentCone_prod_left ht.2) (subset_tangentCone_prod_right hs.2))
-  rw [LinearMap.span_inl_union_inr, SetLike.le_def] at this
+  rw [LinearMap.span_inl_union_inr, SetLike.le_def] at this 
   exact (hs.1.Prod ht.1).mono this
 #align unique_diff_within_at.prod UniqueDiffWithinAt.prod
 
@@ -390,7 +390,7 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
   classical
-    simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h⊢
+    simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h ⊢
     refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
     norm_cast
     simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←

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

@@ -43,7 +43,7 @@ variable (𝕜 : Type _) [NontriviallyNormedField 𝕜]
 
 open Filter Set
 
-open Topology
+open scoped Topology
 
 section TangentCone
 

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

@@ -124,9 +124,6 @@ theorem tangentCone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeA
 #align tangent_cone_mono tangentCone_mono
 -/
 
-/- warning: tangent_cone_at.lim_zero -> tangentConeAt.lim_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tangent_cone_at.lim_zero tangentConeAt.lim_zeroₓ'. -/
 /-- Auxiliary lemma ensuring that, under the assumptions defining the tangent cone,
 the sequence `d` tends to 0 at infinity. -/
 theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {d : α → E}
@@ -147,12 +144,6 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   exact D
 #align tangent_cone_at.lim_zero tangentConeAt.lim_zero
 
-/- warning: tangent_cone_mono_nhds -> tangentCone_mono_nhds is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toHasLe.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.instPartialOrderFilter.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
-Case conversion may be inaccurate. Consider using '#align tangent_cone_mono_nhds tangentCone_mono_nhdsₓ'. -/
 theorem tangentCone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x :=
   by
   rintro y ⟨c, d, ds, ctop, clim⟩
@@ -170,20 +161,11 @@ theorem tangentCone_congr (h : 𝓝[s] x = 𝓝[t] x) : tangentConeAt 𝕜 s x =
 #align tangent_cone_congr tangentCone_congr
 -/
 
-/- warning: tangent_cone_inter_nhds -> tangentCone_inter_nhds is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Eq.{succ u2} (Set.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
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-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Eq.{succ u2} (Set.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.instInterSet.{u2} E) s t) x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
-Case conversion may be inaccurate. Consider using '#align tangent_cone_inter_nhds tangentCone_inter_nhdsₓ'. -/
 /-- Intersecting with a neighborhood of the point does not change the tangent cone. -/
 theorem tangentCone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t) x = tangentConeAt 𝕜 s x :=
   tangentCone_congr (nhdsWithin_restrict' _ ht).symm
 #align tangent_cone_inter_nhds tangentCone_inter_nhds
 
-/- warning: subset_tangent_cone_prod_left -> subset_tangentCone_prod_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_left subset_tangentCone_prod_leftₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The tangent cone of a product contains the tangent cone of its left factor. -/
@@ -208,9 +190,6 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_left subset_tangentCone_prod_left
 
-/- warning: subset_tangent_cone_prod_right -> subset_tangentCone_prod_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_right subset_tangentCone_prod_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The tangent cone of a product contains the tangent cone of its right factor. -/
@@ -235,9 +214,6 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 
-/- warning: maps_to_tangent_cone_pi -> mapsTo_tangentCone_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align maps_to_tangent_cone_pi mapsTo_tangentCone_piₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
@@ -267,12 +243,6 @@ theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
       exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align maps_to_tangent_cone_pi mapsTo_tangentCone_pi
 
-/- warning: mem_tangent_cone_of_open_segment_subset -> mem_tangentCone_of_openSegment_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mem_tangent_cone_of_open_segment_subset mem_tangentCone_of_openSegment_subsetₓ'. -/
 /-- If a subset of a real vector space contains an open segment, then the direction of this
 segment belongs to the tangent cone at its endpoints. -/
 theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSegment ℝ x y ⊆ s) :
@@ -302,12 +272,6 @@ theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSeg
     apply tendsto_const_nhds
 #align mem_tangent_cone_of_open_segment_subset mem_tangentCone_of_openSegment_subset
 
-/- warning: mem_tangent_cone_of_segment_subset -> mem_tangentCone_of_segment_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mem_tangent_cone_of_segment_subset mem_tangentCone_of_segment_subsetₓ'. -/
 /-- If a subset of a real vector space contains a segment, then the direction of this
 segment belongs to the tangent cone at its endpoints. -/
 theorem mem_tangentCone_of_segment_subset {s : Set G} {x y : G} (h : segment ℝ x y ⊆ s) :
@@ -333,40 +297,16 @@ theorem UniqueDiffOn.uniqueDiffWithinAt {s : Set E} {x} (hs : UniqueDiffOn 𝕜
 #align unique_diff_on.unique_diff_within_at UniqueDiffOn.uniqueDiffWithinAt
 -/
 
-/- warning: unique_diff_within_at_univ -> uniqueDiffWithinAt_univ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E}, UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Set.univ.{u2} E) x
-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E}, UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Set.univ.{u1} E) x
-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_univ uniqueDiffWithinAt_univₓ'. -/
 theorem uniqueDiffWithinAt_univ : UniqueDiffWithinAt 𝕜 univ x := by
   rw [uniqueDiffWithinAt_iff, tangentCone_univ]; simp
 #align unique_diff_within_at_univ uniqueDiffWithinAt_univ
 
-/- warning: unique_diff_on_univ -> uniqueDiffOn_univ is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align unique_diff_on_univ uniqueDiffOn_univₓ'. -/
 theorem uniqueDiffOn_univ : UniqueDiffOn 𝕜 (univ : Set E) := fun x hx => uniqueDiffWithinAt_univ
 #align unique_diff_on_univ uniqueDiffOn_univ
 
-/- warning: unique_diff_on_empty -> uniqueDiffOn_empty is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align unique_diff_on_empty uniqueDiffOn_emptyₓ'. -/
 theorem uniqueDiffOn_empty : UniqueDiffOn 𝕜 (∅ : Set E) := fun x hx => hx.elim
 #align unique_diff_on_empty uniqueDiffOn_empty
 
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-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (LE.le.{u1} (Filter.{u1} E) (Preorder.toLE.{u1} (Filter.{u1} E) (PartialOrder.toPreorder.{u1} (Filter.{u1} E) (Filter.instPartialOrderFilter.{u1} E))) (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x s) (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x t)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t x)
-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhdsₓ'. -/
 theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 𝓝[s] x ≤ 𝓝[t] x) :
     UniqueDiffWithinAt 𝕜 t x :=
   by
@@ -375,12 +315,6 @@ theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 
   exact ⟨h.1.mono <| Submodule.span_mono <| tangentCone_mono_nhds st, h.2.mono st⟩
 #align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhds
 
-/- warning: unique_diff_within_at.mono -> UniqueDiffWithinAt.mono is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s t) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s t) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t x)
-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.mono UniqueDiffWithinAt.monoₓ'. -/
 theorem UniqueDiffWithinAt.mono (h : UniqueDiffWithinAt 𝕜 s x) (st : s ⊆ t) :
     UniqueDiffWithinAt 𝕜 t x :=
   h.mono_nhds <| nhdsWithin_mono _ st
@@ -393,45 +327,21 @@ theorem uniqueDiffWithinAt_congr (st : 𝓝[s] x = 𝓝[t] x) :
 #align unique_diff_within_at_congr uniqueDiffWithinAt_congr
 -/
 
-/- warning: unique_diff_within_at_inter -> uniqueDiffWithinAt_inter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
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-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_inter uniqueDiffWithinAt_interₓ'. -/
 theorem uniqueDiffWithinAt_inter (ht : t ∈ 𝓝 x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x ↔ UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_congr <| (nhdsWithin_restrict' _ ht).symm
 #align unique_diff_within_at_inter uniqueDiffWithinAt_inter
 
-/- warning: unique_diff_within_at.inter -> UniqueDiffWithinAt.inter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) t (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) x)
-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.inter UniqueDiffWithinAt.interₓ'. -/
 theorem UniqueDiffWithinAt.inter (hs : UniqueDiffWithinAt 𝕜 s x) (ht : t ∈ 𝓝 x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x :=
   (uniqueDiffWithinAt_inter ht).2 hs
 #align unique_diff_within_at.inter UniqueDiffWithinAt.inter
 
-/- warning: unique_diff_within_at_inter' -> uniqueDiffWithinAt_inter' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) t (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.instInterSet.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_inter' uniqueDiffWithinAt_inter'ₓ'. -/
 theorem uniqueDiffWithinAt_inter' (ht : t ∈ 𝓝[s] x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x ↔ UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_congr <| (nhdsWithin_restrict'' _ ht).symm
 #align unique_diff_within_at_inter' uniqueDiffWithinAt_inter'
 
-/- warning: unique_diff_within_at.inter' -> UniqueDiffWithinAt.inter' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) t (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x s)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) x)
-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.inter' UniqueDiffWithinAt.inter'ₓ'. -/
 theorem UniqueDiffWithinAt.inter' (hs : UniqueDiffWithinAt 𝕜 s x) (ht : t ∈ 𝓝[s] x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x :=
   (uniqueDiffWithinAt_inter' ht).2 hs
@@ -449,12 +359,6 @@ theorem IsOpen.uniqueDiffWithinAt (hs : IsOpen s) (xs : x ∈ s) : UniqueDiffWit
 #align is_open.unique_diff_within_at IsOpen.uniqueDiffWithinAt
 -/
 
-/- warning: unique_diff_on.inter -> UniqueDiffOn.inter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s) -> (IsOpen.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t) -> (UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s) -> (IsOpen.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t) -> (UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t))
-Case conversion may be inaccurate. Consider using '#align unique_diff_on.inter UniqueDiffOn.interₓ'. -/
 theorem UniqueDiffOn.inter (hs : UniqueDiffOn 𝕜 s) (ht : IsOpen t) : UniqueDiffOn 𝕜 (s ∩ t) :=
   fun x hx => (hs x hx.1).inter (IsOpen.mem_nhds ht hx.2)
 #align unique_diff_on.inter UniqueDiffOn.inter
@@ -465,12 +369,6 @@ theorem IsOpen.uniqueDiffOn (hs : IsOpen s) : UniqueDiffOn 𝕜 s := fun x hx =>
 #align is_open.unique_diff_on IsOpen.uniqueDiffOn
 -/
 
-/- warning: unique_diff_within_at.prod -> UniqueDiffWithinAt.prod is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (UniqueDiffWithinAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y) -> (UniqueDiffWithinAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y))
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-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.prod UniqueDiffWithinAt.prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two sets of unique differentiability at points `x` and `y` has unique
@@ -488,12 +386,6 @@ theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 
   exact (hs.1.Prod ht.1).mono this
 #align unique_diff_within_at.prod UniqueDiffWithinAt.prod
 
-/- warning: unique_diff_within_at.univ_pi -> UniqueDiffWithinAt.univ_pi is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_piₓ'. -/
 theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
@@ -506,12 +398,6 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
 
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-Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.pi UniqueDiffWithinAt.piₓ'. -/
 theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
@@ -522,24 +408,12 @@ theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
 #align unique_diff_within_at.pi UniqueDiffWithinAt.pi
 
-/- warning: unique_diff_on.prod -> UniqueDiffOn.prod is a dubious translation:
-lean 3 declaration is
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-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {s : Set.{u1} E} {t : Set.{u3} F}, (UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s) -> (UniqueDiffOn.{u2, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t) -> (UniqueDiffOn.{u2, max u3 u1} 𝕜 _inst_1 (Prod.{u1, u3} E F) (Prod.instAddCommMonoidSum.{u1, u3} E F (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u2, u1, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u1, u3} E F (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u1, u3} E F s t))
-Case conversion may be inaccurate. Consider using '#align unique_diff_on.prod UniqueDiffOn.prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two sets of unique differentiability is a set of unique differentiability. -/
 theorem UniqueDiffOn.prod {t : Set F} (hs : UniqueDiffOn 𝕜 s) (ht : UniqueDiffOn 𝕜 t) :
     UniqueDiffOn 𝕜 (s ×ˢ t) := fun ⟨x, y⟩ h => UniqueDiffWithinAt.prod (hs x h.1) (ht y h.2)
 #align unique_diff_on.prod UniqueDiffOn.prod
 
-/- warning: unique_diff_on.pi -> UniqueDiffOn.pi is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align unique_diff_on.pi UniqueDiffOn.piₓ'. -/
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
 theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, NormedAddCommGroup (E i)]
@@ -548,12 +422,6 @@ theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, No
   UniqueDiffWithinAt.pi _ _ _ _ _ fun i hi => h i hi (x i) (hx i hi)
 #align unique_diff_on.pi UniqueDiffOn.pi
 
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-Case conversion may be inaccurate. Consider using '#align unique_diff_on.univ_pi UniqueDiffOn.univ_piₓ'. -/
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
 theorem UniqueDiffOn.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
@@ -615,12 +483,6 @@ theorem uniqueDiffOn_Iio (a : ℝ) : UniqueDiffOn ℝ (Iio a) :=
 #align unique_diff_on_Iio uniqueDiffOn_Iio
 -/
 
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-but is expected to have type
-  forall {a : Real} {b : Real}, (LT.lt.{0} Real Real.instLTReal a b) -> (UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.instAddCommMonoidReal (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.instPreorderReal a b))
-Case conversion may be inaccurate. Consider using '#align unique_diff_on_Icc uniqueDiffOn_Iccₓ'. -/
 theorem uniqueDiffOn_Icc {a b : ℝ} (hab : a < b) : UniqueDiffOn ℝ (Icc a b) :=
   uniqueDiffOn_convex (convex_Icc a b) <| by simp only [interior_Icc, nonempty_Ioo, hab]
 #align unique_diff_on_Icc uniqueDiffOn_Icc
@@ -647,12 +509,6 @@ theorem uniqueDiffOn_Ioo (a b : ℝ) : UniqueDiffOn ℝ (Ioo a b) :=
 #align unique_diff_on_Ioo uniqueDiffOn_Ioo
 -/
 
-/- warning: unique_diff_on_Icc_zero_one -> uniqueDiffOn_Icc_zero_one is a dubious translation:
-lean 3 declaration is
-  UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.addCommMonoid Real.module (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.instAddCommMonoidReal (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align unique_diff_on_Icc_zero_one uniqueDiffOn_Icc_zero_oneₓ'. -/
 /-- The real interval `[0, 1]` is a set of unique differentiability. -/
 theorem uniqueDiffOn_Icc_zero_one : UniqueDiffOn ℝ (Icc (0 : ℝ) 1) :=
   uniqueDiffOn_Icc zero_lt_one

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

@@ -284,18 +284,11 @@ theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSeg
   show x + d n ∈ openSegment ℝ x y
   · rw [openSegment_eq_image]
     refine' ⟨(c n)⁻¹, ⟨_, _⟩, _⟩
-    · rw [inv_pos]
-      apply pow_pos
-      norm_num
-    · apply inv_lt_one
-      apply one_lt_pow _ (Nat.succ_ne_zero _)
-      norm_num
-    · simp only [d, sub_smul, smul_sub, one_smul]
-      abel
+    · rw [inv_pos]; apply pow_pos; norm_num
+    · apply inv_lt_one; apply one_lt_pow _ (Nat.succ_ne_zero _); norm_num
+    · simp only [d, sub_smul, smul_sub, one_smul]; abel
   show Filter.Tendsto (fun n : ℕ => ‖c n‖) Filter.atTop Filter.atTop
-  · have : (fun n : ℕ => ‖c n‖) = c := by
-      ext n
-      exact abs_of_nonneg (pow_nonneg (by norm_num) _)
+  · have : (fun n : ℕ => ‖c n‖) = c := by ext n; exact abs_of_nonneg (pow_nonneg (by norm_num) _)
     rw [this]
     exact (tendsto_pow_atTop_atTop_of_one_lt (by norm_num)).comp (tendsto_add_at_top_nat 1)
   show Filter.Tendsto (fun n : ℕ => c n • d n) Filter.atTop (𝓝 (y - x))
@@ -346,10 +339,8 @@ lean 3 declaration is
 but is expected to have type
   forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E}, UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Set.univ.{u1} E) x
 Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_univ uniqueDiffWithinAt_univₓ'. -/
-theorem uniqueDiffWithinAt_univ : UniqueDiffWithinAt 𝕜 univ x :=
-  by
-  rw [uniqueDiffWithinAt_iff, tangentCone_univ]
-  simp
+theorem uniqueDiffWithinAt_univ : UniqueDiffWithinAt 𝕜 univ x := by
+  rw [uniqueDiffWithinAt_iff, tangentCone_univ]; simp
 #align unique_diff_within_at_univ uniqueDiffWithinAt_univ
 
 /- warning: unique_diff_on_univ -> uniqueDiffOn_univ is a dubious translation:

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

@@ -125,10 +125,7 @@ theorem tangentCone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeA
 -/
 
 /- warning: tangent_cone_at.lim_zero -> tangentConeAt.lim_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {y : E} {α : Type.{u3}} (l : Filter.{u3} α) {c : α -> 𝕜} {d : α -> E}, (Filter.Tendsto.{u3, 0} α Real (fun (n : α) => Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) (c n)) l (Filter.atTop.{0} Real Real.preorder)) -> (Filter.Tendsto.{u3, u2} α E (fun (n : α) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))) (c n) (d n)) l (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) y)) -> (Filter.Tendsto.{u3, u2} α E d l (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2)))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {y : E} {α : Type.{u3}} (l : Filter.{u3} α) {c : α -> 𝕜} {d : α -> E}, (Filter.Tendsto.{u3, 0} α Real (fun (n : α) => Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)) (c n)) l (Filter.atTop.{0} Real Real.instPreorderReal)) -> (Filter.Tendsto.{u3, u1} α E (fun (n : α) => HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3)))))) (c n) (d n)) l (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) y)) -> (Filter.Tendsto.{u3, u1} α E d l (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tangent_cone_at.lim_zero tangentConeAt.lim_zeroₓ'. -/
 /-- Auxiliary lemma ensuring that, under the assumptions defining the tangent cone,
 the sequence `d` tends to 0 at infinity. -/
@@ -185,10 +182,7 @@ theorem tangentCone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t
 #align tangent_cone_inter_nhds tangentCone_inter_nhds
 
 /- warning: subset_tangent_cone_prod_left -> subset_tangentCone_prod_left is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (coeFn.{max (succ 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(PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
-but is expected to have type
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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_left subset_tangentCone_prod_leftₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -215,10 +209,7 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
 #align subset_tangent_cone_prod_left subset_tangentCone_prod_left
 
 /- warning: subset_tangent_cone_prod_right -> subset_tangentCone_prod_right is a dubious translation:
-lean 3 declaration is
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(NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) => F -> (Prod.{u2, u3} E F)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_right subset_tangentCone_prod_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -245,10 +236,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 
 /- warning: maps_to_tangent_cone_pi -> mapsTo_tangentCone_pi is a dubious translation:
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(DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u3, u2} 𝕜 ι (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u3 u2} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align maps_to_tangent_cone_pi mapsTo_tangentCone_piₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -188,7 +188,7 @@ theorem tangentCone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) => E -> (Prod.{u2, u3} E F)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u3, u3} F (Set.{u3} F) (Set.instMembershipSet.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u2, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u3, u3} F (Set.{u3} F) (Set.instMembershipSet.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u2, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_left subset_tangentCone_prod_leftₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -218,7 +218,7 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) => F -> (Prod.{u2, u3} E F)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_right subset_tangentCone_prod_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -248,7 +248,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u2}} [_inst_8 : DecidableEq.{succ u2} ι] {E : ι -> Type.{u3}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u3} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u3} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u2} ι j i) -> (Membership.Mem.{u3, u3} (E j) (Set.{u3} (E j)) (Set.hasMem.{u3} (E j)) (x j) (closure.{u3} (E j) (UniformSpace.toTopologicalSpace.{u3} (E j) (PseudoMetricSpace.toUniformSpace.{u3} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u3, max u2 u3} (E i) (forall (i : ι), E i) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) ((fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i)) ((fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (fun (i : ι) => (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) ((fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i)) ((fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (fun (i : ι) => (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i))) => (E i) -> (forall (i : ι), E i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (E i) (forall (i : ι), E i) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) ((fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i)) ((fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (fun (i : ι) => (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u2, u3} 𝕜 ι (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u3} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u3} (E i) (PseudoMetricSpace.toUniformSpace.{u3} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i)))) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (E i) (_inst_9 i) (_inst_10 i))) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u3} (E a) (PseudoMetricSpace.toUniformSpace.{u3} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E a) (_inst_9 a)))))) (Set.pi.{u2, u3} ι (fun (i : ι) => E i) (Set.univ.{u2} ι) s) x))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u3}} [_inst_8 : DecidableEq.{succ u3} ι] {E : ι -> Type.{u2}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u2} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u3} ι j i) -> (Membership.mem.{u2, u2} (E j) (Set.{u2} (E j)) (Set.instMembershipSet.{u2} (E j)) (x j) (closure.{u2} (E j) (UniformSpace.toTopologicalSpace.{u2} (E j) (PseudoMetricSpace.toUniformSpace.{u2} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u2, max u3 u2} (E i) (forall (i : ι), E i) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)))) (E i) (fun (_x : E i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E i) => forall (i : ι), E i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (E i) (forall (i : ι), E i) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u3, u2} 𝕜 ι (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u3 u2} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u3}} [_inst_8 : DecidableEq.{succ u3} ι] {E : ι -> Type.{u2}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u2} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u3} ι j i) -> (Membership.mem.{u2, u2} (E j) (Set.{u2} (E j)) (Set.instMembershipSet.{u2} (E j)) (x j) (closure.{u2} (E j) (UniformSpace.toTopologicalSpace.{u2} (E j) (PseudoMetricSpace.toUniformSpace.{u2} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u2, max u3 u2} (E i) (forall (i : ι), E i) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)))) (E i) (fun (_x : E i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E i) => forall (i : ι), E i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (E i) (forall (i : ι), E i) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u3, u2} 𝕜 ι (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u3 u2} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x))
 Case conversion may be inaccurate. Consider using '#align maps_to_tangent_cone_pi mapsTo_tangentCone_piₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -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.calculus.tangent_cone
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! 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.SpecificLimits.Basic
 /-!
 # Tangent cone
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we define two predicates `unique_diff_within_at 𝕜 s x` and `unique_diff_on 𝕜 s`
 ensuring that, if a function has two derivatives, then they have to coincide. As a direct
 definition of this fact (quantifying on all target types and all functions) would depend on
@@ -185,7 +188,7 @@ theorem tangentCone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) => E -> (Prod.{u2, u3} E F)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u3, u3} F (Set.{u3} F) (Set.instMembershipSet.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u2, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u3, u3} F (Set.{u3} F) (Set.instMembershipSet.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u2, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_left subset_tangentCone_prod_leftₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -215,7 +218,7 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) => F -> (Prod.{u2, u3} E F)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
 Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_right subset_tangentCone_prod_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -245,7 +248,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u2}} [_inst_8 : DecidableEq.{succ u2} ι] {E : ι -> Type.{u3}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u3} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u3} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u2} ι j i) -> (Membership.Mem.{u3, u3} (E j) (Set.{u3} (E j)) (Set.hasMem.{u3} (E j)) (x j) (closure.{u3} (E j) (UniformSpace.toTopologicalSpace.{u3} (E j) (PseudoMetricSpace.toUniformSpace.{u3} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u3, max u2 u3} (E i) (forall (i : ι), E i) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) ((fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i)) ((fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (fun (i : ι) => (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) ((fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i)) ((fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (fun (i : ι) => (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i))) => (E i) -> (forall (i : ι), E i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (E i) (forall (i : ι), E i) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) ((fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i)) ((fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) i) (fun (i : ι) => (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) i)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u2, u3} 𝕜 ι (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun {i : ι} => NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u3} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u3} (E i) (PseudoMetricSpace.toUniformSpace.{u3} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun {i : ι} => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i)))) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (E i) (_inst_9 i) (_inst_10 i))) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u3} (E a) (PseudoMetricSpace.toUniformSpace.{u3} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E a) (_inst_9 a)))))) (Set.pi.{u2, u3} ι (fun (i : ι) => E i) (Set.univ.{u2} ι) s) x))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u3}} [_inst_8 : DecidableEq.{succ u3} ι] {E : ι -> Type.{u2}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u2} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u3} ι j i) -> (Membership.mem.{u2, u2} (E j) (Set.{u2} (E j)) (Set.instMembershipSet.{u2} (E j)) (x j) (closure.{u2} (E j) (UniformSpace.toTopologicalSpace.{u2} (E j) (PseudoMetricSpace.toUniformSpace.{u2} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u2, max u3 u2} (E i) (forall (i : ι), E i) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)))) (E i) (fun (_x : E i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E i) => forall (i : ι), E i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (E i) (forall (i : ι), E i) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u3, u2} 𝕜 ι (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u3 u2} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u3}} [_inst_8 : DecidableEq.{succ u3} ι] {E : ι -> Type.{u2}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u2} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u3} ι j i) -> (Membership.mem.{u2, u2} (E j) (Set.{u2} (E j)) (Set.instMembershipSet.{u2} (E j)) (x j) (closure.{u2} (E j) (UniformSpace.toTopologicalSpace.{u2} (E j) (PseudoMetricSpace.toUniformSpace.{u2} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u2, max u3 u2} (E i) (forall (i : ι), E i) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (E i) (forall (i : ι), E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)))) (E i) (fun (_x : E i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E i) => forall (i : ι), E i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} 𝕜 𝕜 (E i) (forall (i : ι), E i) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u3, u2} 𝕜 ι (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u3 u2} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x))
 Case conversion may be inaccurate. Consider using '#align maps_to_tangent_cone_pi mapsTo_tangentCone_piₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -149,7 +149,7 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
 
 /- warning: tangent_cone_mono_nhds -> tangentCone_mono_nhds is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toHasLe.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.instPartialOrderFilter.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
 Case conversion may be inaccurate. Consider using '#align tangent_cone_mono_nhds tangentCone_mono_nhdsₓ'. -/
@@ -381,7 +381,7 @@ theorem uniqueDiffOn_empty : UniqueDiffOn 𝕜 (∅ : Set E) := fun x hx => hx.e
 
 /- warning: unique_diff_within_at.mono_nhds -> UniqueDiffWithinAt.mono_nhds is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x)
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (LE.le.{u2} (Filter.{u2} E) (Preorder.toHasLe.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x)
 but is expected to have type
   forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (LE.le.{u1} (Filter.{u1} E) (Preorder.toLE.{u1} (Filter.{u1} E) (PartialOrder.toPreorder.{u1} (Filter.{u1} E) (Filter.instPartialOrderFilter.{u1} E))) (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x s) (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x t)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t x)
 Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhdsₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -46,6 +46,7 @@ section TangentCone
 
 variable {E : Type _} [AddCommMonoid E] [Module 𝕜 E] [TopologicalSpace E]
 
+#print tangentConeAt /-
 /-- The set of all tangent directions to the set `s` at the point `x`. -/
 def tangentConeAt (s : Set E) (x : E) : Set E :=
   { y : E |
@@ -53,7 +54,9 @@ def tangentConeAt (s : Set E) (x : E) : Set E :=
       (∀ᶠ n in atTop, x + d n ∈ s) ∧
         Tendsto (fun n => ‖c n‖) atTop atTop ∧ Tendsto (fun n => c n • d n) atTop (𝓝 y) }
 #align tangent_cone_at tangentConeAt
+-/
 
+#print UniqueDiffWithinAt /-
 /-- A property ensuring that the tangent cone to `s` at `x` spans a dense subset of the whole space.
 The main role of this property is to ensure that the differential within `s` at `x` is unique,
 hence this name. The uniqueness it asserts is proved in `unique_diff_within_at.eq` in `fderiv.lean`.
@@ -65,7 +68,9 @@ structure UniqueDiffWithinAt (s : Set E) (x : E) : Prop where
   dense_tangent_cone : Dense (Submodule.span 𝕜 (tangentConeAt 𝕜 s x) : Set E)
   mem_closure : x ∈ closure s
 #align unique_diff_within_at UniqueDiffWithinAt
+-/
 
+#print UniqueDiffOn /-
 /-- A property ensuring that the tangent cone to `s` at any of its points spans a dense subset of
 the whole space.  The main role of this property is to ensure that the differential along `s` is
 unique, hence this name. The uniqueness it asserts is proved in `unique_diff_on.eq` in
@@ -73,6 +78,7 @@ unique, hence this name. The uniqueness it asserts is proved in `unique_diff_on.
 def UniqueDiffOn (s : Set E) : Prop :=
   ∀ x ∈ s, UniqueDiffWithinAt 𝕜 s x
 #align unique_diff_on UniqueDiffOn
+-/
 
 end TangentCone
 
@@ -89,7 +95,8 @@ section TangentCone
 -- This section is devoted to the properties of the tangent cone.
 open NormedField
 
-theorem tangent_cone_univ : tangentConeAt 𝕜 univ x = univ :=
+#print tangentCone_univ /-
+theorem tangentCone_univ : tangentConeAt 𝕜 univ x = univ :=
   by
   refine' univ_subset_iff.1 fun y hy => _
   rcases exists_one_lt_norm 𝕜 with ⟨w, hw⟩
@@ -103,14 +110,23 @@ theorem tangent_cone_univ : tangentConeAt 𝕜 univ x = univ :=
       apply pow_ne_zero
       simpa [norm_eq_zero] using (ne_of_lt (lt_trans zero_lt_one hw)).symm
     rw [smul_smul, this, one_smul]
-#align tangent_cone_univ tangent_cone_univ
+#align tangent_cone_univ tangentCone_univ
+-/
 
-theorem tangent_cone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x :=
+#print tangentCone_mono /-
+theorem tangentCone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x :=
   by
   rintro y ⟨c, d, ds, ctop, clim⟩
   exact ⟨c, d, mem_of_superset ds fun n hn => h hn, Ctop, clim⟩
-#align tangent_cone_mono tangent_cone_mono
+#align tangent_cone_mono tangentCone_mono
+-/
 
+/- warning: tangent_cone_at.lim_zero -> tangentConeAt.lim_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {y : E} {α : Type.{u3}} (l : Filter.{u3} α) {c : α -> 𝕜} {d : α -> E}, (Filter.Tendsto.{u3, 0} α Real (fun (n : α) => Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) (c n)) l (Filter.atTop.{0} Real Real.preorder)) -> (Filter.Tendsto.{u3, u2} α E (fun (n : α) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3))))) (c n) (d n)) l (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) y)) -> (Filter.Tendsto.{u3, u2} α E d l (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2)))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {y : E} {α : Type.{u3}} (l : Filter.{u3} α) {c : α -> 𝕜} {d : α -> E}, (Filter.Tendsto.{u3, 0} α Real (fun (n : α) => Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)) (c n)) l (Filter.atTop.{0} Real Real.instPreorderReal)) -> (Filter.Tendsto.{u3, u1} α E (fun (n : α) => HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3)))))) (c n) (d n)) l (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) y)) -> (Filter.Tendsto.{u3, u1} α E d l (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2))))))))))
+Case conversion may be inaccurate. Consider using '#align tangent_cone_at.lim_zero tangentConeAt.lim_zeroₓ'. -/
 /-- Auxiliary lemma ensuring that, under the assumptions defining the tangent cone,
 the sequence `d` tends to 0 at infinity. -/
 theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {d : α → E}
@@ -131,7 +147,13 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   exact D
 #align tangent_cone_at.lim_zero tangentConeAt.lim_zero
 
-theorem tangent_cone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x :=
+/- warning: tangent_cone_mono_nhds -> tangentCone_mono_nhds is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.instPartialOrderFilter.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x))
+Case conversion may be inaccurate. Consider using '#align tangent_cone_mono_nhds tangentCone_mono_nhdsₓ'. -/
+theorem tangentCone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x :=
   by
   rintro y ⟨c, d, ds, ctop, clim⟩
   refine' ⟨c, d, _, Ctop, clim⟩
@@ -139,22 +161,36 @@ theorem tangent_cone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) : tangentConeAt 
   exact tendsto_principal.1 (tendsto_inf.1 this).2
   refine' (tendsto_inf.2 ⟨_, tendsto_principal.2 ds⟩).mono_right h
   simpa only [add_zero] using tendsto_const_nhds.add (tangentConeAt.lim_zero at_top Ctop clim)
-#align tangent_cone_mono_nhds tangent_cone_mono_nhds
+#align tangent_cone_mono_nhds tangentCone_mono_nhds
 
+#print tangentCone_congr /-
 /-- Tangent cone of `s` at `x` depends only on `𝓝[s] x`. -/
-theorem tangent_cone_congr (h : 𝓝[s] x = 𝓝[t] x) : tangentConeAt 𝕜 s x = tangentConeAt 𝕜 t x :=
-  Subset.antisymm (tangent_cone_mono_nhds <| le_of_eq h) (tangent_cone_mono_nhds <| le_of_eq h.symm)
-#align tangent_cone_congr tangent_cone_congr
+theorem tangentCone_congr (h : 𝓝[s] x = 𝓝[t] x) : tangentConeAt 𝕜 s x = tangentConeAt 𝕜 t x :=
+  Subset.antisymm (tangentCone_mono_nhds <| le_of_eq h) (tangentCone_mono_nhds <| le_of_eq h.symm)
+#align tangent_cone_congr tangentCone_congr
+-/
 
+/- warning: tangent_cone_inter_nhds -> tangentCone_inter_nhds is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Eq.{succ u2} (Set.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Eq.{succ u2} (Set.{u2} E) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.instInterSet.{u2} E) s t) x) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
+Case conversion may be inaccurate. Consider using '#align tangent_cone_inter_nhds tangentCone_inter_nhdsₓ'. -/
 /-- Intersecting with a neighborhood of the point does not change the tangent cone. -/
-theorem tangent_cone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t) x = tangentConeAt 𝕜 s x :=
-  tangent_cone_congr (nhdsWithin_restrict' _ ht).symm
-#align tangent_cone_inter_nhds tangent_cone_inter_nhds
-
+theorem tangentCone_inter_nhds (ht : t ∈ 𝓝 x) : tangentConeAt 𝕜 (s ∩ t) x = tangentConeAt 𝕜 s x :=
+  tangentCone_congr (nhdsWithin_restrict' _ ht).symm
+#align tangent_cone_inter_nhds tangentCone_inter_nhds
+
+/- warning: subset_tangent_cone_prod_left -> subset_tangentCone_prod_left is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (coeFn.{max (succ 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_inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u3, u3} F (Set.{u3} F) (Set.instMembershipSet.{u3} F) y (closure.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 E (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inl.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_left subset_tangentCone_prod_leftₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The tangent cone of a product contains the tangent cone of its left factor. -/
-theorem subset_tangent_cone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t) :
+theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t) :
     LinearMap.inl 𝕜 E F '' tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 (s ×ˢ t) (x, y) :=
   by
   rintro _ ⟨v, ⟨c, d, hd, hc, hy⟩, rfl⟩
@@ -173,12 +209,18 @@ theorem subset_tangent_cone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
   · apply tendsto.prod_mk_nhds hy _
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
-#align subset_tangent_cone_prod_left subset_tangent_cone_prod_left
-
+#align subset_tangent_cone_prod_left subset_tangentCone_prod_left
+
+/- warning: subset_tangent_cone_prod_right -> subset_tangentCone_prod_right is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (coeFn.{max (succ 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(NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) => F -> (Prod.{u2, u3} E F)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (closure.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s)) -> (HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.instHasSubsetSet.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F (Prod.{u2, u3} E F) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => Prod.{u2, u3} E F) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} 𝕜 𝕜 F (Prod.{u2, u3} E F) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.inr.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))) (tangentConeAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y)) (tangentConeAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.instAddCommMonoidSum.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y)))
+Case conversion may be inaccurate. Consider using '#align subset_tangent_cone_prod_right subset_tangentCone_prod_rightₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The tangent cone of a product contains the tangent cone of its right factor. -/
-theorem subset_tangent_cone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s) :
+theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s) :
     LinearMap.inr 𝕜 E F '' tangentConeAt 𝕜 t y ⊆ tangentConeAt 𝕜 (s ×ˢ t) (x, y) :=
   by
   rintro _ ⟨w, ⟨c, d, hd, hc, hy⟩, rfl⟩
@@ -197,12 +239,18 @@ theorem subset_tangent_cone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s
   · apply tendsto.prod_mk_nhds _ hy
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
-#align subset_tangent_cone_prod_right subset_tangent_cone_prod_right
-
+#align subset_tangent_cone_prod_right subset_tangentCone_prod_right
+
+/- warning: maps_to_tangent_cone_pi -> mapsTo_tangentCone_pi is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {ι : Type.{u3}} [_inst_8 : DecidableEq.{succ u3} ι] {E : ι -> Type.{u2}} [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] {s : forall (i : ι), Set.{u2} (E i)} {x : forall (i : ι), E i} {i : ι}, (forall (j : ι), (Ne.{succ u3} ι j i) -> (Membership.mem.{u2, u2} (E j) (Set.{u2} (E j)) (Set.instMembershipSet.{u2} (E j)) (x j) (closure.{u2} (E j) (UniformSpace.toTopologicalSpace.{u2} (E j) (PseudoMetricSpace.toUniformSpace.{u2} (E j) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E j) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E j) (_inst_9 j))))) (s j)))) -> (Set.MapsTo.{u2, max u3 u2} (E i) (forall (i : ι), E i) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} 𝕜 𝕜 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(NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (LinearMap.single.{u1, u3, u2} 𝕜 ι (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) E (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (fun (a : ι) (b : ι) => _inst_8 a b) i)) (tangentConeAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) (tangentConeAt.{u1, max u3 u2} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x))
+Case conversion may be inaccurate. Consider using '#align maps_to_tangent_cone_pi mapsTo_tangentCone_piₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
-theorem mapsTo_tangent_cone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
+theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] {s : ∀ i, Set (E i)} {x : ∀ i, E i}
     {i : ι} (hi : ∀ (j) (_ : j ≠ i), x j ∈ closure (s j)) :
     MapsTo (LinearMap.single i : E i →ₗ[𝕜] ∀ j, E j) (tangentConeAt 𝕜 (s i) (x i))
@@ -226,11 +274,17 @@ theorem mapsTo_tangent_cone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _
     · suffices tendsto (fun n => c n • d' n j) at_top (𝓝 0) by simpa [hj]
       refine' squeeze_zero_norm (fun n => (hcd' n j hj).le) _
       exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
-#align maps_to_tangent_cone_pi mapsTo_tangent_cone_pi
-
+#align maps_to_tangent_cone_pi mapsTo_tangentCone_pi
+
+/- warning: mem_tangent_cone_of_open_segment_subset -> mem_tangentCone_of_openSegment_subset is a dubious translation:
+lean 3 declaration is
+  forall {G : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} G] [_inst_7 : NormedSpace.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)] {s : Set.{u1} G} {x : G} {y : G}, (HasSubset.Subset.{u1} (Set.{u1} G) (Set.hasSubset.{u1} G) (openSegment.{0, u1} Real G Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (SMulZeroClass.toHasSmul.{0, u1} Real G (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddCommMonoid.toAddMonoid.{u1} G (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real G (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddCommMonoid.toAddMonoid.{u1} G (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real G (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddCommMonoid.toAddMonoid.{u1} G (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))))) (Module.toMulActionWithZero.{0, u1} Real G (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6))) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7))))) x y) s) -> (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toHasSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (NormedAddGroup.toAddGroup.{u1} G (NormedAddCommGroup.toNormedAddGroup.{u1} G _inst_6))))) y x) (tangentConeAt.{0, u1} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) G (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7) (UniformSpace.toTopologicalSpace.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))) s x))
+but is expected to have type
+  forall {G : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} G] [_inst_7 : NormedSpace.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)] {s : Set.{u1} G} {x : G} {y : G}, (HasSubset.Subset.{u1} (Set.{u1} G) (Set.instHasSubsetSet.{u1} G) (openSegment.{0, u1} Real G Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (SMulZeroClass.toSMul.{0, u1} Real G (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real G Real.instZeroReal (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real G Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)))))) (Module.toMulActionWithZero.{0, u1} Real G Real.semiring (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7))))) x y) s) -> (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (NormedAddGroup.toAddGroup.{u1} G (NormedAddCommGroup.toNormedAddGroup.{u1} G _inst_6))))) y x) (tangentConeAt.{0, u1} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) G (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7) (UniformSpace.toTopologicalSpace.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))) s x))
+Case conversion may be inaccurate. Consider using '#align mem_tangent_cone_of_open_segment_subset mem_tangentCone_of_openSegment_subsetₓ'. -/
 /-- If a subset of a real vector space contains an open segment, then the direction of this
 segment belongs to the tangent cone at its endpoints. -/
-theorem mem_tangent_cone_of_openSegment_subset {s : Set G} {x y : G} (h : openSegment ℝ x y ⊆ s) :
+theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSegment ℝ x y ⊆ s) :
     y - x ∈ tangentConeAt ℝ s x :=
   by
   let c := fun n : ℕ => (2 : ℝ) ^ (n + 1)
@@ -262,14 +316,20 @@ theorem mem_tangent_cone_of_openSegment_subset {s : Set G} {x y : G} (h : openSe
       exact pow_ne_zero _ (by norm_num)
     rw [this]
     apply tendsto_const_nhds
-#align mem_tangent_cone_of_open_segment_subset mem_tangent_cone_of_openSegment_subset
-
+#align mem_tangent_cone_of_open_segment_subset mem_tangentCone_of_openSegment_subset
+
+/- warning: mem_tangent_cone_of_segment_subset -> mem_tangentCone_of_segment_subset is a dubious translation:
+lean 3 declaration is
+  forall {G : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} G] [_inst_7 : NormedSpace.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)] {s : Set.{u1} G} {x : G} {y : G}, (HasSubset.Subset.{u1} (Set.{u1} G) (Set.hasSubset.{u1} G) (segment.{0, u1} Real G Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (SMulZeroClass.toHasSmul.{0, u1} Real G (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddCommMonoid.toAddMonoid.{u1} G (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real G (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddCommMonoid.toAddMonoid.{u1} G (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real G (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddCommMonoid.toAddMonoid.{u1} G (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))))) (Module.toMulActionWithZero.{0, u1} Real G (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} G (SeminormedAddCommGroup.toAddCommGroup.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6))) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7))))) x y) s) -> (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toHasSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (NormedAddGroup.toAddGroup.{u1} G (NormedAddCommGroup.toNormedAddGroup.{u1} G _inst_6))))) y x) (tangentConeAt.{0, u1} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) G (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7) (UniformSpace.toTopologicalSpace.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))) s x))
+but is expected to have type
+  forall {G : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} G] [_inst_7 : NormedSpace.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)] {s : Set.{u1} G} {x : G} {y : G}, (HasSubset.Subset.{u1} (Set.{u1} G) (Set.instHasSubsetSet.{u1} G) (segment.{0, u1} Real G Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (SMulZeroClass.toSMul.{0, u1} Real G (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real G Real.instZeroReal (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real G Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)))))) (Module.toMulActionWithZero.{0, u1} Real G Real.semiring (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7))))) x y) s) -> (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (NormedAddGroup.toAddGroup.{u1} G (NormedAddCommGroup.toNormedAddGroup.{u1} G _inst_6))))) y x) (tangentConeAt.{0, u1} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) G (AddCommGroup.toAddCommMonoid.{u1} G (NormedAddCommGroup.toAddCommGroup.{u1} G _inst_6)) (NormedSpace.toModule.{0, u1} Real G Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6) _inst_7) (UniformSpace.toTopologicalSpace.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} G _inst_6)))) s x))
+Case conversion may be inaccurate. Consider using '#align mem_tangent_cone_of_segment_subset mem_tangentCone_of_segment_subsetₓ'. -/
 /-- If a subset of a real vector space contains a segment, then the direction of this
 segment belongs to the tangent cone at its endpoints. -/
-theorem mem_tangent_cone_of_segment_subset {s : Set G} {x y : G} (h : segment ℝ x y ⊆ s) :
+theorem mem_tangentCone_of_segment_subset {s : Set G} {x y : G} (h : segment ℝ x y ⊆ s) :
     y - x ∈ tangentConeAt ℝ s x :=
-  mem_tangent_cone_of_openSegment_subset ((openSegment_subset_segment ℝ x y).trans h)
-#align mem_tangent_cone_of_segment_subset mem_tangent_cone_of_segment_subset
+  mem_tangentCone_of_openSegment_subset ((openSegment_subset_segment ℝ x y).trans h)
+#align mem_tangent_cone_of_segment_subset mem_tangentCone_of_segment_subset
 
 end TangentCone
 
@@ -282,77 +342,153 @@ This section is devoted to properties of the predicates
 `unique_diff_within_at` and `unique_diff_on`. -/
 
 
+#print UniqueDiffOn.uniqueDiffWithinAt /-
 theorem UniqueDiffOn.uniqueDiffWithinAt {s : Set E} {x} (hs : UniqueDiffOn 𝕜 s) (h : x ∈ s) :
     UniqueDiffWithinAt 𝕜 s x :=
   hs x h
 #align unique_diff_on.unique_diff_within_at UniqueDiffOn.uniqueDiffWithinAt
+-/
 
+/- warning: unique_diff_within_at_univ -> uniqueDiffWithinAt_univ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E}, UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Set.univ.{u2} E) x
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E}, UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Set.univ.{u1} E) x
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_univ uniqueDiffWithinAt_univₓ'. -/
 theorem uniqueDiffWithinAt_univ : UniqueDiffWithinAt 𝕜 univ x :=
   by
-  rw [uniqueDiffWithinAt_iff, tangent_cone_univ]
+  rw [uniqueDiffWithinAt_iff, tangentCone_univ]
   simp
 #align unique_diff_within_at_univ uniqueDiffWithinAt_univ
 
+/- warning: unique_diff_on_univ -> uniqueDiffOn_univ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Set.univ.{u2} E)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)], UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Set.univ.{u1} E)
+Case conversion may be inaccurate. Consider using '#align unique_diff_on_univ uniqueDiffOn_univₓ'. -/
 theorem uniqueDiffOn_univ : UniqueDiffOn 𝕜 (univ : Set E) := fun x hx => uniqueDiffWithinAt_univ
 #align unique_diff_on_univ uniqueDiffOn_univ
 
+/- warning: unique_diff_on_empty -> uniqueDiffOn_empty is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (EmptyCollection.emptyCollection.{u2} (Set.{u2} E) (Set.hasEmptyc.{u2} E))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)], UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on_empty uniqueDiffOn_emptyₓ'. -/
 theorem uniqueDiffOn_empty : UniqueDiffOn 𝕜 (∅ : Set E) := fun x hx => hx.elim
 #align unique_diff_on_empty uniqueDiffOn_empty
 
+/- warning: unique_diff_within_at.mono_nhds -> UniqueDiffWithinAt.mono_nhds is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (LE.le.{u2} (Filter.{u2} E) (Preorder.toLE.{u2} (Filter.{u2} E) (PartialOrder.toPreorder.{u2} (Filter.{u2} E) (Filter.partialOrder.{u2} E))) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s) (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x t)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (LE.le.{u1} (Filter.{u1} E) (Preorder.toLE.{u1} (Filter.{u1} E) (PartialOrder.toPreorder.{u1} (Filter.{u1} E) (Filter.instPartialOrderFilter.{u1} E))) (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x s) (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x t)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t x)
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhdsₓ'. -/
 theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 𝓝[s] x ≤ 𝓝[t] x) :
     UniqueDiffWithinAt 𝕜 t x :=
   by
   simp only [uniqueDiffWithinAt_iff] at *
   rw [mem_closure_iff_nhdsWithin_neBot] at h⊢
-  exact ⟨h.1.mono <| Submodule.span_mono <| tangent_cone_mono_nhds st, h.2.mono st⟩
+  exact ⟨h.1.mono <| Submodule.span_mono <| tangentCone_mono_nhds st, h.2.mono st⟩
 #align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhds
 
+/- warning: unique_diff_within_at.mono -> UniqueDiffWithinAt.mono is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s t) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t x)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s t) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t x)
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.mono UniqueDiffWithinAt.monoₓ'. -/
 theorem UniqueDiffWithinAt.mono (h : UniqueDiffWithinAt 𝕜 s x) (st : s ⊆ t) :
     UniqueDiffWithinAt 𝕜 t x :=
   h.mono_nhds <| nhdsWithin_mono _ st
 #align unique_diff_within_at.mono UniqueDiffWithinAt.mono
 
+#print uniqueDiffWithinAt_congr /-
 theorem uniqueDiffWithinAt_congr (st : 𝓝[s] x = 𝓝[t] x) :
     UniqueDiffWithinAt 𝕜 s x ↔ UniqueDiffWithinAt 𝕜 t x :=
   ⟨fun h => h.mono_nhds <| le_of_eq st, fun h => h.mono_nhds <| le_of_eq st.symm⟩
 #align unique_diff_within_at_congr uniqueDiffWithinAt_congr
+-/
 
+/- warning: unique_diff_within_at_inter -> uniqueDiffWithinAt_inter is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.instInterSet.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_inter uniqueDiffWithinAt_interₓ'. -/
 theorem uniqueDiffWithinAt_inter (ht : t ∈ 𝓝 x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x ↔ UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_congr <| (nhdsWithin_restrict' _ ht).symm
 #align unique_diff_within_at_inter uniqueDiffWithinAt_inter
 
+/- warning: unique_diff_within_at.inter -> UniqueDiffWithinAt.inter is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) t (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) x)
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.inter UniqueDiffWithinAt.interₓ'. -/
 theorem UniqueDiffWithinAt.inter (hs : UniqueDiffWithinAt 𝕜 s x) (ht : t ∈ 𝓝 x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x :=
   (uniqueDiffWithinAt_inter ht).2 hs
 #align unique_diff_within_at.inter UniqueDiffWithinAt.inter
 
+/- warning: unique_diff_within_at_inter' -> uniqueDiffWithinAt_inter' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) t (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s)) -> (Iff (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.instInterSet.{u2} E) s t) x) (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x))
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at_inter' uniqueDiffWithinAt_inter'ₓ'. -/
 theorem uniqueDiffWithinAt_inter' (ht : t ∈ 𝓝[s] x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x ↔ UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_congr <| (nhdsWithin_restrict'' _ ht).symm
 #align unique_diff_within_at_inter' uniqueDiffWithinAt_inter'
 
+/- warning: unique_diff_within_at.inter' -> UniqueDiffWithinAt.inter' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {x : E} {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) t (nhdsWithin.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) x s)) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) x)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {x : E} {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) t (nhdsWithin.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) x s)) -> (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) x)
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.inter' UniqueDiffWithinAt.inter'ₓ'. -/
 theorem UniqueDiffWithinAt.inter' (hs : UniqueDiffWithinAt 𝕜 s x) (ht : t ∈ 𝓝[s] x) :
     UniqueDiffWithinAt 𝕜 (s ∩ t) x :=
   (uniqueDiffWithinAt_inter' ht).2 hs
 #align unique_diff_within_at.inter' UniqueDiffWithinAt.inter'
 
+#print uniqueDiffWithinAt_of_mem_nhds /-
 theorem uniqueDiffWithinAt_of_mem_nhds (h : s ∈ 𝓝 x) : UniqueDiffWithinAt 𝕜 s x := by
   simpa only [univ_inter] using unique_diff_within_at_univ.inter h
 #align unique_diff_within_at_of_mem_nhds uniqueDiffWithinAt_of_mem_nhds
+-/
 
+#print IsOpen.uniqueDiffWithinAt /-
 theorem IsOpen.uniqueDiffWithinAt (hs : IsOpen s) (xs : x ∈ s) : UniqueDiffWithinAt 𝕜 s x :=
   uniqueDiffWithinAt_of_mem_nhds (IsOpen.mem_nhds hs xs)
 #align is_open.unique_diff_within_at IsOpen.uniqueDiffWithinAt
+-/
 
+/- warning: unique_diff_on.inter -> UniqueDiffOn.inter is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {s : Set.{u2} E} {t : Set.{u2} E}, (UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s) -> (IsOpen.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) t) -> (UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {s : Set.{u1} E} {t : Set.{u1} E}, (UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s) -> (IsOpen.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) t) -> (UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on.inter UniqueDiffOn.interₓ'. -/
 theorem UniqueDiffOn.inter (hs : UniqueDiffOn 𝕜 s) (ht : IsOpen t) : UniqueDiffOn 𝕜 (s ∩ t) :=
   fun x hx => (hs x hx.1).inter (IsOpen.mem_nhds ht hx.2)
 #align unique_diff_on.inter UniqueDiffOn.inter
 
+#print IsOpen.uniqueDiffOn /-
 theorem IsOpen.uniqueDiffOn (hs : IsOpen s) : UniqueDiffOn 𝕜 s := fun x hx =>
   IsOpen.uniqueDiffWithinAt hs hx
 #align is_open.unique_diff_on IsOpen.uniqueDiffOn
+-/
 
+/- warning: unique_diff_within_at.prod -> UniqueDiffWithinAt.prod is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {t : Set.{u3} F} {y : F}, (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (UniqueDiffWithinAt.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y) -> (UniqueDiffWithinAt.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t) (Prod.mk.{u2, u3} E F x y))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u1} E} {t : Set.{u3} F} {y : F}, (UniqueDiffWithinAt.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s x) -> (UniqueDiffWithinAt.{u2, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t y) -> (UniqueDiffWithinAt.{u2, max u3 u1} 𝕜 _inst_1 (Prod.{u1, u3} E F) (Prod.instAddCommMonoidSum.{u1, u3} E F (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u2, u1, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u1, u3} E F (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u1, u3} E F s t) (Prod.mk.{u1, u3} E F x y))
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.prod UniqueDiffWithinAt.prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two sets of unique differentiability at points `x` and `y` has unique
@@ -365,11 +501,17 @@ theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 
   refine' ⟨_, hs.2, ht.2⟩
   have : _ ≤ Submodule.span 𝕜 (tangentConeAt 𝕜 (s ×ˢ t) (x, y)) :=
     Submodule.span_mono
-      (union_subset (subset_tangent_cone_prod_left ht.2) (subset_tangent_cone_prod_right hs.2))
+      (union_subset (subset_tangentCone_prod_left ht.2) (subset_tangentCone_prod_right hs.2))
   rw [LinearMap.span_inl_union_inr, SetLike.le_def] at this
   exact (hs.1.Prod ht.1).mono this
 #align unique_diff_within_at.prod UniqueDiffWithinAt.prod
 
+/- warning: unique_diff_within_at.univ_pi -> UniqueDiffWithinAt.univ_pi is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u2}) [_inst_8 : Finite.{succ u2} ι] (E : ι -> Type.{u3}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u3} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u3} (E i)) (x : forall (i : ι), E i), (forall (i : ι), UniqueDiffWithinAt.{u1, u3} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u3} (E i) (PseudoMetricSpace.toUniformSpace.{u3} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))))) (s i) (x i)) -> (UniqueDiffWithinAt.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i)))) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (E i) (_inst_9 i) (_inst_10 i))) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u3} (E a) (PseudoMetricSpace.toUniformSpace.{u3} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E a) (_inst_9 a)))))) (Set.pi.{u2, u3} ι (fun (i : ι) => E i) (Set.univ.{u2} ι) s) x)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u3}) [_inst_8 : Finite.{succ u3} ι] (E : ι -> Type.{u2}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u2} (E i)) (x : forall (i : ι), E i), (forall (i : ι), UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i)) -> (UniqueDiffWithinAt.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s) x)
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_piₓ'. -/
 theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
@@ -379,10 +521,15 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     norm_cast
     simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←
       maps_to']
-    exact fun i =>
-      (mapsTo_tangent_cone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
+    exact fun i => (mapsTo_tangentCone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
 
+/- warning: unique_diff_within_at.pi -> UniqueDiffWithinAt.pi is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u2}) [_inst_8 : Finite.{succ u2} ι] (E : ι -> Type.{u3}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u3} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u3} (E i)) (x : forall (i : ι), E i) (I : Set.{u2} ι), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) -> (UniqueDiffWithinAt.{u1, u3} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u3} (E i) (PseudoMetricSpace.toUniformSpace.{u3} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))))) (s i) (x i))) -> (UniqueDiffWithinAt.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i)))) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (E i) (_inst_9 i) (_inst_10 i))) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u3} (E a) (PseudoMetricSpace.toUniformSpace.{u3} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E a) (_inst_9 a)))))) (Set.pi.{u2, u3} ι (fun (i : ι) => E i) I s) x)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u3}) [_inst_8 : Finite.{succ u3} ι] (E : ι -> Type.{u2}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u2} (E i)) (x : forall (i : ι), E i) (I : Set.{u3} ι), (forall (i : ι), (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) -> (UniqueDiffWithinAt.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i) (x i))) -> (UniqueDiffWithinAt.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) I s) x)
+Case conversion may be inaccurate. Consider using '#align unique_diff_within_at.pi UniqueDiffWithinAt.piₓ'. -/
 theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
@@ -393,12 +540,24 @@ theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
     by_cases hi : i ∈ I <;> simp [*, uniqueDiffWithinAt_univ]
 #align unique_diff_within_at.pi UniqueDiffWithinAt.pi
 
+/- warning: unique_diff_on.prod -> UniqueDiffOn.prod is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {s : Set.{u2} E} {t : Set.{u3} F}, (UniqueDiffOn.{u1, u2} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s) -> (UniqueDiffOn.{u1, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t) -> (UniqueDiffOn.{u1, max u2 u3} 𝕜 _inst_1 (Prod.{u2, u3} E F) (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u1, u2, u3} 𝕜 E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Prod.topologicalSpace.{u2, u3} E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u2, u3} E F s t))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] {E : Type.{u1}} [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {s : Set.{u1} E} {t : Set.{u3} F}, (UniqueDiffOn.{u2, u1} 𝕜 _inst_1 E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) s) -> (UniqueDiffOn.{u2, u3} 𝕜 _inst_1 F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) t) -> (UniqueDiffOn.{u2, max u3 u1} 𝕜 _inst_1 (Prod.{u1, u3} E F) (Prod.instAddCommMonoidSum.{u1, u3} E F (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))) (Prod.module.{u2, u1, u3} 𝕜 E F (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) _inst_3) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instTopologicalSpaceProd.{u1, u3} E F (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (Set.prod.{u1, u3} E F s t))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on.prod UniqueDiffOn.prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two sets of unique differentiability is a set of unique differentiability. -/
 theorem UniqueDiffOn.prod {t : Set F} (hs : UniqueDiffOn 𝕜 s) (ht : UniqueDiffOn 𝕜 t) :
     UniqueDiffOn 𝕜 (s ×ˢ t) := fun ⟨x, y⟩ h => UniqueDiffWithinAt.prod (hs x h.1) (ht y h.2)
 #align unique_diff_on.prod UniqueDiffOn.prod
 
+/- warning: unique_diff_on.pi -> UniqueDiffOn.pi is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u2}) [_inst_8 : Finite.{succ u2} ι] (E : ι -> Type.{u3}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u3} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u3} (E i)) (I : Set.{u2} ι), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) -> (UniqueDiffOn.{u1, u3} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u3} (E i) (PseudoMetricSpace.toUniformSpace.{u3} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))))) (s i))) -> (UniqueDiffOn.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i)))) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (E i) (_inst_9 i) (_inst_10 i))) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u3} (E a) (PseudoMetricSpace.toUniformSpace.{u3} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E a) (_inst_9 a)))))) (Set.pi.{u2, u3} ι (fun (i : ι) => E i) I s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u3}) [_inst_8 : Finite.{succ u3} ι] (E : ι -> Type.{u2}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u2} (E i)) (I : Set.{u3} ι), (forall (i : ι), (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) -> (UniqueDiffOn.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i))) -> (UniqueDiffOn.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) I s))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on.pi UniqueDiffOn.piₓ'. -/
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
 theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, NormedAddCommGroup (E i)]
@@ -407,6 +566,12 @@ theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, No
   UniqueDiffWithinAt.pi _ _ _ _ _ fun i hi => h i hi (x i) (hx i hi)
 #align unique_diff_on.pi UniqueDiffOn.pi
 
+/- warning: unique_diff_on.univ_pi -> UniqueDiffOn.univ_pi is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u2}) [_inst_8 : Finite.{succ u2} ι] (E : ι -> Type.{u3}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u3} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u3} (E i)), (forall (i : ι), UniqueDiffOn.{u1, u3} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u3} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u3} (E i) (PseudoMetricSpace.toUniformSpace.{u3} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E i) (_inst_9 i))))) (s i)) -> (UniqueDiffOn.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i)))) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => E i) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (E i) (NormedAddCommGroup.toAddCommGroup.{u3} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (E i) (_inst_9 i) (_inst_10 i))) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u3} (E a) (PseudoMetricSpace.toUniformSpace.{u3} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (E a) (_inst_9 a)))))) (Set.pi.{u2, u3} ι (fun (i : ι) => E i) (Set.univ.{u2} ι) s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] (ι : Type.{u3}) [_inst_8 : Finite.{succ u3} ι] (E : ι -> Type.{u2}) [_inst_9 : forall (i : ι), NormedAddCommGroup.{u2} (E i)] [_inst_10 : forall (i : ι), NormedSpace.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))] (s : forall (i : ι), Set.{u2} (E i)), (forall (i : ι), UniqueDiffOn.{u1, u2} 𝕜 _inst_1 (E i) (AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i)) (UniformSpace.toTopologicalSpace.{u2} (E i) (PseudoMetricSpace.toUniformSpace.{u2} (E i) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E i) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i))))) (s i)) -> (UniqueDiffOn.{u1, max u2 u3} 𝕜 _inst_1 (forall (i : ι), E i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => E i) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i)))) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => E i) 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (E i) (NormedAddCommGroup.toAddCommGroup.{u2} (E i) (_inst_9 i))) (fun (i : ι) => NormedSpace.toModule.{u1, u2} 𝕜 (E i) (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E i) (_inst_9 i)) (_inst_10 i))) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => E i) (fun (a : ι) => UniformSpace.toTopologicalSpace.{u2} (E a) (PseudoMetricSpace.toUniformSpace.{u2} (E a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (E a) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (E a) (_inst_9 a)))))) (Set.pi.{u3, u2} ι (fun (i : ι) => E i) (Set.univ.{u3} ι) s))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on.univ_pi UniqueDiffOn.univ_piₓ'. -/
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
 theorem UniqueDiffOn.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
@@ -415,6 +580,7 @@ theorem UniqueDiffOn.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
   UniqueDiffOn.pi _ _ _ _ fun i _ => h i
 #align unique_diff_on.univ_pi UniqueDiffOn.univ_pi
 
+#print uniqueDiffWithinAt_convex /-
 /-- In a real vector space, a convex set with nonempty interior is a set of unique
 differentiability at every point of its closure. -/
 theorem uniqueDiffWithinAt_convex {s : Set G} (conv : Convex ℝ s) (hs : (interior s).Nonempty)
@@ -430,69 +596,104 @@ theorem uniqueDiffWithinAt_convex {s : Set G} (conv : Convex ℝ s) (hs : (inter
   replace hy : interior s ∈ 𝓝 y := IsOpen.mem_nhds isOpen_interior hy
   apply mem_of_superset ((isOpenMap_sub_right x).image_mem_nhds hy)
   rintro _ ⟨z, zs, rfl⟩
-  refine' mem_tangent_cone_of_openSegment_subset (subset.trans _ interior_subset)
+  refine' mem_tangentCone_of_openSegment_subset (subset.trans _ interior_subset)
   exact conv.open_segment_closure_interior_subset_interior hx zs
 #align unique_diff_within_at_convex uniqueDiffWithinAt_convex
+-/
 
+#print uniqueDiffOn_convex /-
 /-- In a real vector space, a convex set with nonempty interior is a set of unique
 differentiability. -/
 theorem uniqueDiffOn_convex {s : Set G} (conv : Convex ℝ s) (hs : (interior s).Nonempty) :
     UniqueDiffOn ℝ s := fun x xs => uniqueDiffWithinAt_convex conv hs (subset_closure xs)
 #align unique_diff_on_convex uniqueDiffOn_convex
+-/
 
+#print uniqueDiffOn_Ici /-
 theorem uniqueDiffOn_Ici (a : ℝ) : UniqueDiffOn ℝ (Ici a) :=
   uniqueDiffOn_convex (convex_Ici a) <| by simp only [interior_Ici, nonempty_Ioi]
 #align unique_diff_on_Ici uniqueDiffOn_Ici
+-/
 
+#print uniqueDiffOn_Iic /-
 theorem uniqueDiffOn_Iic (a : ℝ) : UniqueDiffOn ℝ (Iic a) :=
   uniqueDiffOn_convex (convex_Iic a) <| by simp only [interior_Iic, nonempty_Iio]
 #align unique_diff_on_Iic uniqueDiffOn_Iic
+-/
 
+#print uniqueDiffOn_Ioi /-
 theorem uniqueDiffOn_Ioi (a : ℝ) : UniqueDiffOn ℝ (Ioi a) :=
   isOpen_Ioi.UniqueDiffOn
 #align unique_diff_on_Ioi uniqueDiffOn_Ioi
+-/
 
+#print uniqueDiffOn_Iio /-
 theorem uniqueDiffOn_Iio (a : ℝ) : UniqueDiffOn ℝ (Iio a) :=
   isOpen_Iio.UniqueDiffOn
 #align unique_diff_on_Iio uniqueDiffOn_Iio
+-/
 
+/- warning: unique_diff_on_Icc -> uniqueDiffOn_Icc is a dubious translation:
+lean 3 declaration is
+  forall {a : Real} {b : Real}, (LT.lt.{0} Real Real.hasLt a b) -> (UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.addCommMonoid Real.module (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.preorder a b))
+but is expected to have type
+  forall {a : Real} {b : Real}, (LT.lt.{0} Real Real.instLTReal a b) -> (UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.instAddCommMonoidReal (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.instPreorderReal a b))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on_Icc uniqueDiffOn_Iccₓ'. -/
 theorem uniqueDiffOn_Icc {a b : ℝ} (hab : a < b) : UniqueDiffOn ℝ (Icc a b) :=
   uniqueDiffOn_convex (convex_Icc a b) <| by simp only [interior_Icc, nonempty_Ioo, hab]
 #align unique_diff_on_Icc uniqueDiffOn_Icc
 
+#print uniqueDiffOn_Ico /-
 theorem uniqueDiffOn_Ico (a b : ℝ) : UniqueDiffOn ℝ (Ico a b) :=
   if hab : a < b then
     uniqueDiffOn_convex (convex_Ico a b) <| by simp only [interior_Ico, nonempty_Ioo, hab]
   else by simp only [Ico_eq_empty hab, uniqueDiffOn_empty]
 #align unique_diff_on_Ico uniqueDiffOn_Ico
+-/
 
+#print uniqueDiffOn_Ioc /-
 theorem uniqueDiffOn_Ioc (a b : ℝ) : UniqueDiffOn ℝ (Ioc a b) :=
   if hab : a < b then
     uniqueDiffOn_convex (convex_Ioc a b) <| by simp only [interior_Ioc, nonempty_Ioo, hab]
   else by simp only [Ioc_eq_empty hab, uniqueDiffOn_empty]
 #align unique_diff_on_Ioc uniqueDiffOn_Ioc
+-/
 
+#print uniqueDiffOn_Ioo /-
 theorem uniqueDiffOn_Ioo (a b : ℝ) : UniqueDiffOn ℝ (Ioo a b) :=
   isOpen_Ioo.UniqueDiffOn
 #align unique_diff_on_Ioo uniqueDiffOn_Ioo
+-/
 
+/- warning: unique_diff_on_Icc_zero_one -> uniqueDiffOn_Icc_zero_one is a dubious translation:
+lean 3 declaration is
+  UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.addCommMonoid Real.module (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  UniqueDiffOn.{0, 0} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real Real.instAddCommMonoidReal (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align unique_diff_on_Icc_zero_one uniqueDiffOn_Icc_zero_oneₓ'. -/
 /-- The real interval `[0, 1]` is a set of unique differentiability. -/
 theorem uniqueDiffOn_Icc_zero_one : UniqueDiffOn ℝ (Icc (0 : ℝ) 1) :=
   uniqueDiffOn_Icc zero_lt_one
 #align unique_diff_on_Icc_zero_one uniqueDiffOn_Icc_zero_one
 
+#print uniqueDiffWithinAt_Ioo /-
 theorem uniqueDiffWithinAt_Ioo {a b t : ℝ} (ht : t ∈ Set.Ioo a b) :
     UniqueDiffWithinAt ℝ (Set.Ioo a b) t :=
   IsOpen.uniqueDiffWithinAt isOpen_Ioo ht
 #align unique_diff_within_at_Ioo uniqueDiffWithinAt_Ioo
+-/
 
+#print uniqueDiffWithinAt_Ioi /-
 theorem uniqueDiffWithinAt_Ioi (a : ℝ) : UniqueDiffWithinAt ℝ (Ioi a) a :=
   uniqueDiffWithinAt_convex (convex_Ioi a) (by simp) (by simp)
 #align unique_diff_within_at_Ioi uniqueDiffWithinAt_Ioi
+-/
 
+#print uniqueDiffWithinAt_Iio /-
 theorem uniqueDiffWithinAt_Iio (a : ℝ) : UniqueDiffWithinAt ℝ (Iio a) a :=
   uniqueDiffWithinAt_convex (convex_Iio a) (by simp) (by simp)
 #align unique_diff_within_at_Iio uniqueDiffWithinAt_Iio
+-/
 
 end UniqueDiff
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -377,7 +377,7 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h⊢
     refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
     norm_cast
-    simp only [← Submodule.supᵢ_map_single, supᵢ_le_iff, LinearMap.map_span, Submodule.span_le, ←
+    simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le, ←
       maps_to']
     exact fun i =>
       (mapsTo_tangent_cone_pi fun j hj => (h j).2).mono subset.rfl Submodule.subset_span

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -120,7 +120,7 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   have A : tendsto (fun n => ‖c n‖⁻¹) l (𝓝 0) := tendsto_inv_at_top_zero.comp hc
   have B : tendsto (fun n => ‖c n • d n‖) l (𝓝 ‖y‖) := (continuous_norm.tendsto _).comp hd
   have C : tendsto (fun n => ‖c n‖⁻¹ * ‖c n • d n‖) l (𝓝 (0 * ‖y‖)) := A.mul B
-  rw [zero_mul] at C
+  rw [MulZeroClass.zero_mul] at C
   have : ∀ᶠ n in l, ‖c n‖⁻¹ * ‖c n • d n‖ = ‖d n‖ :=
     by
     apply (eventually_ne_of_tendsto_norm_atTop hc 0).mono fun n hn => _

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -199,8 +199,8 @@ theorem subset_tangent_cone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s
     exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_right subset_tangent_cone_prod_right
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangent_cone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] {s : ∀ i, Set (E i)} {x : ∀ i, E i}

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

@@ -112,7 +112,7 @@ theorem tangentConeAt.lim_zero {α : Type*} (l : Filter α) {c : α → 𝕜} {d
   have : ∀ᶠ n in l, ‖c n‖⁻¹ * ‖c n • d n‖ = ‖d n‖ := by
     refine (eventually_ne_of_tendsto_norm_atTop hc 0).mono fun n hn => ?_
     rw [norm_smul, ← mul_assoc, inv_mul_cancel, one_mul]
-    rwa [Ne.def, norm_eq_zero]
+    rwa [Ne, norm_eq_zero]
   have D : Tendsto (fun n => ‖d n‖) l (𝓝 0) := Tendsto.congr' this C
   rw [tendsto_zero_iff_norm_tendsto_zero]
   exact D

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -73,11 +73,8 @@ def UniqueDiffOn (s : Set E) : Prop :=
 end TangentCone
 
 variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
-
 variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-
 variable {G : Type*} [NormedAddCommGroup G] [NormedSpace ℝ G]
-
 variable {𝕜} {x y : E} {s t : Set E}
 
 section TangentCone

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>

@@ -125,8 +125,8 @@ theorem tangentCone_mono_nhds (h : 𝓝[s] x ≤ 𝓝[t] x) :
     tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x := by
   rintro y ⟨c, d, ds, ctop, clim⟩
   refine' ⟨c, d, _, ctop, clim⟩
-  suffices : Tendsto (fun n => x + d n) atTop (𝓝[t] x)
-  exact tendsto_principal.1 (tendsto_inf.1 this).2
+  suffices Tendsto (fun n => x + d n) atTop (𝓝[t] x) from
+    tendsto_principal.1 (tendsto_inf.1 this).2
   refine' (tendsto_inf.2 ⟨_, tendsto_principal.2 ds⟩).mono_right h
   simpa only [add_zero] using tendsto_const_nhds.add (tangentConeAt.lim_zero atTop ctop clim)
 #align tangent_cone_mono_nhds tangentCone_mono_nhds

See here on Zulip.

This PR changes a bunch of names containing nhds_0 or/and lt_1 to nhds_zero or/and lt_one.

@@ -158,7 +158,7 @@ theorem subset_tangentCone_prod_left {t : Set F} {y : F} (ht : y ∈ closure t)
     simp [hn, (hd' n).1]
   · apply Tendsto.prod_mk_nhds hy _
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
-    exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
+    exact tendsto_pow_atTop_nhds_zero_of_lt_one one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_left subset_tangentCone_prod_left
 
 /-- The tangent cone of a product contains the tangent cone of its right factor. -/
@@ -178,7 +178,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
     simp [hn, (hd' n).1]
   · apply Tendsto.prod_mk_nhds _ hy
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _
-    exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
+    exact tendsto_pow_atTop_nhds_zero_of_lt_one one_half_pos.le one_half_lt_one
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
@@ -201,7 +201,7 @@ theorem mapsTo_tangentCone_pi {ι : Type*} [DecidableEq ι] {E : ι → Type*}
     · simp [hy]
     · suffices Tendsto (fun n => c n • d' n j) atTop (𝓝 0) by simpa [hj]
       refine' squeeze_zero_norm (fun n => (hcd' n j hj).le) _
-      exact tendsto_pow_atTop_nhds_0_of_lt_1 one_half_pos.le one_half_lt_one
+      exact tendsto_pow_atTop_nhds_zero_of_lt_one one_half_pos.le one_half_lt_one
 #align maps_to_tangent_cone_pi mapsTo_tangentCone_pi
 
 /-- If a subset of a real vector space contains an open segment, then the direction of this

• @[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
• add Lean.Name.decapitalize
• fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

@@ -56,7 +56,7 @@ The main role of this property is to ensure that the differential within `s` at
 hence this name. The uniqueness it asserts is proved in `UniqueDiffWithinAt.eq` in `Fderiv.Basic`.
 To avoid pathologies in dimension 0, we also require that `x` belongs to the closure of `s` (which
 is automatic when `E` is not `0`-dimensional). -/
-@[mk_iff uniqueDiffWithinAt_iff]
+@[mk_iff]
 structure UniqueDiffWithinAt (s : Set E) (x : E) : Prop where
   dense_tangentCone : Dense (Submodule.span 𝕜 (tangentConeAt 𝕜 s x) : Set E)
   mem_closure : x ∈ closure s

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -184,7 +184,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
 theorem mapsTo_tangentCone_pi {ι : Type*} [DecidableEq ι] {E : ι → Type*}
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] {s : ∀ i, Set (E i)} {x : ∀ i, E i}
-    {i : ι} (hi : ∀ (j) (_ : j ≠ i), x j ∈ closure (s j)) :
+    {i : ι} (hi : ∀ j ≠ i, x j ∈ closure (s j)) :
     MapsTo (LinearMap.single i : E i →ₗ[𝕜] ∀ j, E j) (tangentConeAt 𝕜 (s i) (x i))
       (tangentConeAt 𝕜 (Set.pi univ s) x) := by
   rintro w ⟨c, d, hd, hc, hy⟩

Follow-up #9184

@@ -188,8 +188,7 @@ theorem mapsTo_tangentCone_pi {ι : Type*} [DecidableEq ι] {E : ι → Type*}
     MapsTo (LinearMap.single i : E i →ₗ[𝕜] ∀ j, E j) (tangentConeAt 𝕜 (s i) (x i))
       (tangentConeAt 𝕜 (Set.pi univ s) x) := by
   rintro w ⟨c, d, hd, hc, hy⟩
-  have : ∀ (n) (j) (_ : j ≠ i), ∃ d', x j + d' ∈ s j ∧ ‖c n • d'‖ < (1 / 2 : ℝ) ^ n := by
-    intro n j hj
+  have : ∀ n, ∀ j ≠ i, ∃ d', x j + d' ∈ s j ∧ ‖c n • d'‖ < (1 / 2 : ℝ) ^ n := fun n j hj ↦ by
     rcases mem_closure_iff_nhds.1 (hi j hj) _
         (eventually_nhds_norm_smul_sub_lt (c n) (x j) (pow_pos one_half_pos n)) with
       ⟨z, hz, hzs⟩

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -174,7 +174,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
   choose d' hd' using this
   refine' ⟨c, fun n => (d' n, d n), _, hc, _⟩
   show ∀ᶠ n in atTop, (x, y) + (d' n, d n) ∈ s ×ˢ t
-  · filter_upwards [hd]with n hn
+  · filter_upwards [hd] with n hn
     simp [hn, (hd' n).1]
   · apply Tendsto.prod_mk_nhds _ hy
     refine' squeeze_zero_norm (fun n => (hd' n).2.le) _

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ properties of the tangent cone we prove here.
 -/
 
 
-variable (𝕜 : Type _) [NontriviallyNormedField 𝕜]
+variable (𝕜 : Type*) [NontriviallyNormedField 𝕜]
 
 open Filter Set
 
@@ -41,7 +41,7 @@ open Topology
 
 section TangentCone
 
-variable {E : Type _} [AddCommMonoid E] [Module 𝕜 E] [TopologicalSpace E]
+variable {E : Type*} [AddCommMonoid E] [Module 𝕜 E] [TopologicalSpace E]
 
 /-- The set of all tangent directions to the set `s` at the point `x`. -/
 def tangentConeAt (s : Set E) (x : E) : Set E :=
@@ -72,11 +72,11 @@ def UniqueDiffOn (s : Set E) : Prop :=
 
 end TangentCone
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
 
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
-variable {G : Type _} [NormedAddCommGroup G] [NormedSpace ℝ G]
+variable {G : Type*} [NormedAddCommGroup G] [NormedSpace ℝ G]
 
 variable {𝕜} {x y : E} {s t : Set E}
 
@@ -105,7 +105,7 @@ theorem tangentCone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeA
 
 /-- Auxiliary lemma ensuring that, under the assumptions defining the tangent cone,
 the sequence `d` tends to 0 at infinity. -/
-theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {d : α → E}
+theorem tangentConeAt.lim_zero {α : Type*} (l : Filter α) {c : α → 𝕜} {d : α → E}
     (hc : Tendsto (fun n => ‖c n‖) l atTop) (hd : Tendsto (fun n => c n • d n) l (𝓝 y)) :
     Tendsto d l (𝓝 0) := by
   have A : Tendsto (fun n => ‖c n‖⁻¹) l (𝓝 0) := tendsto_inv_atTop_zero.comp hc
@@ -182,7 +182,7 @@ theorem subset_tangentCone_prod_right {t : Set F} {y : F} (hs : x ∈ closure s)
 #align subset_tangent_cone_prod_right subset_tangentCone_prod_right
 
 /-- The tangent cone of a product contains the tangent cone of each factor. -/
-theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
+theorem mapsTo_tangentCone_pi {ι : Type*} [DecidableEq ι] {E : ι → Type*}
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] {s : ∀ i, Set (E i)} {x : ∀ i, E i}
     {i : ι} (hi : ∀ (j) (_ : j ≠ i), x j ∈ closure (s j)) :
     MapsTo (LinearMap.single i : E i →ₗ[𝕜] ∀ j, E j) (tangentConeAt 𝕜 (s i) (x i))
@@ -322,7 +322,7 @@ theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 
   exact (hs.1.prod ht.1).mono this
 #align unique_diff_within_at.prod UniqueDiffWithinAt.prod
 
-theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
+theorem UniqueDiffWithinAt.univ_pi (ι : Type*) [Finite ι] (E : ι → Type*)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
   classical
@@ -334,7 +334,7 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
   exact fun i => (mapsTo_tangentCone_pi fun j _ => (h j).2).mono Subset.rfl Submodule.subset_span
 #align unique_diff_within_at.univ_pi UniqueDiffWithinAt.univ_pi
 
-theorem UniqueDiffWithinAt.pi (ι : Type _) [Finite ι] (E : ι → Type _)
+theorem UniqueDiffWithinAt.pi (ι : Type*) [Finite ι] (E : ι → Type*)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (I : Set ι) (h : ∀ i ∈ I, UniqueDiffWithinAt 𝕜 (s i) (x i)) :
     UniqueDiffWithinAt 𝕜 (Set.pi I s) x := by
@@ -352,7 +352,7 @@ theorem UniqueDiffOn.prod {t : Set F} (hs : UniqueDiffOn 𝕜 s) (ht : UniqueDif
 
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
-theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, NormedAddCommGroup (E i)]
+theorem UniqueDiffOn.pi (ι : Type*) [Finite ι] (E : ι → Type*) [∀ i, NormedAddCommGroup (E i)]
     [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (I : Set ι)
     (h : ∀ i ∈ I, UniqueDiffOn 𝕜 (s i)) : UniqueDiffOn 𝕜 (Set.pi I s) :=
   fun x hx => UniqueDiffWithinAt.pi _ _ _ _ _ fun i hi => h i hi (x i) (hx i hi)
@@ -360,7 +360,7 @@ theorem UniqueDiffOn.pi (ι : Type _) [Finite ι] (E : ι → Type _) [∀ i, No
 
 /-- The finite product of a family of sets of unique differentiability is a set of unique
 differentiability. -/
-theorem UniqueDiffOn.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
+theorem UniqueDiffOn.univ_pi (ι : Type*) [Finite ι] (E : ι → Type*)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i))
     (h : ∀ i, UniqueDiffOn 𝕜 (s i)) : UniqueDiffOn 𝕜 (Set.pi univ s) :=
   UniqueDiffOn.pi _ _ _ _ fun i _ => h i

• 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) 2019 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.calculus.tangent_cone
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Topology
 import Mathlib.Analysis.NormedSpace.Basic
 import Mathlib.Analysis.SpecificLimits.Basic
 
+#align_import analysis.calculus.tangent_cone from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Tangent cone
 

@@ -88,18 +88,17 @@ section TangentCone
 -- This section is devoted to the properties of the tangent cone.
 open NormedField
 
-theorem tangentCone_univ : tangentConeAt 𝕜 univ x = univ := by
-  refine' univ_subset_iff.1 fun y _ => _
-  rcases exists_one_lt_norm 𝕜 with ⟨w, hw⟩
-  refine' ⟨fun n => w ^ n, fun n => (w ^ n)⁻¹ • y, univ_mem' fun n => mem_univ _, _, _⟩
-  · simp only [norm_pow]
-    exact tendsto_pow_atTop_atTop_of_one_lt hw
-  · convert @tendsto_const_nhds E ℕ _ _ atTop with n
-    have : w ^ n * (w ^ n)⁻¹ = 1 := by
-      apply mul_inv_cancel
-      apply pow_ne_zero
-      simpa [norm_eq_zero] using (ne_of_lt (lt_trans zero_lt_one hw)).symm
-    rw [smul_smul, this, one_smul]
+theorem mem_tangentConeAt_of_pow_smul {r : 𝕜} (hr₀ : r ≠ 0) (hr : ‖r‖ < 1)
+    (hs : ∀ᶠ n : ℕ in atTop, x + r ^ n • y ∈ s) : y ∈ tangentConeAt 𝕜 s x := by
+  refine ⟨fun n ↦ (r ^ n)⁻¹, fun n ↦ r ^ n • y, hs, ?_, ?_⟩
+  · simp only [norm_inv, norm_pow, ← inv_pow]
+    exact tendsto_pow_atTop_atTop_of_one_lt <| one_lt_inv (norm_pos_iff.2 hr₀) hr
+  · simp only [inv_smul_smul₀ (pow_ne_zero _ hr₀), tendsto_const_nhds]
+
+theorem tangentCone_univ : tangentConeAt 𝕜 univ x = univ :=
+  let ⟨_r, hr₀, hr⟩ := exists_norm_lt_one 𝕜
+  eq_univ_of_forall fun _ ↦ mem_tangentConeAt_of_pow_smul (norm_pos_iff.1 hr₀) hr <|
+    eventually_of_forall fun _ ↦ mem_univ _
 #align tangent_cone_univ tangentCone_univ
 
 theorem tangentCone_mono (h : s ⊆ t) : tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x := by
@@ -115,7 +114,7 @@ theorem tangentConeAt.lim_zero {α : Type _} (l : Filter α) {c : α → 𝕜} {
   have A : Tendsto (fun n => ‖c n‖⁻¹) l (𝓝 0) := tendsto_inv_atTop_zero.comp hc
   have B : Tendsto (fun n => ‖c n • d n‖) l (𝓝 ‖y‖) := (continuous_norm.tendsto _).comp hd
   have C : Tendsto (fun n => ‖c n‖⁻¹ * ‖c n • d n‖) l (𝓝 (0 * ‖y‖)) := A.mul B
-  rw [MulZeroClass.zero_mul] at C
+  rw [zero_mul] at C
   have : ∀ᶠ n in l, ‖c n‖⁻¹ * ‖c n • d n‖ = ‖d n‖ := by
     refine (eventually_ne_of_tendsto_norm_atTop hc 0).mono fun n hn => ?_
     rw [norm_smul, ← mul_assoc, inv_mul_cancel, one_mul]
@@ -213,34 +212,13 @@ theorem mapsTo_tangentCone_pi {ι : Type _} [DecidableEq ι] {E : ι → Type _}
 segment belongs to the tangent cone at its endpoints. -/
 theorem mem_tangentCone_of_openSegment_subset {s : Set G} {x y : G} (h : openSegment ℝ x y ⊆ s) :
     y - x ∈ tangentConeAt ℝ s x := by
-  let c := fun n : ℕ => (2 : ℝ) ^ (n + 1)
-  let d := fun n : ℕ => (c n)⁻¹ • (y - x)
-  refine' ⟨c, d, Filter.univ_mem' fun n => h _, _, _⟩
-  show x + d n ∈ openSegment ℝ x y
-  · rw [openSegment_eq_image]
-    refine' ⟨(c n)⁻¹, ⟨_, _⟩, _⟩
-    · rw [inv_pos]
-      apply pow_pos
-      norm_num
-    · apply inv_lt_one
-      apply one_lt_pow _ (Nat.succ_ne_zero _)
-      norm_num
-    · simp only [sub_smul, smul_sub, one_smul]
-      abel
-  show Filter.Tendsto (fun n : ℕ => ‖c n‖) Filter.atTop Filter.atTop
-  · have : (fun n : ℕ => ‖c n‖) = c := by
-      ext n
-      exact abs_of_nonneg (pow_nonneg (by norm_num) _)
-    rw [this]
-    exact (tendsto_pow_atTop_atTop_of_one_lt (by norm_num)).comp (tendsto_add_atTop_nat 1)
-  show Filter.Tendsto (fun n : ℕ => c n • d n) Filter.atTop (𝓝 (y - x))
-  · have : (fun n : ℕ => c n • d n) = fun _ => y - x := by
-      ext n
-      simp only [smul_smul]
-      rw [mul_inv_cancel, one_smul]
-      exact pow_ne_zero _ (by norm_num)
-    rw [this]
-    apply tendsto_const_nhds
+  refine mem_tangentConeAt_of_pow_smul one_half_pos.ne' (by norm_num) ?_
+  refine (eventually_ne_atTop 0).mono fun n hn ↦ (h ?_)
+  rw [openSegment_eq_image]
+  refine ⟨(1 / 2) ^ n, ⟨?_, ?_⟩, ?_⟩
+  · exact pow_pos one_half_pos _
+  · exact pow_lt_one one_half_pos.le one_half_lt_one hn
+  · simp only [sub_smul, one_smul, smul_sub]; abel
 #align mem_tangent_cone_of_open_segment_subset mem_tangentCone_of_openSegment_subset
 
 /-- If a subset of a real vector space contains a segment, then the direction of this

Add lemmas about smoothness in a smooth vector bundle. Also rename the old smoothOn_coordChange to smoothOn_coordChangeL.

@@ -278,6 +278,9 @@ theorem uniqueDiffOn_empty : UniqueDiffOn 𝕜 (∅ : Set E) :=
   fun _ hx => hx.elim
 #align unique_diff_on_empty uniqueDiffOn_empty
 
+theorem UniqueDiffWithinAt.congr_pt (h : UniqueDiffWithinAt 𝕜 s x) (hy : x = y) :
+    UniqueDiffWithinAt 𝕜 s y := hy ▸ h
+
 theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 𝓝[s] x ≤ 𝓝[t] x) :
     UniqueDiffWithinAt 𝕜 t x := by
   simp only [uniqueDiffWithinAt_iff] at *

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -281,7 +281,7 @@ theorem uniqueDiffOn_empty : UniqueDiffOn 𝕜 (∅ : Set E) :=
 theorem UniqueDiffWithinAt.mono_nhds (h : UniqueDiffWithinAt 𝕜 s x) (st : 𝓝[s] x ≤ 𝓝[t] x) :
     UniqueDiffWithinAt 𝕜 t x := by
   simp only [uniqueDiffWithinAt_iff] at *
-  rw [mem_closure_iff_nhdsWithin_neBot] at h⊢
+  rw [mem_closure_iff_nhdsWithin_neBot] at h ⊢
   exact ⟨h.1.mono <| Submodule.span_mono <| tangentCone_mono_nhds st, h.2.mono st⟩
 #align unique_diff_within_at.mono_nhds UniqueDiffWithinAt.mono_nhds
 
@@ -335,7 +335,7 @@ theorem IsOpen.uniqueDiffOn (hs : IsOpen s) : UniqueDiffOn 𝕜 s :=
 differentiability at `(x, y)`. -/
 theorem UniqueDiffWithinAt.prod {t : Set F} {y : F} (hs : UniqueDiffWithinAt 𝕜 s x)
     (ht : UniqueDiffWithinAt 𝕜 t y) : UniqueDiffWithinAt 𝕜 (s ×ˢ t) (x, y) := by
-  rw [uniqueDiffWithinAt_iff] at hs ht⊢
+  rw [uniqueDiffWithinAt_iff] at hs ht ⊢
   rw [closure_prod_eq]
   refine' ⟨_, hs.2, ht.2⟩
   have : _ ≤ Submodule.span 𝕜 (tangentConeAt 𝕜 (s ×ˢ t) (x, y)) := Submodule.span_mono
@@ -348,7 +348,7 @@ theorem UniqueDiffWithinAt.univ_pi (ι : Type _) [Finite ι] (E : ι → Type _)
     [∀ i, NormedAddCommGroup (E i)] [∀ i, NormedSpace 𝕜 (E i)] (s : ∀ i, Set (E i)) (x : ∀ i, E i)
     (h : ∀ i, UniqueDiffWithinAt 𝕜 (s i) (x i)) : UniqueDiffWithinAt 𝕜 (Set.pi univ s) x := by
   classical
-  simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h⊢
+  simp only [uniqueDiffWithinAt_iff, closure_pi_set] at h ⊢
   refine' ⟨(dense_pi univ fun i _ => (h i).1).mono _, fun i _ => (h i).2⟩
   norm_cast
   simp only [← Submodule.iSup_map_single, iSup_le_iff, LinearMap.map_span, Submodule.span_le,

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>