analysis.locally_convex.with_seminorms ⟷ Mathlib.Analysis.LocallyConvex.WithSeminorms

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

@@ -402,7 +402,7 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print WithSeminorms.T1_of_separating /-
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
@@ -434,7 +434,7 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print WithSeminorms.separating_iff_T1 /-
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :

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

@@ -380,7 +380,7 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
   ext sr : 1
   have : (sr.fst.sup p).ball (x +ᵥ 0) sr.snd = x +ᵥ (sr.fst.sup p).ball 0 sr.snd :=
     Eq.symm (Seminorm.vadd_ball (sr.fst.sup p))
-  rwa [vadd_eq_add, add_zero] at this 
+  rwa [vadd_eq_add, add_zero] at this
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
 -/
 
@@ -622,12 +622,12 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   rw [hp.has_basis.isVonNBounded_iff]
   constructor
   · intro h I
-    simp only [id.def] at h 
+    simp only [id.def] at h
     specialize h ((I.sup p).ball 0 1) (p.basis_sets_mem I zero_lt_one)
     rcases h with ⟨r, hr, h⟩
     cases' NormedField.exists_lt_norm 𝕜 r with a ha
     specialize h a (le_of_lt ha)
-    rw [Seminorm.smul_ball_zero (norm_pos_iff.1 <| hr.trans ha), mul_one] at h 
+    rw [Seminorm.smul_ball_zero (norm_pos_iff.1 <| hr.trans ha), mul_one] at h
     refine' ⟨‖a‖, lt_trans hr ha, _⟩
     intro x hx
     specialize h hx
@@ -636,7 +636,7 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   rcases p.basis_sets_iff.mp hs' with ⟨I, r, hr, hs'⟩
   rw [id.def, hs']
   rcases h I with ⟨r', hr', h'⟩
-  simp_rw [← (I.sup p).mem_ball_zero] at h' 
+  simp_rw [← (I.sup p).mem_ball_zero] at h'
   refine' Absorbs.mono_right _ h'
   exact (Finset.sup I p).ball_zero_absorbs_ball_zero hr
 #align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded
@@ -647,7 +647,7 @@ theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G →
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔
       ∀ I : Finset ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, I.sup p (f x) < r :=
-  by simp_rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded, Set.ball_image_iff]
+  by simp_rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded, Set.forall_mem_image]
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
 -/
 
@@ -679,7 +679,7 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, p i (f x) < r :=
-  by simp_rw [hp.is_vonN_bounded_iff_seminorm_bounded, Set.ball_image_iff]
+  by simp_rw [hp.is_vonN_bounded_iff_seminorm_bounded, Set.forall_mem_image]
 #align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_bounded
 -/
 
@@ -752,7 +752,7 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι) (C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
     Continuous f := by
-  rw [← Seminorm.isBounded_const (Fin 1)] at hf 
+  rw [← Seminorm.isBounded_const (Fin 1)] at hf
   exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 -/
@@ -762,7 +762,7 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
     Continuous f := by
-  rw [← Seminorm.const_isBounded (Fin 1)] at hf 
+  rw [← Seminorm.const_isBounded (Fin 1)] at hf
   exact continuous_from_bounded (norm_withSeminorms 𝕝 E) hq f hf
 #align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminorms
 -/
@@ -786,8 +786,8 @@ theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
   · rw [hp.1, AddGroupFilterBasis.nhds_eq _, AddGroupFilterBasis.N_zero]
     exact FilterBasis.hasBasis _
   · intro s hs
-    change s ∈ Set.iUnion _ at hs 
-    simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs 
+    change s ∈ Set.iUnion _ at hs
+    simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs
     rcases hs with ⟨I, r, hr, rfl⟩
     exact convex_ball _ _ _
 #align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpace

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

@@ -113,7 +113,20 @@ theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
 
 #print SeminormFamily.basisSets_intersect /-
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
-    ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by classical
+    ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
+  classical
+  rcases p.basis_sets_iff.mp hU with ⟨s, r₁, hr₁, hU⟩
+  rcases p.basis_sets_iff.mp hV with ⟨t, r₂, hr₂, hV⟩
+  use((s ∪ t).sup p).ball 0 (min r₁ r₂)
+  refine' ⟨p.basis_sets_mem (s ∪ t) (lt_min_iff.mpr ⟨hr₁, hr₂⟩), _⟩
+  rw [hU, hV, ball_finset_sup_eq_Inter _ _ _ (lt_min_iff.mpr ⟨hr₁, hr₂⟩),
+    ball_finset_sup_eq_Inter _ _ _ hr₁, ball_finset_sup_eq_Inter _ _ _ hr₂]
+  exact
+    Set.subset_inter
+      (Set.iInter₂_mono' fun i hi =>
+        ⟨i, Finset.subset_union_left _ _ hi, ball_mono <| min_le_left _ _⟩)
+      (Set.iInter₂_mono' fun i hi =>
+        ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
 -/
 
@@ -281,7 +294,22 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
 #print Seminorm.isBounded_sup /-
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
-    ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by classical
+    ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
+  classical
+  obtain rfl | hs' := s'.eq_empty_or_nonempty
+  · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
+  choose fₛ fC hf using hf
+  use s'.card • s'.sup fC, Finset.biUnion s' fₛ
+  have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.biUnion s' fₛ).sup p :=
+    by
+    intro i hi
+    refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
+    exact Finset.sup_mono (Finset.subset_biUnion_of_mem fₛ hi)
+  refine' (comp_mono f (finset_sup_le_sum q s')).trans _
+  simp_rw [← pullback_apply, map_sum, pullback_apply]
+  refine' (Finset.sum_le_sum hs).trans _
+  rw [Finset.sum_const, smul_assoc]
+  exact le_rfl
 #align seminorm.is_bounded_sup Seminorm.isBounded_sup
 -/
 

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

@@ -113,20 +113,7 @@ theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
 
 #print SeminormFamily.basisSets_intersect /-
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
-    ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
-  classical
-  rcases p.basis_sets_iff.mp hU with ⟨s, r₁, hr₁, hU⟩
-  rcases p.basis_sets_iff.mp hV with ⟨t, r₂, hr₂, hV⟩
-  use((s ∪ t).sup p).ball 0 (min r₁ r₂)
-  refine' ⟨p.basis_sets_mem (s ∪ t) (lt_min_iff.mpr ⟨hr₁, hr₂⟩), _⟩
-  rw [hU, hV, ball_finset_sup_eq_Inter _ _ _ (lt_min_iff.mpr ⟨hr₁, hr₂⟩),
-    ball_finset_sup_eq_Inter _ _ _ hr₁, ball_finset_sup_eq_Inter _ _ _ hr₂]
-  exact
-    Set.subset_inter
-      (Set.iInter₂_mono' fun i hi =>
-        ⟨i, Finset.subset_union_left _ _ hi, ball_mono <| min_le_left _ _⟩)
-      (Set.iInter₂_mono' fun i hi =>
-        ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
+    ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by classical
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
 -/
 
@@ -294,22 +281,7 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
 #print Seminorm.isBounded_sup /-
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
-    ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
-  classical
-  obtain rfl | hs' := s'.eq_empty_or_nonempty
-  · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
-  choose fₛ fC hf using hf
-  use s'.card • s'.sup fC, Finset.biUnion s' fₛ
-  have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.biUnion s' fₛ).sup p :=
-    by
-    intro i hi
-    refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
-    exact Finset.sup_mono (Finset.subset_biUnion_of_mem fₛ hi)
-  refine' (comp_mono f (finset_sup_le_sum q s')).trans _
-  simp_rw [← pullback_apply, map_sum, pullback_apply]
-  refine' (Finset.sum_le_sum hs).trans _
-  rw [Finset.sum_const, smul_assoc]
-  exact le_rfl
+    ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by classical
 #align seminorm.is_bounded_sup Seminorm.isBounded_sup
 -/
 

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

@@ -619,7 +619,7 @@ variable [TopologicalSpace E]
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
   by
-  rw [hp.has_basis.isVonNBounded_basis_iff]
+  rw [hp.has_basis.isVonNBounded_iff]
   constructor
   · intro h I
     simp only [id.def] at h 

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

@@ -306,7 +306,7 @@ theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂
     refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
     exact Finset.sup_mono (Finset.subset_biUnion_of_mem fₛ hi)
   refine' (comp_mono f (finset_sup_le_sum q s')).trans _
-  simp_rw [← pullback_apply, AddMonoidHom.map_sum, pullback_apply]
+  simp_rw [← pullback_apply, map_sum, pullback_apply]
   refine' (Finset.sum_le_sum hs).trans _
   rw [Finset.sum_const, smul_assoc]
   exact le_rfl
@@ -426,7 +426,7 @@ theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
 theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
     ∃ i, p i x ≠ 0 := by
   have := ((t1Space_TFAE E).out 0 9).mp inferInstance
-  by_contra' h
+  by_contra! h
   refine' hx (this _)
   rw [hp.has_basis_zero_ball.specializes_iff]
   rintro ⟨s, r⟩ (hr : 0 < r)

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

@@ -568,7 +568,7 @@ theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf [u : UniformSpace
   by
   rw [p.with_seminorms_iff_nhds_eq_infi,
     UniformAddGroup.ext_iff inferInstance (uniformAddGroup_iInf fun i => inferInstance),
-    toTopologicalSpace_iInf, nhds_iInf]
+    UniformSpace.toTopologicalSpace_iInf, nhds_iInf]
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup

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

@@ -888,8 +888,7 @@ variable [UniformSpace E] [UniformAddGroup E]
 #print WithSeminorms.first_countable /-
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology
 is first countable. -/
-theorem WithSeminorms.first_countable (hp : WithSeminorms p) :
-    TopologicalSpace.FirstCountableTopology E :=
+theorem WithSeminorms.first_countable (hp : WithSeminorms p) : FirstCountableTopology E :=
   by
   have : (𝓝 (0 : E)).IsCountablyGenerated :=
     by

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
 -/
-import Mathbin.Analysis.Seminorm
-import Mathbin.Analysis.LocallyConvex.Bounded
-import Mathbin.Topology.Algebra.FilterBasis
-import Mathbin.Topology.Algebra.Module.LocallyConvex
+import Analysis.Seminorm
+import Analysis.LocallyConvex.Bounded
+import Topology.Algebra.FilterBasis
+import Topology.Algebra.Module.LocallyConvex
 
 #align_import analysis.locally_convex.with_seminorms from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
 
@@ -402,7 +402,7 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print WithSeminorms.T1_of_separating /-
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
@@ -434,7 +434,7 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print WithSeminorms.separating_iff_T1 /-
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -117,7 +117,7 @@ theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈
   classical
   rcases p.basis_sets_iff.mp hU with ⟨s, r₁, hr₁, hU⟩
   rcases p.basis_sets_iff.mp hV with ⟨t, r₂, hr₂, hV⟩
-  use ((s ∪ t).sup p).ball 0 (min r₁ r₂)
+  use((s ∪ t).sup p).ball 0 (min r₁ r₂)
   refine' ⟨p.basis_sets_mem (s ∪ t) (lt_min_iff.mpr ⟨hr₁, hr₂⟩), _⟩
   rw [hU, hV, ball_finset_sup_eq_Inter _ _ _ (lt_min_iff.mpr ⟨hr₁, hr₂⟩),
     ball_finset_sup_eq_Inter _ _ _ hr₁, ball_finset_sup_eq_Inter _ _ _ hr₂]
@@ -144,7 +144,7 @@ theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E) (H : V ∈ p.basis_sets), V + V ⊆ U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨s, r, hr, hU⟩
-  use (s.sup p).ball 0 (r / 2)
+  use(s.sup p).ball 0 (r / 2)
   refine' ⟨p.basis_sets_mem s (div_pos hr zero_lt_two), _⟩
   refine' Set.Subset.trans (ball_add_ball_subset (s.sup p) (r / 2) (r / 2) 0 0) _
   rw [hU, add_zero, add_halves']
@@ -207,7 +207,7 @@ theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
   rw [hU]
   by_cases h : x ≠ 0
   · rw [(s.sup p).smul_ball_preimage 0 r x h, smul_zero]
-    use (s.sup p).ball 0 (r / ‖x‖)
+    use(s.sup p).ball 0 (r / ‖x‖)
     exact ⟨p.basis_sets_mem s (div_pos hr (norm_pos_iff.mpr h)), subset.rfl⟩
   refine' ⟨(s.sup p).ball 0 r, p.basis_sets_mem s hr, _⟩
   simp only [not_ne_iff.mp h, subset_def, mem_ball_zero, hr, mem_univ, map_zero, imp_true_iff,
@@ -286,7 +286,7 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
   constructor <;> intro h i
   · rcases h i with ⟨s, C, h⟩
     exact ⟨C, le_trans h (smul_le_smul (Finset.sup_le fun _ _ => le_rfl) le_rfl)⟩
-  use {Classical.arbitrary ι}
+  use{Classical.arbitrary ι}
   simp only [h, Finset.sup_singleton]
 #align seminorm.const_is_bounded Seminorm.const_isBounded
 -/

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.locally_convex.with_seminorms
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Seminorm
 import Mathbin.Analysis.LocallyConvex.Bounded
 import Mathbin.Topology.Algebra.FilterBasis
 import Mathbin.Topology.Algebra.Module.LocallyConvex
 
+#align_import analysis.locally_convex.with_seminorms from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 # Topology induced by a family of seminorms
 
@@ -405,7 +402,7 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print WithSeminorms.T1_of_separating /-
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
@@ -437,7 +434,7 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print WithSeminorms.separating_iff_T1 /-
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :

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

@@ -86,18 +86,24 @@ def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
 
 variable (p : SeminormFamily 𝕜 E ι)
 
+#print SeminormFamily.basisSets_iff /-
 theorem basisSets_iff {U : Set E} :
     U ∈ p.basis_sets ↔ ∃ (i : Finset ι) (r : _) (hr : 0 < r), U = ball (i.sup p) 0 r := by
   simp only [basis_sets, mem_Union, mem_singleton_iff]
 #align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iff
+-/
 
+#print SeminormFamily.basisSets_mem /-
 theorem basisSets_mem (i : Finset ι) {r : ℝ} (hr : 0 < r) : (i.sup p).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨i, _, hr, rfl⟩
 #align seminorm_family.basis_sets_mem SeminormFamily.basisSets_mem
+-/
 
+#print SeminormFamily.basisSets_singleton_mem /-
 theorem basisSets_singleton_mem (i : ι) {r : ℝ} (hr : 0 < r) : (p i).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨{i}, _, hr, by rw [Finset.sup_singleton]⟩
 #align seminorm_family.basis_sets_singleton_mem SeminormFamily.basisSets_singleton_mem
+-/
 
 #print SeminormFamily.basisSets_nonempty /-
 theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
@@ -108,6 +114,7 @@ theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
 #align seminorm_family.basis_sets_nonempty SeminormFamily.basisSets_nonempty
 -/
 
+#print SeminormFamily.basisSets_intersect /-
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
     ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
   classical
@@ -124,14 +131,18 @@ theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈
       (Set.iInter₂_mono' fun i hi =>
         ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
+-/
 
+#print SeminormFamily.basisSets_zero /-
 theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨ι', r, hr, hU⟩
   rw [hU, mem_ball_zero, map_zero]
   exact hr
 #align seminorm_family.basis_sets_zero SeminormFamily.basisSets_zero
+-/
 
+#print SeminormFamily.basisSets_add /-
 theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E) (H : V ∈ p.basis_sets), V + V ⊆ U :=
   by
@@ -141,7 +152,9 @@ theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
   refine' Set.Subset.trans (ball_add_ball_subset (s.sup p) (r / 2) (r / 2) 0 0) _
   rw [hU, add_zero, add_halves']
 #align seminorm_family.basis_sets_add SeminormFamily.basisSets_add
+-/
 
+#print SeminormFamily.basisSets_neg /-
 theorem basisSets_neg (U) (hU' : U ∈ p.basis_sets) :
     ∃ (V : Set E) (H : V ∈ p.basis_sets), V ⊆ (fun x : E => -x) ⁻¹' U :=
   by
@@ -149,6 +162,7 @@ theorem basisSets_neg (U) (hU' : U ∈ p.basis_sets) :
   rw [hU, neg_preimage, neg_ball (s.sup p), neg_zero]
   exact ⟨U, hU', Eq.subset hU⟩
 #align seminorm_family.basis_sets_neg SeminormFamily.basisSets_neg
+-/
 
 #print SeminormFamily.addGroupFilterBasis /-
 /-- The `add_group_filter_basis` induced by the filter basis `seminorm_basis_zero`. -/
@@ -158,6 +172,7 @@ protected def addGroupFilterBasis [Nonempty ι] : AddGroupFilterBasis E :=
 #align seminorm_family.add_group_filter_basis SeminormFamily.addGroupFilterBasis
 -/
 
+#print SeminormFamily.basisSets_smul_right /-
 theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∀ᶠ x : 𝕜 in 𝓝 0, x • v ∈ U :=
   by
@@ -171,9 +186,11 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
   simp_rw [le_antisymm (not_lt.mp h) (map_nonneg _ v), MulZeroClass.mul_zero, hr]
   exact IsOpen.mem_nhds isOpen_univ (mem_univ 0)
 #align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_right
+-/
 
 variable [Nonempty ι]
 
+#print SeminormFamily.basisSets_smul /-
 theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set 𝕜) (H : V ∈ 𝓝 (0 : 𝕜)) (W : Set E) (H : W ∈ p.AddGroupFilterBasis.sets), V • W ⊆ U :=
   by
@@ -183,7 +200,9 @@ theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
   refine' Set.Subset.trans (ball_smul_ball (s.sup p) r.sqrt r.sqrt) _
   rw [hU, Real.mul_self_sqrt (le_of_lt hr)]
 #align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smul
+-/
 
+#print SeminormFamily.basisSets_smul_left /-
 theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E) (H : V ∈ p.AddGroupFilterBasis.sets), V ⊆ (fun y : E => x • y) ⁻¹' U :=
   by
@@ -197,6 +216,7 @@ theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
   simp only [not_ne_iff.mp h, subset_def, mem_ball_zero, hr, mem_univ, map_zero, imp_true_iff,
     preimage_const_of_mem, zero_smul]
 #align seminorm_family.basis_sets_smul_left SeminormFamily.basisSets_smul_left
+-/
 
 #print SeminormFamily.moduleFilterBasis /-
 /-- The `module_filter_basis` induced by the filter basis `seminorm_basis_zero`. -/
@@ -209,6 +229,7 @@ protected def moduleFilterBasis : ModuleFilterBasis 𝕜 E
 #align seminorm_family.module_filter_basis SeminormFamily.moduleFilterBasis
 -/
 
+#print SeminormFamily.filter_eq_iInf /-
 theorem filter_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     p.ModuleFilterBasis.toFilterBasis.filterₓ = ⨅ i, (𝓝 0).comap (p i) :=
   by
@@ -229,6 +250,7 @@ theorem filter_eq_iInf (p : SeminormFamily 𝕜 E ι) :
         ⟨Metric.ball 0 r, Metric.ball_mem_nhds 0 hr,
           Eq.subset (p i).ball_zero_eq_preimage_ball.symm⟩
 #align seminorm_family.filter_eq_infi SeminormFamily.filter_eq_iInf
+-/
 
 end SeminormFamily
 
@@ -252,12 +274,15 @@ def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f :
 #align seminorm.is_bounded Seminorm.IsBounded
 -/
 
+#print Seminorm.isBounded_const /-
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
     IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι) (C : ℝ≥0), q.comp f ≤ C • s.sup p := by
   simp only [is_bounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
+-/
 
+#print Seminorm.const_isBounded /-
 theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) : IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, (q i).comp f ≤ C • p :=
   by
@@ -267,7 +292,9 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
   use {Classical.arbitrary ι}
   simp only [h, Finset.sup_singleton]
 #align seminorm.const_is_bounded Seminorm.const_isBounded
+-/
 
+#print Seminorm.isBounded_sup /-
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
     ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
@@ -287,6 +314,7 @@ theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂
   rw [Finset.sum_const, smul_assoc]
   exact le_rfl
 #align seminorm.is_bounded_sup Seminorm.isBounded_sup
+-/
 
 end Seminorm
 
@@ -303,28 +331,35 @@ structure WithSeminorms (p : SeminormFamily 𝕜 E ι) [t : TopologicalSpace E]
 #align with_seminorms WithSeminorms
 -/
 
+#print WithSeminorms.withSeminorms_eq /-
 theorem WithSeminorms.withSeminorms_eq {p : SeminormFamily 𝕜 E ι} [t : TopologicalSpace E]
     (hp : WithSeminorms p) : t = p.ModuleFilterBasis.topology :=
   hp.1
 #align with_seminorms.with_seminorms_eq WithSeminorms.withSeminorms_eq
+-/
 
 variable [TopologicalSpace E]
 
 variable {p : SeminormFamily 𝕜 E ι}
 
+#print WithSeminorms.topologicalAddGroup /-
 theorem WithSeminorms.topologicalAddGroup (hp : WithSeminorms p) : TopologicalAddGroup E :=
   by
   rw [hp.with_seminorms_eq]
   exact AddGroupFilterBasis.isTopologicalAddGroup _
 #align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroup
+-/
 
+#print WithSeminorms.hasBasis /-
 theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id :=
   by
   rw [congr_fun (congr_arg (@nhds E) hp.1) 0]
   exact AddGroupFilterBasis.nhds_zero_hasBasis _
 #align with_seminorms.has_basis WithSeminorms.hasBasis
+-/
 
+#print WithSeminorms.hasBasis_zero_ball /-
 theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball 0 sr.2 :=
   by
@@ -336,7 +371,9 @@ theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
   · rintro ⟨s, r, hr, hV⟩
     exact ⟨_, ⟨s, r, hr, rfl⟩, hV⟩
 #align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ball
+-/
 
+#print WithSeminorms.hasBasis_ball /-
 theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (𝓝 (x : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 :=
   by
@@ -348,22 +385,28 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     Eq.symm (Seminorm.vadd_ball (sr.fst.sup p))
   rwa [vadd_eq_add, add_zero] at this 
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
+-/
 
+#print WithSeminorms.mem_nhds_iff /-
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around `x`.-/
 theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
     U ∈ nhds x ↔ ∃ s : Finset ι, ∃ r > 0, (s.sup p).ball x r ⊆ U := by
   rw [hp.has_basis_ball.mem_iff, Prod.exists]
 #align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iff
+-/
 
+#print WithSeminorms.isOpen_iff_mem_balls /-
 /-- The open sets of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around all of their points.-/
 theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
     IsOpen U ↔ ∀ x ∈ U, ∃ s : Finset ι, ∃ r > 0, (s.sup p).ball x r ⊆ U := by
   simp_rw [← WithSeminorms.mem_nhds_iff hp _ U, isOpen_iff_mem_nhds]
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+#print WithSeminorms.T1_of_separating /-
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
 and `topological_add_group.t3_space` -/
@@ -379,7 +422,9 @@ theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
   refine' ⟨{i}, p i x, by positivity, subset_compl_singleton_iff.mpr _⟩
   rw [Finset.sup_singleton, mem_ball, zero_sub, map_neg_eq_map, not_lt]
 #align with_seminorms.t1_of_separating WithSeminorms.T1_of_separating
+-/
 
+#print WithSeminorms.separating_of_T1 /-
 /-- A family of seminorms inducing a T₁ topology is separating. -/
 theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
     ∃ i, p i x ≠ 0 := by
@@ -390,8 +435,10 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
   rintro ⟨s, r⟩ (hr : 0 < r)
   simp only [ball_finset_sup_eq_Inter _ _ _ hr, mem_Inter₂, mem_ball_zero, h, hr, forall_true_iff]
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+#print WithSeminorms.separating_iff_T1 /-
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :
     (∀ (x) (_ : x ≠ 0), ∃ i, p i x ≠ 0) ↔ T1Space E :=
@@ -400,6 +447,7 @@ theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :
   intro
   exact WithSeminorms.separating_of_T1 hp
 #align with_seminorms.separating_iff_t1 WithSeminorms.separating_iff_T1
+-/
 
 end Topology
 
@@ -409,6 +457,7 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [Topo
 
 variable {p : SeminormFamily 𝕜 E ι}
 
+#print WithSeminorms.tendsto_nhds' /-
 /-- Convergence along filters for `with_seminorms`.
 
 Variant with `finset.sup`. -/
@@ -416,7 +465,9 @@ theorem WithSeminorms.tendsto_nhds' (hp : WithSeminorms p) (u : F → E) {f : Fi
     Filter.Tendsto u f (𝓝 y₀) ↔ ∀ (s : Finset ι) (ε), 0 < ε → ∀ᶠ x in f, s.sup p (u x - y₀) < ε :=
   by simp [hp.has_basis_ball.tendsto_right_iff]
 #align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'
+-/
 
+#print WithSeminorms.tendsto_nhds /-
 /-- Convergence along filters for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
     Filter.Tendsto u f (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∀ᶠ x in f, p i (u x - y₀) < ε :=
@@ -426,9 +477,11 @@ theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Fil
     ⟨fun h i => by simpa only [Finset.sup_singleton] using h {i}, fun h s ε hε =>
       (s.eventually_all.2 fun i _ => h i ε hε).mono fun _ => finset_sup_apply_lt hε⟩
 #align with_seminorms.tendsto_nhds WithSeminorms.tendsto_nhds
+-/
 
 variable [SemilatticeSup F] [Nonempty F]
 
+#print WithSeminorms.tendsto_nhds_atTop /-
 /-- Limit `→ ∞` for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds_atTop (hp : WithSeminorms p) (u : F → E) (y₀ : E) :
     Filter.Tendsto u Filter.atTop (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∃ x₀, ∀ x, x₀ ≤ x → p i (u x - y₀) < ε :=
@@ -436,6 +489,7 @@ theorem WithSeminorms.tendsto_nhds_atTop (hp : WithSeminorms p) (u : F → E) (y
   rw [hp.tendsto_nhds u y₀]
   exact forall₃_congr fun _ _ _ => Filter.eventually_atTop
 #align with_seminorms.tendsto_nhds_at_top WithSeminorms.tendsto_nhds_atTop
+-/
 
 end Tendsto
 
@@ -447,8 +501,7 @@ variable [t : TopologicalSpace E] [TopologicalAddGroup E]
 
 variable [Nonempty ι]
 
-include t
-
+#print SeminormFamily.withSeminorms_of_nhds /-
 theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
     (h : 𝓝 (0 : E) = p.ModuleFilterBasis.toFilterBasis.filterₓ) : WithSeminorms p :=
   by
@@ -457,13 +510,17 @@ theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
   rw [AddGroupFilterBasis.nhds_zero_eq]
   exact h
 #align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminorms_of_nhds
+-/
 
+#print SeminormFamily.withSeminorms_of_hasBasis /-
 theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
     (h : (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id) : WithSeminorms p :=
   p.withSeminorms_of_nhds <|
     Filter.HasBasis.eq_of_same_basis h p.AddGroupFilterBasis.toFilterBasis.HasBasis
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
+-/
 
+#print SeminormFamily.withSeminorms_iff_nhds_eq_iInf /-
 theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 0 : Filter E) = ⨅ i, (𝓝 0).comap (p i) :=
   by
@@ -472,7 +529,9 @@ theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E
   rw [h.topology_eq_with_seminorms]
   exact AddGroupFilterBasis.nhds_zero_eq _
 #align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInf
+-/
 
+#print WithSeminorms.continuous_seminorm /-
 theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
     [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
     Continuous (p i) := by
@@ -480,8 +539,10 @@ theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module
   rw [p.with_seminorms_iff_nhds_eq_infi.mp hp, ball_zero_eq_preimage_ball]
   exact Filter.mem_iInf_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
+#print SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf /-
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
 each seminorm individually. We express this as a characterization of `with_seminorms p`. -/
 theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormFamily 𝕜 E ι) :
@@ -497,10 +558,10 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormF
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
   all_goals infer_instance
 #align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf
-
-omit t
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
+#print SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf /-
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
 induced by each seminorm individually. We express this as a characterization of
 `with_seminorms p`. -/
@@ -516,11 +577,13 @@ theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf [u : UniformSpace
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
   all_goals infer_instance
 #align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf
+-/
 
 end TopologicalAddGroup
 
 section NormedSpace
 
+#print norm_withSeminorms /-
 /-- The topology of a `normed_space 𝕜 E` is induced by the seminorm `norm_seminorm 𝕜 E`. -/
 theorem norm_withSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E] [NormedSpace 𝕜 E] :
     WithSeminorms fun _ : Fin 1 => normSeminorm 𝕜 E :=
@@ -543,6 +606,7 @@ theorem norm_withSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E
   rw [finset.not_nonempty_iff_eq_empty.mp h, Finset.sup_empty, ball_bot _ hr]
   exact Set.subset_univ _
 #align norm_with_seminorms norm_withSeminorms
+-/
 
 end NormedSpace
 
@@ -554,6 +618,7 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 variable [TopologicalSpace E]
 
+#print WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded /-
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
   by
@@ -578,14 +643,18 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   refine' Absorbs.mono_right _ h'
   exact (Finset.sup I p).ball_zero_absorbs_ball_zero hr
 #align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded
+-/
 
+#print WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded /-
 theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔
       ∀ I : Finset ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, I.sup p (f x) < r :=
   by simp_rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded, Set.ball_image_iff]
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
+-/
 
+#print WithSeminorms.isVonNBounded_iff_seminorm_bounded /-
 theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ i : ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, p i x < r :=
   by
@@ -607,12 +676,15 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
     exists_prop]
   exact ⟨1, zero_lt_one, fun _ _ => zero_lt_one⟩
 #align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_bounded
+-/
 
+#print WithSeminorms.image_isVonNBounded_iff_seminorm_bounded /-
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, p i (f x) < r :=
   by simp_rw [hp.is_vonN_bounded_iff_seminorm_bounded, Set.ball_image_iff]
 #align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_bounded
+-/
 
 end NontriviallyNormedField
 
@@ -634,6 +706,7 @@ variable {τ₁₂ : 𝕝 →+* 𝕝₂} [RingHomIsometric τ₁₂]
 
 variable [Nonempty ι] [Nonempty ι']
 
+#print Seminorm.continuous_of_continuous_comp /-
 theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i, Continuous ((q i).comp f)) : Continuous f :=
@@ -645,13 +718,17 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
   convert (hf i).ContinuousAt
   exact (map_zero _).symm
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
+-/
 
+#print Seminorm.continuous_iff_continuous_comp /-
 theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul 𝕜₂ F]
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) : Continuous f ↔ ∀ i, Continuous ((q i).comp f) :=
   ⟨fun h i => Continuous.comp (hq.continuous_seminorm i) h, continuous_of_continuous_comp hq f⟩
 #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp
+-/
 
+#print Seminorm.continuous_from_bounded /-
 theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'}
     [TopologicalSpace E] [TopologicalAddGroup E] (hp : WithSeminorms p) [TopologicalSpace F]
     [TopologicalAddGroup F] (hq : WithSeminorms q) (f : E →ₛₗ[τ₁₂] F)
@@ -671,7 +748,9 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
   refine' ball_antitone (smul_le_smul le_rfl _)
   simp only [le_add_iff_nonneg_right, zero_le']
 #align seminorm.continuous_from_bounded Seminorm.continuous_from_bounded
+-/
 
+#print Seminorm.cont_withSeminorms_normedSpace /-
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι) (C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
@@ -679,7 +758,9 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
   rw [← Seminorm.isBounded_const (Fin 1)] at hf 
   exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
+-/
 
+#print Seminorm.cont_normedSpace_to_withSeminorms /-
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
@@ -687,6 +768,7 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
   rw [← Seminorm.const_isBounded (Fin 1)] at hf 
   exact continuous_from_bounded (norm_withSeminorms 𝕝 E) hq f hf
 #align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminorms
+-/
 
 end Seminorm
 
@@ -699,6 +781,7 @@ open LocallyConvexSpace
 variable [Nonempty ι] [NormedField 𝕜] [NormedSpace ℝ 𝕜] [AddCommGroup E] [Module 𝕜 E] [Module ℝ E]
   [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E] [TopologicalAddGroup E]
 
+#print WithSeminorms.toLocallyConvexSpace /-
 theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
     LocallyConvexSpace ℝ E :=
   by
@@ -711,6 +794,7 @@ theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
     rcases hs with ⟨I, r, hr, rfl⟩
     exact convex_ball _ _ _
 #align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpace
+-/
 
 end LocallyConvexSpace
 
@@ -718,12 +802,14 @@ section NormedSpace
 
 variable (𝕜) [NormedField 𝕜] [NormedSpace ℝ 𝕜] [SeminormedAddCommGroup E]
 
+#print NormedSpace.toLocallyConvexSpace' /-
 /-- Not an instance since `𝕜` can't be inferred. See `normed_space.to_locally_convex_space` for a
 slightly weaker instance version. -/
 theorem NormedSpace.toLocallyConvexSpace' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
     LocallyConvexSpace ℝ E :=
   (norm_withSeminorms 𝕜 E).toLocallyConvexSpace
 #align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'
+-/
 
 #print NormedSpace.toLocallyConvexSpace /-
 /-- See `normed_space.to_locally_convex_space'` for a slightly stronger version which is not an
@@ -750,11 +836,14 @@ def SeminormFamily.comp (q : SeminormFamily 𝕜₂ F ι) (f : E →ₛₗ[σ₁
 #align seminorm_family.comp SeminormFamily.comp
 -/
 
+#print SeminormFamily.comp_apply /-
 theorem SeminormFamily.comp_apply (q : SeminormFamily 𝕜₂ F ι) (i : ι) (f : E →ₛₗ[σ₁₂] F) :
     q.comp f i = (q i).comp f :=
   rfl
 #align seminorm_family.comp_apply SeminormFamily.comp_apply
+-/
 
+#print SeminormFamily.finset_sup_comp /-
 theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Finset ι)
     (f : E →ₛₗ[σ₁₂] F) : (s.sup q).comp f = s.sup (q.comp f) :=
   by
@@ -762,9 +851,11 @@ theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Fi
   rw [Seminorm.comp_apply, Seminorm.finset_sup_apply, Seminorm.finset_sup_apply]
   rfl
 #align seminorm_family.finset_sup_comp SeminormFamily.finset_sup_comp
+-/
 
 variable [TopologicalSpace F] [TopologicalAddGroup F]
 
+#print LinearMap.withSeminorms_induced /-
 theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
     @WithSeminorms 𝕜 E ι _ _ _ _ (q.comp f) (induced f inferInstance) :=
@@ -776,13 +867,16 @@ theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily
   refine' iInf_congr fun i => _
   exact Filter.comap_comap
 #align linear_map.with_seminorms_induced LinearMap.withSeminorms_induced
+-/
 
+#print Inducing.withSeminorms /-
 theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι} (hq : WithSeminorms q)
     [TopologicalSpace E] {f : E →ₛₗ[σ₁₂] F} (hf : Inducing f) : WithSeminorms (q.comp f) :=
   by
   rw [hf.induced]
   exact f.with_seminorms_induced hq
 #align inducing.with_seminorms Inducing.withSeminorms
+-/
 
 end TopologicalConstructions
 
@@ -794,6 +888,7 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 variable [UniformSpace E] [UniformAddGroup E]
 
+#print WithSeminorms.first_countable /-
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology
 is first countable. -/
 theorem WithSeminorms.first_countable (hp : WithSeminorms p) :
@@ -806,6 +901,7 @@ theorem WithSeminorms.first_countable (hp : WithSeminorms p) :
   haveI : (uniformity E).IsCountablyGenerated := UniformAddGroup.uniformity_countably_generated
   exact UniformSpace.firstCountableTopology E
 #align with_seminorms.first_countable WithSeminorms.first_countable
+-/
 
 end TopologicalProperties
 

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

@@ -363,7 +363,7 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
   simp_rw [← WithSeminorms.mem_nhds_iff hp _ U, isOpen_iff_mem_nhds]
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
 and `topological_add_group.t3_space` -/
@@ -391,7 +391,7 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
   simp only [ball_finset_sup_eq_Inter _ _ _ hr, mem_Inter₂, mem_ball_zero, h, hr, forall_true_iff]
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :
     (∀ (x) (_ : x ≠ 0), ∃ i, p i x ≠ 0) ↔ T1Space E :=

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

@@ -111,18 +111,18 @@ theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
     ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
   classical
-    rcases p.basis_sets_iff.mp hU with ⟨s, r₁, hr₁, hU⟩
-    rcases p.basis_sets_iff.mp hV with ⟨t, r₂, hr₂, hV⟩
-    use ((s ∪ t).sup p).ball 0 (min r₁ r₂)
-    refine' ⟨p.basis_sets_mem (s ∪ t) (lt_min_iff.mpr ⟨hr₁, hr₂⟩), _⟩
-    rw [hU, hV, ball_finset_sup_eq_Inter _ _ _ (lt_min_iff.mpr ⟨hr₁, hr₂⟩),
-      ball_finset_sup_eq_Inter _ _ _ hr₁, ball_finset_sup_eq_Inter _ _ _ hr₂]
-    exact
-      Set.subset_inter
-        (Set.iInter₂_mono' fun i hi =>
-          ⟨i, Finset.subset_union_left _ _ hi, ball_mono <| min_le_left _ _⟩)
-        (Set.iInter₂_mono' fun i hi =>
-          ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
+  rcases p.basis_sets_iff.mp hU with ⟨s, r₁, hr₁, hU⟩
+  rcases p.basis_sets_iff.mp hV with ⟨t, r₂, hr₂, hV⟩
+  use ((s ∪ t).sup p).ball 0 (min r₁ r₂)
+  refine' ⟨p.basis_sets_mem (s ∪ t) (lt_min_iff.mpr ⟨hr₁, hr₂⟩), _⟩
+  rw [hU, hV, ball_finset_sup_eq_Inter _ _ _ (lt_min_iff.mpr ⟨hr₁, hr₂⟩),
+    ball_finset_sup_eq_Inter _ _ _ hr₁, ball_finset_sup_eq_Inter _ _ _ hr₂]
+  exact
+    Set.subset_inter
+      (Set.iInter₂_mono' fun i hi =>
+        ⟨i, Finset.subset_union_left _ _ hi, ball_mono <| min_le_left _ _⟩)
+      (Set.iInter₂_mono' fun i hi =>
+        ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
 
 theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
@@ -272,20 +272,20 @@ theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂
     (hf : IsBounded p q f) (s' : Finset ι') :
     ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
   classical
-    obtain rfl | hs' := s'.eq_empty_or_nonempty
-    · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
-    choose fₛ fC hf using hf
-    use s'.card • s'.sup fC, Finset.biUnion s' fₛ
-    have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.biUnion s' fₛ).sup p :=
-      by
-      intro i hi
-      refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
-      exact Finset.sup_mono (Finset.subset_biUnion_of_mem fₛ hi)
-    refine' (comp_mono f (finset_sup_le_sum q s')).trans _
-    simp_rw [← pullback_apply, AddMonoidHom.map_sum, pullback_apply]
-    refine' (Finset.sum_le_sum hs).trans _
-    rw [Finset.sum_const, smul_assoc]
-    exact le_rfl
+  obtain rfl | hs' := s'.eq_empty_or_nonempty
+  · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
+  choose fₛ fC hf using hf
+  use s'.card • s'.sup fC, Finset.biUnion s' fₛ
+  have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.biUnion s' fₛ).sup p :=
+    by
+    intro i hi
+    refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
+    exact Finset.sup_mono (Finset.subset_biUnion_of_mem fₛ hi)
+  refine' (comp_mono f (finset_sup_le_sum q s')).trans _
+  simp_rw [← pullback_apply, AddMonoidHom.map_sum, pullback_apply]
+  refine' (Finset.sum_le_sum hs).trans _
+  rw [Finset.sum_const, smul_assoc]
+  exact le_rfl
 #align seminorm.is_bounded_sup Seminorm.isBounded_sup
 
 end Seminorm
@@ -642,7 +642,7 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
   simp_rw [ContinuousAt, f.map_zero, q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.tendsto_iInf,
     Filter.tendsto_comap_iff]
   intro i
-  convert(hf i).ContinuousAt
+  convert (hf i).ContinuousAt
   exact (map_zero _).symm
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
 

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

@@ -87,7 +87,7 @@ def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
 variable (p : SeminormFamily 𝕜 E ι)
 
 theorem basisSets_iff {U : Set E} :
-    U ∈ p.basis_sets ↔ ∃ (i : Finset ι)(r : _)(hr : 0 < r), U = ball (i.sup p) 0 r := by
+    U ∈ p.basis_sets ↔ ∃ (i : Finset ι) (r : _) (hr : 0 < r), U = ball (i.sup p) 0 r := by
   simp only [basis_sets, mem_Union, mem_singleton_iff]
 #align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iff
 
@@ -109,7 +109,7 @@ theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
 -/
 
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
-    ∃ (z : Set E)(H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
+    ∃ (z : Set E) (H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
   classical
     rcases p.basis_sets_iff.mp hU with ⟨s, r₁, hr₁, hU⟩
     rcases p.basis_sets_iff.mp hV with ⟨t, r₂, hr₂, hV⟩
@@ -133,7 +133,7 @@ theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
 #align seminorm_family.basis_sets_zero SeminormFamily.basisSets_zero
 
 theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
-    ∃ (V : Set E)(H : V ∈ p.basis_sets), V + V ⊆ U :=
+    ∃ (V : Set E) (H : V ∈ p.basis_sets), V + V ⊆ U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨s, r, hr, hU⟩
   use (s.sup p).ball 0 (r / 2)
@@ -143,7 +143,7 @@ theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
 #align seminorm_family.basis_sets_add SeminormFamily.basisSets_add
 
 theorem basisSets_neg (U) (hU' : U ∈ p.basis_sets) :
-    ∃ (V : Set E)(H : V ∈ p.basis_sets), V ⊆ (fun x : E => -x) ⁻¹' U :=
+    ∃ (V : Set E) (H : V ∈ p.basis_sets), V ⊆ (fun x : E => -x) ⁻¹' U :=
   by
   rcases p.basis_sets_iff.mp hU' with ⟨s, r, hr, hU⟩
   rw [hU, neg_preimage, neg_ball (s.sup p), neg_zero]
@@ -175,7 +175,7 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
 variable [Nonempty ι]
 
 theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
-    ∃ (V : Set 𝕜)(H : V ∈ 𝓝 (0 : 𝕜))(W : Set E)(H : W ∈ p.AddGroupFilterBasis.sets), V • W ⊆ U :=
+    ∃ (V : Set 𝕜) (H : V ∈ 𝓝 (0 : 𝕜)) (W : Set E) (H : W ∈ p.AddGroupFilterBasis.sets), V • W ⊆ U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨s, r, hr, hU⟩
   refine' ⟨Metric.ball 0 r.sqrt, Metric.ball_mem_nhds 0 (real.sqrt_pos.mpr hr), _⟩
@@ -185,7 +185,7 @@ theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
 #align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smul
 
 theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
-    ∃ (V : Set E)(H : V ∈ p.AddGroupFilterBasis.sets), V ⊆ (fun y : E => x • y) ⁻¹' U :=
+    ∃ (V : Set E) (H : V ∈ p.AddGroupFilterBasis.sets), V ⊆ (fun y : E => x • y) ⁻¹' U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨s, r, hr, hU⟩
   rw [hU]
@@ -254,7 +254,7 @@ def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f :
 
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
-    IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι)(C : ℝ≥0), q.comp f ≤ C • s.sup p := by
+    IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι) (C : ℝ≥0), q.comp f ≤ C • s.sup p := by
   simp only [is_bounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
@@ -270,7 +270,7 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
 
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
-    ∃ (C : ℝ≥0)(s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
+    ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
   classical
     obtain rfl | hs' := s'.eq_empty_or_nonempty
     · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
@@ -346,7 +346,7 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
   ext sr : 1
   have : (sr.fst.sup p).ball (x +ᵥ 0) sr.snd = x +ᵥ (sr.fst.sup p).ball 0 sr.snd :=
     Eq.symm (Seminorm.vadd_ball (sr.fst.sup p))
-  rwa [vadd_eq_add, add_zero] at this
+  rwa [vadd_eq_add, add_zero] at this 
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
 
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
@@ -555,17 +555,17 @@ variable {p : SeminormFamily 𝕜 E ι}
 variable [TopologicalSpace E]
 
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
-    Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
+    Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
   by
   rw [hp.has_basis.isVonNBounded_basis_iff]
   constructor
   · intro h I
-    simp only [id.def] at h
+    simp only [id.def] at h 
     specialize h ((I.sup p).ball 0 1) (p.basis_sets_mem I zero_lt_one)
     rcases h with ⟨r, hr, h⟩
     cases' NormedField.exists_lt_norm 𝕜 r with a ha
     specialize h a (le_of_lt ha)
-    rw [Seminorm.smul_ball_zero (norm_pos_iff.1 <| hr.trans ha), mul_one] at h
+    rw [Seminorm.smul_ball_zero (norm_pos_iff.1 <| hr.trans ha), mul_one] at h 
     refine' ⟨‖a‖, lt_trans hr ha, _⟩
     intro x hx
     specialize h hx
@@ -574,7 +574,7 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   rcases p.basis_sets_iff.mp hs' with ⟨I, r, hr, hs'⟩
   rw [id.def, hs']
   rcases h I with ⟨r', hr', h'⟩
-  simp_rw [← (I.sup p).mem_ball_zero] at h'
+  simp_rw [← (I.sup p).mem_ball_zero] at h' 
   refine' Absorbs.mono_right _ h'
   exact (Finset.sup I p).ball_zero_absorbs_ball_zero hr
 #align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded
@@ -582,12 +582,12 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
 theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔
-      ∀ I : Finset ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, I.sup p (f x) < r :=
+      ∀ I : Finset ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, I.sup p (f x) < r :=
   by simp_rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded, Set.ball_image_iff]
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
 
 theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
-    Bornology.IsVonNBounded 𝕜 s ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i x < r :=
+    Bornology.IsVonNBounded 𝕜 s ↔ ∀ i : ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, p i x < r :=
   by
   rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded]
   constructor
@@ -610,7 +610,7 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
 
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
-    Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i (f x) < r :=
+    Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ (r : _) (hr : 0 < r), ∀ x ∈ s, p i (f x) < r :=
   by simp_rw [hp.is_vonN_bounded_iff_seminorm_bounded, Set.ball_image_iff]
 #align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_bounded
 
@@ -674,9 +674,9 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
 
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
-    (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι)(C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
+    (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι) (C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
     Continuous f := by
-  rw [← Seminorm.isBounded_const (Fin 1)] at hf
+  rw [← Seminorm.isBounded_const (Fin 1)] at hf 
   exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 
@@ -684,7 +684,7 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
     Continuous f := by
-  rw [← Seminorm.const_isBounded (Fin 1)] at hf
+  rw [← Seminorm.const_isBounded (Fin 1)] at hf 
   exact continuous_from_bounded (norm_withSeminorms 𝕝 E) hq f hf
 #align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminorms
 
@@ -706,8 +706,8 @@ theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
   · rw [hp.1, AddGroupFilterBasis.nhds_eq _, AddGroupFilterBasis.N_zero]
     exact FilterBasis.hasBasis _
   · intro s hs
-    change s ∈ Set.iUnion _ at hs
-    simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs
+    change s ∈ Set.iUnion _ at hs 
+    simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs 
     rcases hs with ⟨I, r, hr, rfl⟩
     exact convex_ball _ _ _
 #align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpace

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

@@ -56,7 +56,7 @@ seminorm, locally convex
 
 open NormedField Set Seminorm TopologicalSpace
 
-open BigOperators NNReal Pointwise Topology
+open scoped BigOperators NNReal Pointwise Topology
 
 variable {𝕜 𝕜₂ 𝕝 𝕝₂ E F G ι ι' : Type _}
 

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

@@ -86,27 +86,15 @@ def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
 
 variable (p : SeminormFamily 𝕜 E ι)
 
-/- warning: seminorm_family.basis_sets_iff -> SeminormFamily.basisSets_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iffₓ'. -/
 theorem basisSets_iff {U : Set E} :
     U ∈ p.basis_sets ↔ ∃ (i : Finset ι)(r : _)(hr : 0 < r), U = ball (i.sup p) 0 r := by
   simp only [basis_sets, mem_Union, mem_singleton_iff]
 #align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iff
 
-/- warning: seminorm_family.basis_sets_mem -> SeminormFamily.basisSets_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_mem SeminormFamily.basisSets_memₓ'. -/
 theorem basisSets_mem (i : Finset ι) {r : ℝ} (hr : 0 < r) : (i.sup p).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨i, _, hr, rfl⟩
 #align seminorm_family.basis_sets_mem SeminormFamily.basisSets_mem
 
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-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_singleton_mem SeminormFamily.basisSets_singleton_memₓ'. -/
 theorem basisSets_singleton_mem (i : ι) {r : ℝ} (hr : 0 < r) : (p i).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨{i}, _, hr, by rw [Finset.sup_singleton]⟩
 #align seminorm_family.basis_sets_singleton_mem SeminormFamily.basisSets_singleton_mem
@@ -120,12 +108,6 @@ theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
 #align seminorm_family.basis_sets_nonempty SeminormFamily.basisSets_nonempty
 -/
 
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-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersectₓ'. -/
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
     ∃ (z : Set E)(H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
   classical
@@ -143,12 +125,6 @@ theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈
           ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
 
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-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_zero SeminormFamily.basisSets_zeroₓ'. -/
 theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨ι', r, hr, hU⟩
@@ -156,12 +132,6 @@ theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
   exact hr
 #align seminorm_family.basis_sets_zero SeminormFamily.basisSets_zero
 
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-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_add SeminormFamily.basisSets_addₓ'. -/
 theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.basis_sets), V + V ⊆ U :=
   by
@@ -172,12 +142,6 @@ theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
   rw [hU, add_zero, add_halves']
 #align seminorm_family.basis_sets_add SeminormFamily.basisSets_add
 
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-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_neg SeminormFamily.basisSets_negₓ'. -/
 theorem basisSets_neg (U) (hU' : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.basis_sets), V ⊆ (fun x : E => -x) ⁻¹' U :=
   by
@@ -194,9 +158,6 @@ protected def addGroupFilterBasis [Nonempty ι] : AddGroupFilterBasis E :=
 #align seminorm_family.add_group_filter_basis SeminormFamily.addGroupFilterBasis
 -/
 
-/- warning: seminorm_family.basis_sets_smul_right -> SeminormFamily.basisSets_smul_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_rightₓ'. -/
 theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∀ᶠ x : 𝕜 in 𝓝 0, x • v ∈ U :=
   by
@@ -213,9 +174,6 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
 
 variable [Nonempty ι]
 
-/- warning: seminorm_family.basis_sets_smul -> SeminormFamily.basisSets_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smulₓ'. -/
 theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set 𝕜)(H : V ∈ 𝓝 (0 : 𝕜))(W : Set E)(H : W ∈ p.AddGroupFilterBasis.sets), V • W ⊆ U :=
   by
@@ -226,9 +184,6 @@ theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
   rw [hU, Real.mul_self_sqrt (le_of_lt hr)]
 #align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smul
 
-/- warning: seminorm_family.basis_sets_smul_left -> SeminormFamily.basisSets_smul_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul_left SeminormFamily.basisSets_smul_leftₓ'. -/
 theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.AddGroupFilterBasis.sets), V ⊆ (fun y : E => x • y) ⁻¹' U :=
   by
@@ -254,9 +209,6 @@ protected def moduleFilterBasis : ModuleFilterBasis 𝕜 E
 #align seminorm_family.module_filter_basis SeminormFamily.moduleFilterBasis
 -/
 
-/- warning: seminorm_family.filter_eq_infi -> SeminormFamily.filter_eq_iInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.filter_eq_infi SeminormFamily.filter_eq_iInfₓ'. -/
 theorem filter_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     p.ModuleFilterBasis.toFilterBasis.filterₓ = ⨅ i, (𝓝 0).comap (p i) :=
   by
@@ -300,18 +252,12 @@ def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f :
 #align seminorm.is_bounded Seminorm.IsBounded
 -/
 
-/- warning: seminorm.is_bounded_const -> Seminorm.isBounded_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.is_bounded_const Seminorm.isBounded_constₓ'. -/
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
     IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι)(C : ℝ≥0), q.comp f ≤ C • s.sup p := by
   simp only [is_bounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
-/- warning: seminorm.const_is_bounded -> Seminorm.const_isBounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.const_is_bounded Seminorm.const_isBoundedₓ'. -/
 theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) : IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, (q i).comp f ≤ C • p :=
   by
@@ -322,9 +268,6 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
   simp only [h, Finset.sup_singleton]
 #align seminorm.const_is_bounded Seminorm.const_isBounded
 
-/- warning: seminorm.is_bounded_sup -> Seminorm.isBounded_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.is_bounded_sup Seminorm.isBounded_supₓ'. -/
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
     ∃ (C : ℝ≥0)(s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
@@ -360,12 +303,6 @@ structure WithSeminorms (p : SeminormFamily 𝕜 E ι) [t : TopologicalSpace E]
 #align with_seminorms WithSeminorms
 -/
 
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-Case conversion may be inaccurate. Consider using '#align with_seminorms.with_seminorms_eq WithSeminorms.withSeminorms_eqₓ'. -/
 theorem WithSeminorms.withSeminorms_eq {p : SeminormFamily 𝕜 E ι} [t : TopologicalSpace E]
     (hp : WithSeminorms p) : t = p.ModuleFilterBasis.topology :=
   hp.1
@@ -375,24 +312,12 @@ variable [TopologicalSpace E]
 
 variable {p : SeminormFamily 𝕜 E ι}
 
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-Case conversion may be inaccurate. Consider using '#align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroupₓ'. -/
 theorem WithSeminorms.topologicalAddGroup (hp : WithSeminorms p) : TopologicalAddGroup E :=
   by
   rw [hp.with_seminorms_eq]
   exact AddGroupFilterBasis.isTopologicalAddGroup _
 #align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroup
 
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-Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis WithSeminorms.hasBasisₓ'. -/
 theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id :=
   by
@@ -400,9 +325,6 @@ theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
   exact AddGroupFilterBasis.nhds_zero_hasBasis _
 #align with_seminorms.has_basis WithSeminorms.hasBasis
 
-/- warning: with_seminorms.has_basis_zero_ball -> WithSeminorms.hasBasis_zero_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ballₓ'. -/
 theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball 0 sr.2 :=
   by
@@ -415,9 +337,6 @@ theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
     exact ⟨_, ⟨s, r, hr, rfl⟩, hV⟩
 #align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ball
 
-/- warning: with_seminorms.has_basis_ball -> WithSeminorms.hasBasis_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ballₓ'. -/
 theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (𝓝 (x : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 :=
   by
@@ -430,9 +349,6 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
   rwa [vadd_eq_add, add_zero] at this
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
 
-/- warning: with_seminorms.mem_nhds_iff -> WithSeminorms.mem_nhds_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iffₓ'. -/
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around `x`.-/
 theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
@@ -440,9 +356,6 @@ theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
   rw [hp.has_basis_ball.mem_iff, Prod.exists]
 #align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iff
 
-/- warning: with_seminorms.is_open_iff_mem_balls -> WithSeminorms.isOpen_iff_mem_balls is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_ballsₓ'. -/
 /-- The open sets of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around all of their points.-/
 theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
@@ -450,9 +363,6 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
   simp_rw [← WithSeminorms.mem_nhds_iff hp _ U, isOpen_iff_mem_nhds]
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 
-/- warning: with_seminorms.t1_of_separating -> WithSeminorms.T1_of_separating is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.t1_of_separating WithSeminorms.T1_of_separatingₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
@@ -470,9 +380,6 @@ theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
   rw [Finset.sup_singleton, mem_ball, zero_sub, map_neg_eq_map, not_lt]
 #align with_seminorms.t1_of_separating WithSeminorms.T1_of_separating
 
-/- warning: with_seminorms.separating_of_t1 -> WithSeminorms.separating_of_T1 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1ₓ'. -/
 /-- A family of seminorms inducing a T₁ topology is separating. -/
 theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
     ∃ i, p i x ≠ 0 := by
@@ -484,9 +391,6 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
   simp only [ball_finset_sup_eq_Inter _ _ _ hr, mem_Inter₂, mem_ball_zero, h, hr, forall_true_iff]
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
 
-/- warning: with_seminorms.separating_iff_t1 -> WithSeminorms.separating_iff_T1 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.separating_iff_t1 WithSeminorms.separating_iff_T1ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :
@@ -505,9 +409,6 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [Topo
 
 variable {p : SeminormFamily 𝕜 E ι}
 
-/- warning: with_seminorms.tendsto_nhds' -> WithSeminorms.tendsto_nhds' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'ₓ'. -/
 /-- Convergence along filters for `with_seminorms`.
 
 Variant with `finset.sup`. -/
@@ -516,9 +417,6 @@ theorem WithSeminorms.tendsto_nhds' (hp : WithSeminorms p) (u : F → E) {f : Fi
   by simp [hp.has_basis_ball.tendsto_right_iff]
 #align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'
 
-/- warning: with_seminorms.tendsto_nhds -> WithSeminorms.tendsto_nhds is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds WithSeminorms.tendsto_nhdsₓ'. -/
 /-- Convergence along filters for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
     Filter.Tendsto u f (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∀ᶠ x in f, p i (u x - y₀) < ε :=
@@ -531,9 +429,6 @@ theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Fil
 
 variable [SemilatticeSup F] [Nonempty F]
 
-/- warning: with_seminorms.tendsto_nhds_at_top -> WithSeminorms.tendsto_nhds_atTop is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds_at_top WithSeminorms.tendsto_nhds_atTopₓ'. -/
 /-- Limit `→ ∞` for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds_atTop (hp : WithSeminorms p) (u : F → E) (y₀ : E) :
     Filter.Tendsto u Filter.atTop (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∃ x₀, ∀ x, x₀ ≤ x → p i (u x - y₀) < ε :=
@@ -554,12 +449,6 @@ variable [Nonempty ι]
 
 include t
 
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 theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
     (h : 𝓝 (0 : E) = p.ModuleFilterBasis.toFilterBasis.filterₓ) : WithSeminorms p :=
   by
@@ -569,21 +458,12 @@ theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
   exact h
 #align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminorms_of_nhds
 
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 theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
     (h : (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id) : WithSeminorms p :=
   p.withSeminorms_of_nhds <|
     Filter.HasBasis.eq_of_same_basis h p.AddGroupFilterBasis.toFilterBasis.HasBasis
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
-/- warning: seminorm_family.with_seminorms_iff_nhds_eq_infi -> SeminormFamily.withSeminorms_iff_nhds_eq_iInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInfₓ'. -/
 theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 0 : Filter E) = ⨅ i, (𝓝 0).comap (p i) :=
   by
@@ -593,9 +473,6 @@ theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E
   exact AddGroupFilterBasis.nhds_zero_eq _
 #align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInf
 
-/- warning: with_seminorms.continuous_seminorm -> WithSeminorms.continuous_seminorm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminormₓ'. -/
 theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
     [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
     Continuous (p i) := by
@@ -604,9 +481,6 @@ theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module
   exact Filter.mem_iInf_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
 
-/- warning: seminorm_family.with_seminorms_iff_topological_space_eq_infi -> SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
 each seminorm individually. We express this as a characterization of `with_seminorms p`. -/
@@ -626,9 +500,6 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormF
 
 omit t
 
-/- warning: seminorm_family.with_seminorms_iff_uniform_space_eq_infi -> SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
 induced by each seminorm individually. We express this as a characterization of
@@ -650,12 +521,6 @@ end TopologicalAddGroup
 
 section NormedSpace
 
-/- warning: norm_with_seminorms -> norm_withSeminorms is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2], WithSeminorms.{u1, u2, 0} 𝕜 E (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) _inst_1 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (instNonempty.{1} (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.inhabited (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) => normSeminorm.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)))
-but is expected to have type
-  forall (𝕜 : Type.{u2}) (E : Type.{u1}) [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2], WithSeminorms.{u2, u1, 0} 𝕜 E (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) _inst_1 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) (instNonempty.{1} (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instInhabitedFinSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) => normSeminorm.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)))
-Case conversion may be inaccurate. Consider using '#align norm_with_seminorms norm_withSeminormsₓ'. -/
 /-- The topology of a `normed_space 𝕜 E` is induced by the seminorm `norm_seminorm 𝕜 E`. -/
 theorem norm_withSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E] [NormedSpace 𝕜 E] :
     WithSeminorms fun _ : Fin 1 => normSeminorm 𝕜 E :=
@@ -689,9 +554,6 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 variable [TopologicalSpace E]
 
-/- warning: with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded -> WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedₓ'. -/
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
   by
@@ -717,9 +579,6 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   exact (Finset.sup I p).ball_zero_absorbs_ball_zero hr
 #align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded
 
-/- warning: with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded -> WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_boundedₓ'. -/
 theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔
@@ -727,9 +586,6 @@ theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G →
   by simp_rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded, Set.ball_image_iff]
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
 
-/- warning: with_seminorms.is_vonN_bounded_iff_seminorm_bounded -> WithSeminorms.isVonNBounded_iff_seminorm_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_boundedₓ'. -/
 theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i x < r :=
   by
@@ -752,9 +608,6 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
   exact ⟨1, zero_lt_one, fun _ _ => zero_lt_one⟩
 #align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_bounded
 
-/- warning: with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded -> WithSeminorms.image_isVonNBounded_iff_seminorm_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_boundedₓ'. -/
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i (f x) < r :=
@@ -781,9 +634,6 @@ variable {τ₁₂ : 𝕝 →+* 𝕝₂} [RingHomIsometric τ₁₂]
 
 variable [Nonempty ι] [Nonempty ι']
 
-/- warning: seminorm.continuous_of_continuous_comp -> Seminorm.continuous_of_continuous_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_compₓ'. -/
 theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i, Continuous ((q i).comp f)) : Continuous f :=
@@ -796,18 +646,12 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
   exact (map_zero _).symm
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
 
-/- warning: seminorm.continuous_iff_continuous_comp -> Seminorm.continuous_iff_continuous_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_compₓ'. -/
 theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul 𝕜₂ F]
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) : Continuous f ↔ ∀ i, Continuous ((q i).comp f) :=
   ⟨fun h i => Continuous.comp (hq.continuous_seminorm i) h, continuous_of_continuous_comp hq f⟩
 #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp
 
-/- warning: seminorm.continuous_from_bounded -> Seminorm.continuous_from_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.continuous_from_bounded Seminorm.continuous_from_boundedₓ'. -/
 theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'}
     [TopologicalSpace E] [TopologicalAddGroup E] (hp : WithSeminorms p) [TopologicalSpace F]
     [TopologicalAddGroup F] (hq : WithSeminorms q) (f : E →ₛₗ[τ₁₂] F)
@@ -828,9 +672,6 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
   simp only [le_add_iff_nonneg_right, zero_le']
 #align seminorm.continuous_from_bounded Seminorm.continuous_from_bounded
 
-/- warning: seminorm.cont_with_seminorms_normed_space -> Seminorm.cont_withSeminorms_normedSpace is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpaceₓ'. -/
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι)(C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
@@ -839,9 +680,6 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
   exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 
-/- warning: seminorm.cont_normed_space_to_with_seminorms -> Seminorm.cont_normedSpace_to_withSeminorms is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminormsₓ'. -/
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
@@ -861,9 +699,6 @@ open LocallyConvexSpace
 variable [Nonempty ι] [NormedField 𝕜] [NormedSpace ℝ 𝕜] [AddCommGroup E] [Module 𝕜 E] [Module ℝ E]
   [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E] [TopologicalAddGroup E]
 
-/- warning: with_seminorms.to_locally_convex_space -> WithSeminorms.toLocallyConvexSpace is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpaceₓ'. -/
 theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
     LocallyConvexSpace ℝ E :=
   by
@@ -883,9 +718,6 @@ section NormedSpace
 
 variable (𝕜) [NormedField 𝕜] [NormedSpace ℝ 𝕜] [SeminormedAddCommGroup E]
 
-/- warning: normed_space.to_locally_convex_space' -> NormedSpace.toLocallyConvexSpace' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'ₓ'. -/
 /-- Not an instance since `𝕜` can't be inferred. See `normed_space.to_locally_convex_space` for a
 slightly weaker instance version. -/
 theorem NormedSpace.toLocallyConvexSpace' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
@@ -918,17 +750,11 @@ def SeminormFamily.comp (q : SeminormFamily 𝕜₂ F ι) (f : E →ₛₗ[σ₁
 #align seminorm_family.comp SeminormFamily.comp
 -/
 
-/- warning: seminorm_family.comp_apply -> SeminormFamily.comp_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.comp_apply SeminormFamily.comp_applyₓ'. -/
 theorem SeminormFamily.comp_apply (q : SeminormFamily 𝕜₂ F ι) (i : ι) (f : E →ₛₗ[σ₁₂] F) :
     q.comp f i = (q i).comp f :=
   rfl
 #align seminorm_family.comp_apply SeminormFamily.comp_apply
 
-/- warning: seminorm_family.finset_sup_comp -> SeminormFamily.finset_sup_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align seminorm_family.finset_sup_comp SeminormFamily.finset_sup_compₓ'. -/
 theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Finset ι)
     (f : E →ₛₗ[σ₁₂] F) : (s.sup q).comp f = s.sup (q.comp f) :=
   by
@@ -939,9 +765,6 @@ theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Fi
 
 variable [TopologicalSpace F] [TopologicalAddGroup F]
 
-/- warning: linear_map.with_seminorms_induced -> LinearMap.withSeminorms_induced is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.with_seminorms_induced LinearMap.withSeminorms_inducedₓ'. -/
 theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
     @WithSeminorms 𝕜 E ι _ _ _ _ (q.comp f) (induced f inferInstance) :=
@@ -954,9 +777,6 @@ theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily
   exact Filter.comap_comap
 #align linear_map.with_seminorms_induced LinearMap.withSeminorms_induced
 
-/- warning: inducing.with_seminorms -> Inducing.withSeminorms is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inducing.with_seminorms Inducing.withSeminormsₓ'. -/
 theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι} (hq : WithSeminorms q)
     [TopologicalSpace E] {f : E →ₛₗ[σ₁₂] F} (hf : Inducing f) : WithSeminorms (q.comp f) :=
   by
@@ -974,12 +794,6 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 variable [UniformSpace E] [UniformAddGroup E]
 
-/- warning: with_seminorms.first_countable -> WithSeminorms.first_countable is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : Countable.{succ u3} ι] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_6 : UniformSpace.{u2} E] [_inst_7 : UniformAddGroup.{u2} E _inst_6 (AddCommGroup.toAddGroup.{u2} E _inst_2)], (WithSeminorms.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p (UniformSpace.toTopologicalSpace.{u2} E _inst_6)) -> (TopologicalSpace.FirstCountableTopology.{u2} E (UniformSpace.toTopologicalSpace.{u2} E _inst_6))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : Countable.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_6 : UniformSpace.{u2} E] [_inst_7 : UniformAddGroup.{u2} E _inst_6 (AddCommGroup.toAddGroup.{u2} E _inst_2)], (WithSeminorms.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p (UniformSpace.toTopologicalSpace.{u2} E _inst_6)) -> (TopologicalSpace.FirstCountableTopology.{u2} E (UniformSpace.toTopologicalSpace.{u2} E _inst_6))
-Case conversion may be inaccurate. Consider using '#align with_seminorms.first_countable WithSeminorms.first_countableₓ'. -/
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology
 is first countable. -/
 theorem WithSeminorms.first_countable (hp : WithSeminorms p) :

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

@@ -741,8 +741,7 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
   intro hi I
   by_cases hI : I.nonempty
   · choose r hr h using hi
-    have h' : 0 < I.sup' hI r := by
-      rcases hI.bex with ⟨i, hi⟩
+    have h' : 0 < I.sup' hI r := by rcases hI.bex with ⟨i, hi⟩;
       exact lt_of_lt_of_le (hr i) (Finset.le_sup' r hi)
     refine' ⟨I.sup' hI r, h', fun x hx => finset_sup_apply_lt h' fun i hi => _⟩
     refine' lt_of_lt_of_le (h i x hx) _

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

@@ -87,10 +87,7 @@ def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
 variable (p : SeminormFamily 𝕜 E ι)
 
 /- warning: seminorm_family.basis_sets_iff -> SeminormFamily.basisSets_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) {U : Set.{u2} E}, Iff (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (Exists.{succ u3} (Finset.{u3} ι) (fun (i : Finset.{u3} ι) => Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => Eq.{succ u2} (Set.{u2} E) U (Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 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𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) r)))))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) {U : Set.{u3} E}, Iff (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (Exists.{succ u1} (Finset.{u1} ι) (fun (i : Finset.{u1} ι) => Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) (fun (hr : LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) => Eq.{succ u3} (Set.{u3} E) U (Seminorm.ball.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Finset.sup.{u3, u1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))))) r)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iffₓ'. -/
 theorem basisSets_iff {U : Set E} :
     U ∈ p.basis_sets ↔ ∃ (i : Finset ι)(r : _)(hr : 0 < r), U = ball (i.sup p) 0 r := by
@@ -98,10 +95,7 @@ theorem basisSets_iff {U : Set E} :
 #align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iff
 
 /- warning: seminorm_family.basis_sets_mem -> SeminormFamily.basisSets_mem is a dubious translation:
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𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E 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(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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) r) (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (i : Finset.{u3} ι) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Membership.mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.instMembershipSet.{u2} (Set.{u2} E)) (Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))))) r) (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_mem SeminormFamily.basisSets_memₓ'. -/
 theorem basisSets_mem (i : Finset ι) {r : ℝ} (hr : 0 < r) : (i.sup p).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨i, _, hr, rfl⟩
@@ -201,10 +195,7 @@ protected def addGroupFilterBasis [Nonempty ι] : AddGroupFilterBasis E :=
 -/
 
 /- warning: seminorm_family.basis_sets_smul_right -> SeminormFamily.basisSets_smul_right is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_rightₓ'. -/
 theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∀ᶠ x : 𝕜 in 𝓝 0, x • v ∈ U :=
@@ -223,10 +214,7 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
 variable [Nonempty ι]
 
 /- warning: seminorm_family.basis_sets_smul -> SeminormFamily.basisSets_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smulₓ'. -/
 theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set 𝕜)(H : V ∈ 𝓝 (0 : 𝕜))(W : Set E)(H : W ∈ p.AddGroupFilterBasis.sets), V • W ⊆ U :=
@@ -239,10 +227,7 @@ theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
 #align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smul
 
 /- warning: seminorm_family.basis_sets_smul_left -> SeminormFamily.basisSets_smul_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul_left SeminormFamily.basisSets_smul_leftₓ'. -/
 theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.AddGroupFilterBasis.sets), V ⊆ (fun y : E => x • y) ⁻¹' U :=
@@ -270,10 +255,7 @@ protected def moduleFilterBasis : ModuleFilterBasis 𝕜 E
 -/
 
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_inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i)) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.filter_eq_infi SeminormFamily.filter_eq_iInfₓ'. -/
 theorem filter_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     p.ModuleFilterBasis.toFilterBasis.filterₓ = ⨅ i, (𝓝 0).comap (p i) :=
@@ -319,10 +301,7 @@ def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f :
 -/
 
 /- warning: seminorm.is_bounded_const -> Seminorm.isBounded_const is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (ι' : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι'] {p : ι -> (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))} {q : Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))} (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u1, u2, u3, u4, u5, u6} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p (fun (_x : ι') => q) f) (Exists.{succ u5} (Finset.{u5} ι) (fun (s : Finset.{u5} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.partialOrder.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 q f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (Finset.sup.{u3, u5} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {𝕜₂ : Type.{u3}} {E : Type.{u4}} {F : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : AddCommGroup.{u4} E] [_inst_3 : Module.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2)] [_inst_4 : NormedField.{u3} 𝕜₂] [_inst_5 : AddCommGroup.{u2} F] [_inst_6 : Module.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)] {σ₁₂ : RingHom.{u5, u3} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u5, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u5} 𝕜 _inst_1) (NormedField.toNorm.{u3} 𝕜₂ _inst_4) σ₁₂] (ι' : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι'] {p : ι -> (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3)))))} {q : Seminorm.{u3, u2} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u2} F _inst_5) (SMulZeroClass.toSMul.{u3, u2} 𝕜₂ F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜₂ F (CommMonoidWithZero.toZero.{u3} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜₂ (Semifield.toCommGroupWithZero.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (Module.toMulActionWithZero.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6))))} (f : LinearMap.{u5, u3, u4, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u5, u3, u4, u2, u1, u6} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p (fun (_x : ι') => q) f) (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Preorder.toLE.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instPartialOrder.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))))) (Seminorm.comp.{u5, u3, u4, u2} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 q f) (HSMul.hSMul.{0, u4, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (instHSMul.{0, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instSMul.{0, u5, u4} NNReal 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (Finset.sup.{u4, u1} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.is_bounded_const Seminorm.isBounded_constₓ'. -/
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
@@ -331,10 +310,7 @@ theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
 /- warning: seminorm.const_is_bounded -> Seminorm.const_isBounded is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι' : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (ι : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι] {p : Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))} {q : ι' -> (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6)))))} (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u1, u2, u3, u4, u6, u5} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 (fun (_x : ι) => p) q f) (forall (i : ι'), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.partialOrder.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C p)))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {𝕜₂ : Type.{u3}} {E : Type.{u4}} {F : Type.{u2}} {ι' : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : AddCommGroup.{u4} E] [_inst_3 : Module.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2)] [_inst_4 : NormedField.{u3} 𝕜₂] [_inst_5 : AddCommGroup.{u2} F] [_inst_6 : Module.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)] {σ₁₂ : RingHom.{u5, u3} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u5, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u5} 𝕜 _inst_1) (NormedField.toNorm.{u3} 𝕜₂ _inst_4) σ₁₂] (ι : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι] {p : Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))} {q : ι' -> (Seminorm.{u3, u2} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u2} F _inst_5) (SMulZeroClass.toSMul.{u3, u2} 𝕜₂ F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜₂ F (CommMonoidWithZero.toZero.{u3} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜₂ (Semifield.toCommGroupWithZero.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (Module.toMulActionWithZero.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6)))))} (f : LinearMap.{u5, u3, u4, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u5, u3, u4, u2, u6, u1} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 (fun (_x : ι) => p) q f) (forall (i : ι'), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Preorder.toLE.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instPartialOrder.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))))) (Seminorm.comp.{u5, u3, u4, u2} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f) (HSMul.hSMul.{0, u4, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (instHSMul.{0, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instSMul.{0, u5, u4} NNReal 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C p)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.const_is_bounded Seminorm.const_isBoundedₓ'. -/
 theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) : IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, (q i).comp f ≤ C • p :=
@@ -347,10 +323,7 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
 #align seminorm.const_is_bounded Seminorm.const_isBounded
 
 /- warning: seminorm.is_bounded_sup -> Seminorm.isBounded_sup is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} {ι' : Type.{u6}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] {p : ι -> (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))} {q : ι' -> (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6)))))} {f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6}, (Seminorm.IsBounded.{u1, u2, u3, u4, u5, u6} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p q f) -> (forall (s' : Finset.{u6} ι'), Exists.{1} NNReal (fun (C : NNReal) => Exists.{succ u5} (Finset.{u5} ι) (fun (s : Finset.{u5} ι) => LE.le.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.partialOrder.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u4, u6} (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) ι' (Seminorm.semilatticeSup.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) (Seminorm.orderBot.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) _inst_5 _inst_6) s' q) f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (Finset.sup.{u3, u5} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
-but is expected to have type
-  forall {𝕜 : Type.{u6}} {𝕜₂ : Type.{u4}} {E : Type.{u5}} {F : Type.{u3}} {ι : Type.{u2}} {ι' : Type.{u1}} [_inst_1 : NormedField.{u6} 𝕜] [_inst_2 : AddCommGroup.{u5} E] [_inst_3 : Module.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2)] [_inst_4 : NormedField.{u4} 𝕜₂] [_inst_5 : AddCommGroup.{u3} F] [_inst_6 : Module.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5)] {σ₁₂ : RingHom.{u6, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u6, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u6} 𝕜 _inst_1) (NormedField.toNorm.{u4} 𝕜₂ _inst_4) σ₁₂] {p : ι -> (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3)))))} {q : ι' -> (Seminorm.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u3} F _inst_5) (SMulZeroClass.toSMul.{u4, u3} 𝕜₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜₂ F (CommMonoidWithZero.toZero.{u4} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜₂ (Semifield.toCommGroupWithZero.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (Module.toMulActionWithZero.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_6)))))} {f : LinearMap.{u6, u4, u5, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6}, (Seminorm.IsBounded.{u6, u4, u5, u3, u2, u1} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p q f) -> (forall (s' : Finset.{u1} ι'), Exists.{1} NNReal (fun (C : NNReal) => Exists.{succ u2} (Finset.{u2} ι) (fun (s : Finset.{u2} ι) => LE.le.{u5} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Preorder.toLE.{u5} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u5} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.instPartialOrder.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))))) (Seminorm.comp.{u6, u4, u5, u3} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u3, u1} (Seminorm.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u3} F _inst_5) (SMulZeroClass.toSMul.{u4, u3} 𝕜₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜₂ F (CommMonoidWithZero.toZero.{u4} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜₂ (Semifield.toCommGroupWithZero.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (Module.toMulActionWithZero.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_6))))) ι' (Seminorm.instSemilatticeSup.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u3} F _inst_5) (SMulZeroClass.toSMul.{u4, u3} 𝕜₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜₂ F (CommMonoidWithZero.toZero.{u4} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜₂ (Semifield.toCommGroupWithZero.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (Module.toMulActionWithZero.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_6))))) (Seminorm.instOrderBot.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) _inst_5 _inst_6) s' q) f) (HSMul.hSMul.{0, u5, u5} NNReal (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (instHSMul.{0, u5} NNReal (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.instSMul.{0, u6, u5} NNReal 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (Finset.sup.{u5, u2} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.is_bounded_sup Seminorm.isBounded_supₓ'. -/
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
@@ -428,10 +401,7 @@ theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
 #align with_seminorms.has_basis WithSeminorms.hasBasis
 
 /- warning: with_seminorms.has_basis_zero_ball -> WithSeminorms.hasBasis_zero_ball is a dubious translation:
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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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u3, 0} (Finset.{u3} ι) Real sr) p) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) (Prod.snd.{u3, 0} (Finset.{u3} ι) Real sr)))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Filter.HasBasis.{u2, succ u1} E (Prod.{u1, 0} (Finset.{u1} ι) Real) (nhds.{u2} E _inst_5 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) (fun (sr : Prod.{u1, 0} (Finset.{u1} ι) Real) => LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)) (fun (sr : Prod.{u1, 0} (Finset.{u1} ι) Real) => Seminorm.ball.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u1, 0} (Finset.{u1} ι) Real sr) p) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))))) (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ballₓ'. -/
 theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball 0 sr.2 :=
@@ -446,10 +416,7 @@ theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
 #align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ball
 
 /- warning: with_seminorms.has_basis_ball -> WithSeminorms.hasBasis_ball is a dubious translation:
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(SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u1, 0} (Finset.{u1} ι) Real sr) p) x (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ballₓ'. -/
 theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (𝓝 (x : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 :=
@@ -464,10 +431,7 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
 
 /- warning: with_seminorms.mem_nhds_iff -> WithSeminorms.mem_nhds_iff is a dubious translation:
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_inst_1))) _inst_2 _inst_3) s p) x r) U)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iffₓ'. -/
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around `x`.-/
@@ -477,10 +441,7 @@ theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
 #align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iff
 
 /- warning: with_seminorms.is_open_iff_mem_balls -> WithSeminorms.isOpen_iff_mem_balls is a dubious translation:
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_inst_1))) _inst_2 _inst_3) s p) x r) U))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_ballsₓ'. -/
 /-- The open sets of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around all of their points.-/
@@ -490,10 +451,7 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 
 /- warning: with_seminorms.t1_of_separating -> WithSeminorms.T1_of_separating is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.t1_of_separating WithSeminorms.T1_of_separatingₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /- Note that through the following lemmas, one also immediately has that separating families
@@ -513,10 +471,7 @@ theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
 #align with_seminorms.t1_of_separating WithSeminorms.T1_of_separating
 
 /- warning: with_seminorms.separating_of_t1 -> WithSeminorms.separating_of_T1 is a dubious translation:
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(Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u2, u3} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E 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(Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))))) (p i) x) (OfNat.ofNat.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) 0 (Zero.toOfNat0.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instZeroReal)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1ₓ'. -/
 /-- A family of seminorms inducing a T₁ topology is separating. -/
 theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
@@ -530,10 +485,7 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
 
 /- warning: with_seminorms.separating_iff_t1 -> WithSeminorms.separating_iff_T1 is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (forall (x : E), (Ne.{succ u2} E x (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) -> (Exists.{succ u3} ι (fun (i : ι) => Ne.{1} Real (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 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+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.separating_iff_t1 WithSeminorms.separating_iff_T1ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
@@ -554,10 +506,7 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [Topo
 variable {p : SeminormFamily 𝕜 E ι}
 
 /- warning: with_seminorms.tendsto_nhds' -> WithSeminorms.tendsto_nhds' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) {f : Filter.{u3} F} (y₀ : E), Iff (Filter.Tendsto.{u3, u2} F E u f (nhds.{u2} E _inst_5 y₀)) (forall (s : Finset.{u4} ι) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Filter.Eventually.{u3} F (fun (x : F) => LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Finset.sup.{u2, u4} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) (u x) y₀)) ε) f)))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {F : Type.{u1}} {ι : Type.{u2}} [_inst_1 : NormedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u2} ι] [_inst_5 : TopologicalSpace.{u3} E] {p : SeminormFamily.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) {f : Filter.{u1} F} (y₀ : E), Iff (Filter.Tendsto.{u1, u3} F E u f (nhds.{u3} E _inst_5 y₀)) (forall (s : Finset.{u2} ι) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Filter.Eventually.{u1} F (fun (x : F) => LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real 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(MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u4, u3} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))))) (Finset.sup.{u3, u2} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) _inst_2 _inst_3) s p) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) ε) f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'ₓ'. -/
 /-- Convergence along filters for `with_seminorms`.
 
@@ -568,10 +517,7 @@ theorem WithSeminorms.tendsto_nhds' (hp : WithSeminorms p) (u : F → E) {f : Fi
 #align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'
 
 /- warning: with_seminorms.tendsto_nhds -> WithSeminorms.tendsto_nhds is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds WithSeminorms.tendsto_nhdsₓ'. -/
 /-- Convergence along filters for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
@@ -586,10 +532,7 @@ theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Fil
 variable [SemilatticeSup F] [Nonempty F]
 
 /- warning: with_seminorms.tendsto_nhds_at_top -> WithSeminorms.tendsto_nhds_atTop is a dubious translation:
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(AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) (u x) y₀)) ε)))))
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forall (x : F), (LE.le.{u1} F (Preorder.toLE.{u1} F (PartialOrder.toPreorder.{u1} F (SemilatticeSup.toPartialOrder.{u1} F _inst_6))) x₀ x) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 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(AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E 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(AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds_at_top WithSeminorms.tendsto_nhds_atTopₓ'. -/
 /-- Limit `→ ∞` for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds_atTop (hp : WithSeminorms p) (u : F → E) (y₀ : E) :
@@ -639,10 +582,7 @@ theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
 /- warning: seminorm_family.with_seminorms_iff_nhds_eq_infi -> SeminormFamily.withSeminorms_iff_nhds_eq_iInf is a dubious translation:
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(NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i)) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInfₓ'. -/
 theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 0 : Filter E) = ⨅ i, (𝓝 0).comap (p i) :=
@@ -654,10 +594,7 @@ theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E
 #align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInf
 
 /- warning: with_seminorms.continuous_seminorm -> WithSeminorms.continuous_seminorm is a dubious translation:
-lean 3 declaration is
-  forall {𝕝 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_2 : AddCommGroup.{u2} E] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] [_inst_6 : NontriviallyNormedField.{u1} 𝕝] [_inst_7 : Module.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_8 : ContinuousConstSMul.{u1, u2} 𝕝 E t (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))] {p : SeminormFamily.{u1, u2, u3} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6) _inst_2 _inst_7}, (WithSeminorms.{u1, u2, u3} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6) _inst_2 _inst_7 _inst_5 p t) -> (forall (i : ι), Continuous.{u2, 0} E Real t (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 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(NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) (fun (_x : Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E 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_inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) (p i)))
-but is expected to have type
-  forall {𝕝 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_2 : AddCommGroup.{u2} E] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : NontriviallyNormedField.{u3} 𝕝] [_inst_7 : Module.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_8 : ContinuousConstSMul.{u3, u2} 𝕝 E _inst_4 (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))] {p : SeminormFamily.{u3, u2, u1} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6) _inst_2 _inst_7}, (WithSeminorms.{u3, u2, u1} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6) _inst_2 _inst_7 t p _inst_4) -> (forall (i : ι), Continuous.{u2, 0} E Real _inst_4 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7)))) (Seminorm.instSeminormClass.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7)))))))) (p i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminormₓ'. -/
 theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
     [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
@@ -668,10 +605,7 @@ theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
 
 /- warning: seminorm_family.with_seminorms_iff_topological_space_eq_infi -> SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p t) (Eq.{succ u2} (TopologicalSpace.{u2} E) t (iInf.{u2, succ u3} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toHasInf.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.completeLattice.{u2} E))) ι (fun (i : ι) => UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u2} E _inst_2 (Seminorm.toAddGroupSeminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i))))))))
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-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 t p _inst_4) (Eq.{succ u2} (TopologicalSpace.{u2} E) _inst_4 (iInf.{u2, succ u1} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toInfSet.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{u2} E))) ι (fun (i : ι) => UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u2} E _inst_2 (Seminorm.toAddGroupSeminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
@@ -693,10 +627,7 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormF
 omit t
 
 /- warning: seminorm_family.with_seminorms_iff_uniform_space_eq_infi -> SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] [u : UniformSpace.{u2} E] [_inst_6 : UniformAddGroup.{u2} E u (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p (UniformSpace.toTopologicalSpace.{u2} E u)) (Eq.{succ u2} (UniformSpace.{u2} E) u (iInf.{u2, succ u3} (UniformSpace.{u2} E) (UniformSpace.hasInf.{u2} E) ι (fun (i : ι) => PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u2} E _inst_2 (Seminorm.toAddGroupSeminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i)))))))
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-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Nonempty.{succ u1} ι] [u : UniformSpace.{u3} E] [_inst_6 : UniformAddGroup.{u3} E u (AddCommGroup.toAddGroup.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p (UniformSpace.toTopologicalSpace.{u3} E u)) (Eq.{succ u3} (UniformSpace.{u3} E) u (iInf.{u3, succ u1} (UniformSpace.{u3} E) (instInfSetUniformSpace.{u3} E) ι (fun (i : ι) => PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u3} E _inst_2 (Seminorm.toAddGroupSeminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (p i)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
@@ -759,10 +690,7 @@ variable {p : SeminormFamily 𝕜 E ι}
 variable [TopologicalSpace E]
 
 /- warning: with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded -> WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] {s : Set.{u2} E}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E 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(AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 s) (forall (I : Finset.{u3} ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} 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(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 _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 _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) x) r)))))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 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.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u2, u3, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u3} E] {s : Set.{u3} E}, (WithSeminorms.{u2, u3, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) _inst_5 s) (forall (I : Finset.{u1} ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u2, u3} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))))))) (Finset.sup.{u3, u1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) x) r)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedₓ'. -/
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
@@ -790,10 +718,7 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
 #align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded
 
 /- warning: with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded -> WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {G : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u3} G}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 (Set.image.{u3, u2} G E f s)) (forall (I : Finset.{u4} ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : G), (Membership.Mem.{u3, u3} G (Set.{u3} G) (Set.hasMem.{u3} G) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Finset.sup.{u2, u4} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) (f x)) r)))))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {G : Type.{u4}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u4} G}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_5 (Set.image.{u4, u2} G E f s)) (forall (I : Finset.{u1} ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : G), (Membership.mem.{u4, u4} G (Set.{u4} G) (Set.instMembershipSet.{u4} G) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (f x)) Real.instLTReal (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (Finset.sup.{u2, u1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) (f x)) r)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_boundedₓ'. -/
 theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
@@ -803,10 +728,7 @@ theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G →
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
 
 /- warning: with_seminorms.is_vonN_bounded_iff_seminorm_bounded -> WithSeminorms.isVonNBounded_iff_seminorm_bounded is a dubious translation:
-lean 3 declaration is
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_inst_3))))) (p i) x) r)))))
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(SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => 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(AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u2, u3} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))))))) (p i) x) r)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_boundedₓ'. -/
 theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i x < r :=
@@ -832,10 +754,7 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
 #align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_bounded
 
 /- warning: with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded -> WithSeminorms.image_isVonNBounded_iff_seminorm_bounded is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {G : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u3} G}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 (Set.image.{u3, u2} G E f s)) (forall (i : ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : G), (Membership.Mem.{u3, u3} G (Set.{u3} G) (Set.hasMem.{u3} G) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (p i) (f x)) r)))))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {G : Type.{u4}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u4} G}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_5 (Set.image.{u4, u2} G E f s)) (forall (i : ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : G), (Membership.mem.{u4, u4} G (Set.{u4} G) (Set.instMembershipSet.{u4} G) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (f x)) Real.instLTReal (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i) (f x)) r)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_boundedₓ'. -/
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
@@ -864,10 +783,7 @@ variable {τ₁₂ : 𝕝 →+* 𝕝₂} [RingHomIsometric τ₁₂]
 variable [Nonempty ι] [Nonempty ι']
 
 /- warning: seminorm.continuous_of_continuous_comp -> Seminorm.continuous_of_continuous_comp is a dubious translation:
-lean 3 declaration is
-  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι' : Type.{u5}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_7 : AddCommGroup.{u4} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u4} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_14 : Nonempty.{succ u5} ι'] {q : SeminormFamily.{u2, u4, u5} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u3} E] [_inst_16 : TopologicalAddGroup.{u3} E _inst_15 (AddCommGroup.toAddGroup.{u3} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)], (WithSeminorms.{u2, u4, u5} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10), (forall (i : ι'), Continuous.{u3, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u3, succ u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (fun (_x : Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕝 𝕝₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 _inst_7 _inst_5 _inst_10 (q i) f))) -> (Continuous.{u3, u4} E F _inst_15 _inst_17 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10 τ₁₂) f)))
-but is expected to have type
-  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u5}} {E : Type.{u2}} {F : Type.{u4}} {ι' : Type.{u3}} [_inst_2 : AddCommGroup.{u2} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u2} 𝕝 E (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_7 : AddCommGroup.{u4} F] [_inst_9 : NormedField.{u5} 𝕝₂] [_inst_10 : Module.{u5, u4} 𝕝₂ F (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {τ₁₂ : RingHom.{u1, u5} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u1} 𝕝 (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u5} 𝕝₂ (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u5} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u1} 𝕝 _inst_4) (NormedField.toNorm.{u5} 𝕝₂ _inst_9) τ₁₂] [_inst_14 : Nonempty.{succ u3} ι'] {q : SeminormFamily.{u5, u4, u3} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u2} E] [_inst_16 : TopologicalAddGroup.{u2} E _inst_15 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)], (WithSeminorms.{u5, u4, u3} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u5, u2, u4} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10), (forall (i : ι'), Continuous.{u2, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u1, u2} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (Seminorm.instSeminormClass.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))))))) (Seminorm.comp.{u1, u5, u2, u4} 𝕝 𝕝₂ E F (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕝₂ (NormedField.toNormedCommRing.{u5} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 _inst_7 _inst_5 _inst_10 (q i) f))) -> (Continuous.{u2, u4} E F _inst_15 _inst_17 (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u5, u2, u4} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u1, u5, u2, u4} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10 τ₁₂) f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_compₓ'. -/
 theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] (hq : WithSeminorms q)
@@ -882,10 +798,7 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
 
 /- warning: seminorm.continuous_iff_continuous_comp -> Seminorm.continuous_iff_continuous_comp is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι' : Type.{u5}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 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.{u3} E _inst_2)] [_inst_6 : NontriviallyNormedField.{u2} 𝕜₂] [_inst_7 : AddCommGroup.{u4} F] [_inst_8 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))))} [_inst_11 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (NormedField.toHasNorm.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) (NormedField.toHasNorm.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6)) σ₁₂] [_inst_14 : Nonempty.{succ u5} ι'] {q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6) _inst_7 _inst_8} [_inst_15 : TopologicalSpace.{u3} E] [_inst_16 : TopologicalAddGroup.{u3} E _inst_15 (AddCommGroup.toAddGroup.{u3} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)] [_inst_19 : ContinuousConstSMul.{u2, u4} 𝕜₂ F _inst_17 (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))))))) (AddZeroClass.toHasZero.{u4} F 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F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕜 𝕜₂ 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.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8 σ₁₂) f)) (forall (i : ι'), Continuous.{u3, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u3, succ u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6)))) σ₁₂ _inst_11 _inst_2 _inst_7 _inst_3 _inst_8 (q i) f))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u5}} {E : Type.{u2}} {F : Type.{u4}} {ι' : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (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 _inst_2)] [_inst_6 : NontriviallyNormedField.{u5} 𝕜₂] [_inst_7 : AddCommGroup.{u4} F] [_inst_8 : Module.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {σ₁₂ : RingHom.{u1, u5} 𝕜 𝕜₂ (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)))))) (Semiring.toNonAssocSemiring.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))))} [_inst_11 : RingHomIsometric.{u1, u5} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (NormedField.toNorm.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) (NormedField.toNorm.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)) σ₁₂] [_inst_14 : Nonempty.{succ u3} ι'] {q : SeminormFamily.{u5, u4, u3} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6) _inst_7 _inst_8} [_inst_15 : TopologicalSpace.{u2} E] [_inst_16 : TopologicalAddGroup.{u2} E _inst_15 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)] [_inst_19 : ContinuousConstSMul.{u5, u4} 𝕜₂ F _inst_17 (SMulZeroClass.toSMul.{u5, u4} 𝕜₂ F (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_7))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜₂ F (CommMonoidWithZero.toZero.{u5} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜₂ (Semifield.toCommGroupWithZero.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_7))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_7))))) (Module.toMulActionWithZero.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_8))))], (WithSeminorms.{u5, u4, u3} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6) _inst_7 _inst_8 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u5, u2, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8), Iff (Continuous.{u2, u4} E F _inst_15 _inst_17 (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u5, u2, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u1, u5, u2, u4} 𝕜 𝕜₂ 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.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8 σ₁₂) f)) (forall (i : ι'), Continuous.{u2, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u1, u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (Seminorm.comp.{u1, u5, u2, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)))) σ₁₂ _inst_11 _inst_2 _inst_7 _inst_3 _inst_8 (q i) f))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_compₓ'. -/
 theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul 𝕜₂ F]
@@ -894,10 +807,7 @@ theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [Topol
 #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp
 
 /- warning: seminorm.continuous_from_bounded -> Seminorm.continuous_from_bounded is a dubious translation:
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-  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} {ι' : Type.{u6}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_7 : AddCommGroup.{u4} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u4} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u5} ι] [_inst_14 : Nonempty.{succ u6} ι'] {p : SeminormFamily.{u1, u3, u5} 𝕝 E ι _inst_4 _inst_2 _inst_5} {q : SeminormFamily.{u2, u4, u6} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u3} E] [_inst_16 : TopologicalAddGroup.{u3} E _inst_15 (AddCommGroup.toAddGroup.{u3} E _inst_2)], (WithSeminorms.{u1, u3, u5} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p _inst_15) -> (forall [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)], (WithSeminorms.{u2, u4, u6} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10), (Seminorm.IsBounded.{u1, u2, u3, u4, u5, u6} 𝕝 𝕝₂ E F ι ι' _inst_4 _inst_2 _inst_5 _inst_9 _inst_7 _inst_10 τ₁₂ _inst_12 p q f) -> (Continuous.{u3, u4} E F _inst_15 _inst_17 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10 τ₁₂) f))))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.continuous_from_bounded Seminorm.continuous_from_boundedₓ'. -/
 theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'}
     [TopologicalSpace E] [TopologicalAddGroup E] (hp : WithSeminorms p) [TopologicalSpace F]
@@ -920,10 +830,7 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
 #align seminorm.continuous_from_bounded Seminorm.continuous_from_bounded
 
 /- warning: seminorm.cont_with_seminorms_normed_space -> Seminorm.cont_withSeminorms_normedSpace is a dubious translation:
-lean 3 declaration is
-  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {E : Type.{u3}} {ι : Type.{u4}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_9 : NormedField.{u2} 𝕝₂] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u4} ι] (F : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} F] [_inst_16 : NormedSpace.{u2, u5} 𝕝₂ F _inst_9 _inst_15] [_inst_17 : UniformSpace.{u3} E] [_inst_18 : UniformAddGroup.{u3} E _inst_17 (AddCommGroup.toAddGroup.{u3} E _inst_2)] {p : ι -> (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))))}, (WithSeminorms.{u1, u3, u4} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p (UniformSpace.toTopologicalSpace.{u3} E _inst_17)) -> (forall (f : LinearMap.{u1, u2, u3, u5} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)), (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.partialOrder.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))))) (Seminorm.comp.{u1, u2, u3, u5} 𝕝 𝕝₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) (normSeminorm.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) 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(NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)) (fun (_x : LinearMap.{u1, u2, u3, u5} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u5} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) τ₁₂) f)))
-but is expected to have type
-  forall {𝕝 : Type.{u2}} {𝕝₂ : Type.{u4}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u2} 𝕝] [_inst_5 : Module.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_9 : NormedField.{u4} 𝕝₂] {τ₁₂ : RingHom.{u2, u4} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u4} 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u2, u4} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u2} 𝕝 _inst_4) (NormedField.toNorm.{u4} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u1} ι] (F : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} F] [_inst_16 : NormedSpace.{u4, u5} 𝕝₂ F _inst_9 _inst_15] [_inst_17 : UniformSpace.{u3} E] [_inst_18 : UniformAddGroup.{u3} E _inst_17 (AddCommGroup.toAddGroup.{u3} E _inst_2)] {p : ι -> (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 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(AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))))}, (WithSeminorms.{u2, u3, u1} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p (UniformSpace.toTopologicalSpace.{u3} E _inst_17)) -> (forall (f : LinearMap.{u2, u4, u3, u5} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)), (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 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(SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Preorder.toLE.{u3} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.instPartialOrder.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))))) (Seminorm.comp.{u2, u4, u3, u5} 𝕝 𝕝₂ E F (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (SeminormedCommRing.toSeminormedRing.{u4} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕝₂ (NormedField.toNormedCommRing.{u4} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) (normSeminorm.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) f) (HSMul.hSMul.{0, u3, u3} NNReal (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (instHSMul.{0, u3} NNReal (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.instSMul.{0, u2, u3} NNReal 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (Finset.sup.{u3, u1} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) ι (Seminorm.instSemilatticeSup.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.instOrderBot.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) _inst_2 _inst_5) s p))))) -> (Continuous.{u3, u5} E F (UniformSpace.toTopologicalSpace.{u3} E _inst_17) (UniformSpace.toTopologicalSpace.{u5} F (PseudoMetricSpace.toUniformSpace.{u5} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F _inst_15))) (FunLike.coe.{max (succ u3) (succ u5), succ u3, succ u5} (LinearMap.{u2, u4, u3, u5} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u4, u3, u5} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) τ₁₂) f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpaceₓ'. -/
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
@@ -934,10 +841,7 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 
 /- warning: seminorm.cont_normed_space_to_with_seminorms -> Seminorm.cont_normedSpace_to_withSeminorms is a dubious translation:
-lean 3 declaration is
-  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {F : Type.{u3}} {ι : Type.{u4}} [_inst_4 : NormedField.{u1} 𝕝] [_inst_7 : AddCommGroup.{u3} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u3} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u4} ι] (E : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} E] [_inst_16 : NormedSpace.{u1, u5} 𝕝 E _inst_4 _inst_15] [_inst_17 : UniformSpace.{u3} F] [_inst_18 : UniformAddGroup.{u3} F _inst_17 (AddCommGroup.toAddGroup.{u3} F _inst_7)] {q : ι -> (Seminorm.{u2, u3} 𝕝₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) (AddCommGroup.toAddGroup.{u3} F _inst_7) (SMulZeroClass.toHasSmul.{u2, u3} 𝕝₂ F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝₂ F (MulZeroClass.toHasZero.{u2} 𝕝₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕝₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕝₂ (Semiring.toMonoidWithZero.{u2} 𝕝₂ (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝₂ F (Semiring.toMonoidWithZero.{u2} 𝕝₂ (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)))) (Module.toMulActionWithZero.{u2, u3} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) _inst_10)))))}, (WithSeminorms.{u2, u3, u4} 𝕝₂ F ι _inst_9 _inst_7 _inst_10 _inst_13 q (UniformSpace.toTopologicalSpace.{u3} F _inst_17)) -> (forall (f : LinearMap.{u1, u2, u5, u3} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10), (forall (i : ι), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u5} (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 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𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (PartialOrder.toPreorder.{u5} (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) 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_inst_15 _inst_16) _inst_10 (q i) f) (SMul.smul.{0, u5} NNReal (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E 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(AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16))))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (normSeminorm.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))) -> (Continuous.{u5, u3} E F (UniformSpace.toTopologicalSpace.{u5} E (PseudoMetricSpace.toUniformSpace.{u5} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} E _inst_15))) (UniformSpace.toTopologicalSpace.{u3} F _inst_17) (coeFn.{max (succ u5) (succ u3), max (succ u5) (succ u3)} (LinearMap.{u1, u2, u5, u3} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10) (fun (_x : LinearMap.{u1, u2, u5, u3} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u5, u3} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 τ₁₂) f)))
-but is expected to have type
-  forall {𝕝 : Type.{u4}} {𝕝₂ : Type.{u2}} {F : Type.{u3}} {ι : Type.{u1}} [_inst_4 : NormedField.{u4} 𝕝] [_inst_7 : AddCommGroup.{u3} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u3} 𝕝₂ F (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)] {τ₁₂ : RingHom.{u4, u2} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u2} 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u4, u2} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u4} 𝕝 _inst_4) (NormedField.toNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u1} ι] (E : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} E] [_inst_16 : NormedSpace.{u4, u5} 𝕝 E _inst_4 _inst_15] [_inst_17 : UniformSpace.{u3} F] [_inst_18 : UniformAddGroup.{u3} F _inst_17 (AddCommGroup.toAddGroup.{u3} F _inst_7)] {q : ι -> (Seminorm.{u2, u3} 𝕝₂ F (SeminormedCommRing.toSeminormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) (AddCommGroup.toAddGroup.{u3} F _inst_7) (SMulZeroClass.toSMul.{u2, u3} 𝕝₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_7))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝₂ F (CommMonoidWithZero.toZero.{u2} 𝕝₂ 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_inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) _inst_10)))))}, (WithSeminorms.{u2, u3, u1} 𝕝₂ F ι _inst_9 _inst_7 _inst_10 _inst_13 q (UniformSpace.toTopologicalSpace.{u3} F _inst_17)) -> (forall (f : LinearMap.{u4, u2, u5, u3} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10), (forall (i : ι), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u5} (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Preorder.toLE.{u5} (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (PartialOrder.toPreorder.{u5} (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.instPartialOrder.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))))) (Seminorm.comp.{u4, u2, u5, u3} 𝕝 𝕝₂ E F (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedCommRing.toSeminormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15) _inst_7 (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 (q i) f) (HSMul.hSMul.{0, u5, u5} NNReal (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (instHSMul.{0, u5} NNReal (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.instSMul.{0, u4, u5} NNReal 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16))))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (normSeminorm.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))) -> (Continuous.{u5, u3} E F (UniformSpace.toTopologicalSpace.{u5} E (PseudoMetricSpace.toUniformSpace.{u5} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} E _inst_15))) (UniformSpace.toTopologicalSpace.{u3} F _inst_17) (FunLike.coe.{max (succ u3) (succ u5), succ u5, succ u3} (LinearMap.{u4, u2, u5, u3} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u4, u2, u5, u3} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 τ₁₂) f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminormsₓ'. -/
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
@@ -959,10 +863,7 @@ variable [Nonempty ι] [NormedField 𝕜] [NormedSpace ℝ 𝕜] [AddCommGroup E
   [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E] [TopologicalAddGroup E]
 
 /- warning: with_seminorms.to_locally_convex_space -> WithSeminorms.toLocallyConvexSpace is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : Nonempty.{succ u3} ι] [_inst_2 : NormedField.{u1} 𝕜] [_inst_3 : NormedSpace.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_6 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_7 : IsScalarTower.{0, u1, u2} Real 𝕜 E (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2))))))) (NormedSpace.toModule.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2))))) _inst_3))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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 _inst_2)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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 _inst_2))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_5)))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6))))] [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : TopologicalAddGroup.{u2} E _inst_8 (AddCommGroup.toAddGroup.{u2} E _inst_4)] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_2 _inst_4 _inst_5}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_2 _inst_4 _inst_5 _inst_1 p _inst_8) -> (LocallyConvexSpace.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6 _inst_8)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : Nonempty.{succ u1} ι] [_inst_2 : NormedField.{u3} 𝕜] [_inst_3 : NormedSpace.{0, u3} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕜 (NormedRing.toNonUnitalNormedRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_2)))))] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_6 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_7 : IsScalarTower.{0, u3, u2} Real 𝕜 E (SMulZeroClass.toSMul.{0, u3} Real 𝕜 (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u3} Real 𝕜 Real.instZeroReal (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u3} Real 𝕜 Real.instMonoidWithZeroReal (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (Module.toMulActionWithZero.{0, u3} Real 𝕜 Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_2))))))) (NormedSpace.toModule.{0, u3} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕜 (NormedRing.toNonUnitalNormedRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_2))))) _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{0, u2} Real E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{0, u2} Real E Real.instZeroReal (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6))))] [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : TopologicalAddGroup.{u2} E _inst_8 (AddCommGroup.toAddGroup.{u2} E _inst_4)] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_2 _inst_4 _inst_5}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_2 _inst_4 _inst_5 _inst_1 p _inst_8) -> (LocallyConvexSpace.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6 _inst_8)
+<too large>
 Case conversion may be inaccurate. Consider using '#align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpaceₓ'. -/
 theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
     LocallyConvexSpace ℝ E :=
@@ -984,10 +885,7 @@ section NormedSpace
 variable (𝕜) [NormedField 𝕜] [NormedSpace ℝ 𝕜] [SeminormedAddCommGroup E]
 
 /- warning: normed_space.to_locally_convex_space' -> NormedSpace.toLocallyConvexSpace' is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedSpace.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_3] [_inst_5 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_6 : IsScalarTower.{0, u1, u2} Real 𝕜 E (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (NormedSpace.toModule.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) _inst_2))))) (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 _inst_3))))) (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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_5))))], LocallyConvexSpace.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_5 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3)))
-but is expected to have type
-  forall (𝕜 : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : NormedSpace.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_3] [_inst_5 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3))] [_inst_6 : IsScalarTower.{0, u2, u1} Real 𝕜 E (SMulZeroClass.toSMul.{0, u2} Real 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u2} Real 𝕜 Real.instZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real 𝕜 Real.instMonoidWithZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Module.toMulActionWithZero.{0, u2} Real 𝕜 Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))))) (NormedSpace.toModule.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) _inst_2))))) (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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)) _inst_5))))], LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)) _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'ₓ'. -/
 /-- Not an instance since `𝕜` can't be inferred. See `normed_space.to_locally_convex_space` for a
 slightly weaker instance version. -/
@@ -1022,10 +920,7 @@ def SeminormFamily.comp (q : SeminormFamily 𝕜₂ F ι) (f : E →ₛₗ[σ₁
 -/
 
 /- warning: seminorm_family.comp_apply -> SeminormFamily.comp_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (i : ι) (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f i) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {𝕜₂ : Type.{u5}} {E : Type.{u1}} {F : Type.{u4}} {ι : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormedField.{u5} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u2, u5} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u2, u5} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u2} 𝕜 _inst_1) (NormedField.toNorm.{u5} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u5, u4, u3} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (i : ι) (f : LinearMap.{u2, u5, u1, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u1} (Seminorm.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) (SeminormFamily.comp.{u2, u5, u1, u4, u3} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f i) (Seminorm.comp.{u2, u5, u1, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.comp_apply SeminormFamily.comp_applyₓ'. -/
 theorem SeminormFamily.comp_apply (q : SeminormFamily 𝕜₂ F ι) (i : ι) (f : E →ₛₗ[σ₁₂] F) :
     q.comp f i = (q i).comp f :=
@@ -1033,10 +928,7 @@ theorem SeminormFamily.comp_apply (q : SeminormFamily 𝕜₂ F ι) (i : ι) (f
 #align seminorm_family.comp_apply SeminormFamily.comp_apply
 
 /- warning: seminorm_family.finset_sup_comp -> SeminormFamily.finset_sup_comp is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (s : Finset.{u5} ι) (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u3} (Seminorm.{u1, u3} 𝕜 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(SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u4, u5} (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) ι (Seminorm.semilatticeSup.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) (Seminorm.orderBot.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) _inst_5 _inst_6) s q) f) (Finset.sup.{u3, u5} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {𝕜₂ : Type.{u5}} {E : Type.{u1}} {F : Type.{u4}} {ι : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormedField.{u5} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u2, u5} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u2, u5} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u2} 𝕜 _inst_1) (NormedField.toNorm.{u5} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u5, u4, u3} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (s : Finset.{u3} ι) (f : LinearMap.{u2, u5, u1, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u1} (Seminorm.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) (Seminorm.comp.{u2, u5, u1, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u4, u3} (Seminorm.{u5, u4} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toSMul.{u5, u4} 𝕜₂ F (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜₂ F (CommMonoidWithZero.toZero.{u5} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜₂ (Semifield.toCommGroupWithZero.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (Module.toMulActionWithZero.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) ι (Seminorm.instSemilatticeSup.{u5, u4} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toSMul.{u5, u4} 𝕜₂ F (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜₂ F (CommMonoidWithZero.toZero.{u5} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜₂ (Semifield.toCommGroupWithZero.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (Module.toMulActionWithZero.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) (Seminorm.instOrderBot.{u5, u4} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) _inst_5 _inst_6) s q) f) (Finset.sup.{u1, u3} (Seminorm.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 _inst_3) s (SeminormFamily.comp.{u2, u5, u1, u4, u3} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align seminorm_family.finset_sup_comp SeminormFamily.finset_sup_compₓ'. -/
 theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Finset ι)
     (f : E →ₛₗ[σ₁₂] F) : (s.sup q).comp f = s.sup (q.comp f) :=
@@ -1049,10 +941,7 @@ theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Fi
 variable [TopologicalSpace F] [TopologicalAddGroup F]
 
 /- warning: linear_map.with_seminorms_induced -> LinearMap.withSeminorms_induced is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u4} F] [_inst_9 : TopologicalAddGroup.{u4} F _inst_8 (AddCommGroup.toAddGroup.{u4} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), WithSeminorms.{u1, u3, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) (TopologicalSpace.induced.{u3, u4} E F (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6 σ₁₂) f) (inferInstance.{succ u4} (TopologicalSpace.{u4} F) _inst_8)))
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-  forall {𝕜 : Type.{u2}} {𝕜₂ : Type.{u4}} {E : Type.{u1}} {F : Type.{u3}} {ι : Type.{u5}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormedField.{u4} 𝕜₂] [_inst_5 : AddCommGroup.{u3} F] [_inst_6 : Module.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5)] {σ₁₂ : RingHom.{u2, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u2, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u2} 𝕜 _inst_1) (NormedField.toNorm.{u4} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u3} F] [_inst_9 : TopologicalAddGroup.{u3} F _inst_8 (AddCommGroup.toAddGroup.{u3} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u4, u3, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u4, u3, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall (f : LinearMap.{u2, u4, u1, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6), WithSeminorms.{u2, u1, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u2, u4, u1, u3, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) (TopologicalSpace.induced.{u1, u3} E F (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u4, u1, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u4, u1, u3} 𝕜 𝕜₂ E F (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6 σ₁₂) f) (inferInstance.{succ u3} (TopologicalSpace.{u3} F) _inst_8)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.with_seminorms_induced LinearMap.withSeminorms_inducedₓ'. -/
 theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
@@ -1067,10 +956,7 @@ theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily
 #align linear_map.with_seminorms_induced LinearMap.withSeminorms_induced
 
 /- warning: inducing.with_seminorms -> Inducing.withSeminorms is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u4} F] [_inst_9 : TopologicalAddGroup.{u4} F _inst_8 (AddCommGroup.toAddGroup.{u4} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall [_inst_10 : TopologicalSpace.{u3} E] {f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6}, (Inducing.{u3, u4} E F _inst_10 _inst_8 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6 σ₁₂) f)) -> (WithSeminorms.{u1, u3, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) _inst_10))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align inducing.with_seminorms Inducing.withSeminormsₓ'. -/
 theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι} (hq : WithSeminorms q)
     [TopologicalSpace E] {f : E →ₛₗ[σ₁₂] F} (hf : Inducing f) : WithSeminorms (q.comp f) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.with_seminorms
-! leanprover-community/mathlib commit b31173ee05c911d61ad6a05bd2196835c932e0ec
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.Module.LocallyConvex
 /-!
 # Topology induced by a family of seminorms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `seminorm_family.basis_sets`: The set of open seminorm balls for a family of seminorms.

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

@@ -63,42 +63,72 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable (𝕜 E ι)
 
+#print SeminormFamily /-
 /-- An abbreviation for indexed families of seminorms. This is mainly to allow for dot-notation. -/
 abbrev SeminormFamily :=
   ι → Seminorm 𝕜 E
 #align seminorm_family SeminormFamily
+-/
 
 variable {𝕜 E ι}
 
 namespace SeminormFamily
 
+#print SeminormFamily.basisSets /-
 /-- The sets of a filter basis for the neighborhood filter of 0. -/
 def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
   ⋃ (s : Finset ι) (r) (hr : 0 < r), singleton <| ball (s.sup p) (0 : E) r
 #align seminorm_family.basis_sets SeminormFamily.basisSets
+-/
 
 variable (p : SeminormFamily 𝕜 E ι)
 
+/- warning: seminorm_family.basis_sets_iff -> SeminormFamily.basisSets_iff is a dubious translation:
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𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) r)))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) {U : Set.{u3} E}, Iff (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (Exists.{succ u1} (Finset.{u1} ι) (fun (i : Finset.{u1} ι) => Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) (fun (hr : LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) => Eq.{succ u3} (Set.{u3} E) U (Seminorm.ball.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Finset.sup.{u3, u1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))))) r)))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iffₓ'. -/
 theorem basisSets_iff {U : Set E} :
     U ∈ p.basis_sets ↔ ∃ (i : Finset ι)(r : _)(hr : 0 < r), U = ball (i.sup p) 0 r := by
   simp only [basis_sets, mem_Union, mem_singleton_iff]
 #align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iff
 
+/- warning: seminorm_family.basis_sets_mem -> SeminormFamily.basisSets_mem is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (i : Finset.{u3} ι) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) (Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) r) (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (i : Finset.{u3} ι) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Membership.mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.instMembershipSet.{u2} (Set.{u2} E)) (Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) i p) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))))) r) (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_mem SeminormFamily.basisSets_memₓ'. -/
 theorem basisSets_mem (i : Finset ι) {r : ℝ} (hr : 0 < r) : (i.sup p).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨i, _, hr, rfl⟩
 #align seminorm_family.basis_sets_mem SeminormFamily.basisSets_mem
 
+/- warning: seminorm_family.basis_sets_singleton_mem -> SeminormFamily.basisSets_singleton_mem is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (i : ι) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) (Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) r) (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) (i : ι) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) (Seminorm.ball.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (p i) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))))) r) (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_singleton_mem SeminormFamily.basisSets_singleton_memₓ'. -/
 theorem basisSets_singleton_mem (i : ι) {r : ℝ} (hr : 0 < r) : (p i).ball 0 r ∈ p.basis_sets :=
   (basisSets_iff _).mpr ⟨{i}, _, hr, by rw [Finset.sup_singleton]⟩
 #align seminorm_family.basis_sets_singleton_mem SeminormFamily.basisSets_singleton_mem
 
+#print SeminormFamily.basisSets_nonempty /-
 theorem basisSets_nonempty [Nonempty ι] : p.basis_sets.Nonempty :=
   by
   let i := Classical.arbitrary ι
   refine' set.nonempty_def.mpr ⟨(p i).ball 0 1, _⟩
   exact p.basis_sets_singleton_mem i zero_lt_one
 #align seminorm_family.basis_sets_nonempty SeminormFamily.basisSets_nonempty
+-/
 
+/- warning: seminorm_family.basis_sets_intersect -> SeminormFamily.basisSets_intersect is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u2} E) (V : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u2} (Set.{u2} E) (fun (z : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) z (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) z (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) z (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) U V))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u3} E) (V : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) V (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u3} (Set.{u3} E) (fun (z : Set.{u3} E) => And (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) z (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) z (Inter.inter.{u3} (Set.{u3} E) (Set.instInterSet.{u3} E) U V))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersectₓ'. -/
 theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈ p.basis_sets) :
     ∃ (z : Set E)(H : z ∈ p.basis_sets), z ⊆ U ∩ V := by
   classical
@@ -116,6 +146,12 @@ theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈
           ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
 
+/- warning: seminorm_family.basis_sets_zero -> SeminormFamily.basisSets_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) U)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))))) U)
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_zero SeminormFamily.basisSets_zeroₓ'. -/
 theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
   by
   rcases p.basis_sets_iff.mp hU with ⟨ι', r, hr, hU⟩
@@ -123,6 +159,12 @@ theorem basisSets_zero (U) (hU : U ∈ p.basis_sets) : (0 : E) ∈ U :=
   exact hr
 #align seminorm_family.basis_sets_zero SeminormFamily.basisSets_zero
 
+/- warning: seminorm_family.basis_sets_add -> SeminormFamily.basisSets_add is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u2} (Set.{u2} E) (fun (V : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))) V V) U)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u3} (Set.{u3} E) (fun (V : Set.{u3} E) => And (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) V (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) (HAdd.hAdd.{u3, u3, u3} (Set.{u3} E) (Set.{u3} E) (Set.{u3} E) (instHAdd.{u3} (Set.{u3} E) (Set.add.{u3} E (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))))) V V) U)))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_add SeminormFamily.basisSets_addₓ'. -/
 theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.basis_sets), V + V ⊆ U :=
   by
@@ -133,6 +175,12 @@ theorem basisSets_add (U) (hU : U ∈ p.basis_sets) :
   rw [hU, add_zero, add_halves']
 #align seminorm_family.basis_sets_add SeminormFamily.basisSets_add
 
+/- warning: seminorm_family.basis_sets_neg -> SeminormFamily.basisSets_neg is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u2} (Set.{u2} E) (fun (V : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) V (Set.preimage.{u2, u2} E E (fun (x : E) => Neg.neg.{u2} E (SubNegMonoid.toHasNeg.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) x) U))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) (U : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u3} (Set.{u3} E) (fun (V : Set.{u3} E) => And (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) V (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) V (Set.preimage.{u3, u3} E E (fun (x : E) => Neg.neg.{u3} E (NegZeroClass.toNeg.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) x) U))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_neg SeminormFamily.basisSets_negₓ'. -/
 theorem basisSets_neg (U) (hU' : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.basis_sets), V ⊆ (fun x : E => -x) ⁻¹' U :=
   by
@@ -141,12 +189,20 @@ theorem basisSets_neg (U) (hU' : U ∈ p.basis_sets) :
   exact ⟨U, hU', Eq.subset hU⟩
 #align seminorm_family.basis_sets_neg SeminormFamily.basisSets_neg
 
+#print SeminormFamily.addGroupFilterBasis /-
 /-- The `add_group_filter_basis` induced by the filter basis `seminorm_basis_zero`. -/
 protected def addGroupFilterBasis [Nonempty ι] : AddGroupFilterBasis E :=
   addGroupFilterBasisOfComm p.basis_sets p.basisSets_nonempty p.basisSets_intersect p.basisSets_zero
     p.basisSets_add p.basisSets_neg
 #align seminorm_family.add_group_filter_basis SeminormFamily.addGroupFilterBasis
+-/
 
+/- warning: seminorm_family.basis_sets_smul_right -> SeminormFamily.basisSets_smul_right is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) (v : E) (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Filter.Eventually.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (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 _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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x v) U) (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) (v : E) (U : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Filter.Eventually.{u2} 𝕜 (fun (x : 𝕜) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (HSMul.hSMul.{u2, u3, u3} 𝕜 E E (instHSMul.{u2, u3} 𝕜 E (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) x v) U) (nhds.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_rightₓ'. -/
 theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∀ᶠ x : 𝕜 in 𝓝 0, x • v ∈ U :=
   by
@@ -163,6 +219,12 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
 
 variable [Nonempty ι]
 
+/- warning: seminorm_family.basis_sets_smul -> SeminormFamily.basisSets_smul is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) [_inst_4 : Nonempty.{succ u3} ι] (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u1} (Set.{u1} 𝕜) (fun (V : Set.{u1} 𝕜) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} 𝕜) (Filter.{u1} 𝕜) (Filter.hasMem.{u1} 𝕜) V (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} 𝕜) (Filter.{u1} 𝕜) (Filter.hasMem.{u1} 𝕜) V (nhds.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))) => Exists.{succ u2} (Set.{u2} E) (fun (W : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) W (FilterBasis.sets.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (SeminormFamily.addGroupFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) W (FilterBasis.sets.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (SeminormFamily.addGroupFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (SMul.smul.{u1, u2} (Set.{u1} 𝕜) (Set.{u2} E) (Set.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 _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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) V W) U)))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) [_inst_4 : Nonempty.{succ u1} ι] (U : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u2} (Set.{u2} 𝕜) (fun (V : Set.{u2} 𝕜) => And (Membership.mem.{u2, u2} (Set.{u2} 𝕜) (Filter.{u2} 𝕜) (instMembershipSetFilter.{u2} 𝕜) V (nhds.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))))))) (Exists.{succ u3} (Set.{u3} E) (fun (W : Set.{u3} E) => And (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) W (FilterBasis.sets.{u3} E (AddGroupFilterBasis.toFilterBasis.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2) (SeminormFamily.addGroupFilterBasis.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) (HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) (HSMul.hSMul.{u2, u3, u3} (Set.{u2} 𝕜) (Set.{u3} E) (Set.{u3} E) (instHSMul.{u2, u3} (Set.{u2} 𝕜) (Set.{u3} E) (Set.smul.{u2, u3} 𝕜 E (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))) V W) U)))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smulₓ'. -/
 theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set 𝕜)(H : V ∈ 𝓝 (0 : 𝕜))(W : Set E)(H : W ∈ p.AddGroupFilterBasis.sets), V • W ⊆ U :=
   by
@@ -173,6 +235,12 @@ theorem basisSets_smul (U) (hU : U ∈ p.basis_sets) :
   rw [hU, Real.mul_self_sqrt (le_of_lt hr)]
 #align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smul
 
+/- warning: seminorm_family.basis_sets_smul_left -> SeminormFamily.basisSets_smul_left is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3) [_inst_4 : Nonempty.{succ u3} ι] (x : 𝕜) (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) U (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u2} (Set.{u2} E) (fun (V : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (FilterBasis.sets.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (SeminormFamily.addGroupFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) V (FilterBasis.sets.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (SeminormFamily.addGroupFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) V (Set.preimage.{u2, u2} E E (fun (y : E) => 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 _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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) U))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3) [_inst_4 : Nonempty.{succ u1} ι] (x : 𝕜) (U : Set.{u3} E), (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) U (SeminormFamily.basisSets.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) -> (Exists.{succ u3} (Set.{u3} E) (fun (V : Set.{u3} E) => And (Membership.mem.{u3, u3} (Set.{u3} E) (Set.{u3} (Set.{u3} E)) (Set.instMembershipSet.{u3} (Set.{u3} E)) V (FilterBasis.sets.{u3} E (AddGroupFilterBasis.toFilterBasis.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2) (SeminormFamily.addGroupFilterBasis.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) (HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) V (Set.preimage.{u3, u3} E E (fun (y : E) => HSMul.hSMul.{u2, u3, u3} 𝕜 E E (instHSMul.{u2, u3} 𝕜 E (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) x y) U))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.basis_sets_smul_left SeminormFamily.basisSets_smul_leftₓ'. -/
 theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
     ∃ (V : Set E)(H : V ∈ p.AddGroupFilterBasis.sets), V ⊆ (fun y : E => x • y) ⁻¹' U :=
   by
@@ -187,6 +255,7 @@ theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basis_sets) :
     preimage_const_of_mem, zero_smul]
 #align seminorm_family.basis_sets_smul_left SeminormFamily.basisSets_smul_left
 
+#print SeminormFamily.moduleFilterBasis /-
 /-- The `module_filter_basis` induced by the filter basis `seminorm_basis_zero`. -/
 protected def moduleFilterBasis : ModuleFilterBasis 𝕜 E
     where
@@ -195,7 +264,14 @@ protected def moduleFilterBasis : ModuleFilterBasis 𝕜 E
   smul_left' := p.basisSets_smul_left
   smul_right' := p.basisSets_smul_right
 #align seminorm_family.module_filter_basis SeminormFamily.moduleFilterBasis
+-/
 
+/- warning: seminorm_family.filter_eq_infi -> SeminormFamily.filter_eq_iInf is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Filter.{u2} E) (FilterBasis.filter.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (ModuleFilterBasis.toAddGroupFilterBasis.{u1, u2} 𝕜 E (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (SeminormFamily.moduleFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) (iInf.{u2, succ u3} (Filter.{u2} E) (ConditionallyCompleteLattice.toHasInf.{u2} (Filter.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Filter.{u2} E) (Filter.completeLattice.{u2} E))) ι (fun (i : ι) => Filter.comap.{u2, 0} E Real (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i)) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] (p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Filter.{u2} E) (FilterBasis.filter.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (ModuleFilterBasis.toAddGroupFilterBasis.{u3, u2} 𝕜 E (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) _inst_2 _inst_3 (SeminormFamily.moduleFilterBasis.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))) (iInf.{u2, succ u1} (Filter.{u2} E) (ConditionallyCompleteLattice.toInfSet.{u2} (Filter.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Filter.{u2} E) (Filter.instCompleteLatticeFilter.{u2} E))) ι (fun (i : ι) => Filter.comap.{u2, 0} E Real (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i)) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.filter_eq_infi SeminormFamily.filter_eq_iInfₓ'. -/
 theorem filter_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     p.ModuleFilterBasis.toFilterBasis.filterₓ = ⨅ i, (𝓝 0).comap (p i) :=
   by
@@ -231,18 +307,32 @@ variable [NormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F]
 
 variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
+#print Seminorm.IsBounded /-
 -- Todo: This should be phrased entirely in terms of the von Neumann bornology.
 /-- The proposition that a linear map is bounded between spaces with families of seminorms. -/
 def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f : E →ₛₗ[σ₁₂] F) : Prop :=
   ∀ i, ∃ s : Finset ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • s.sup p
 #align seminorm.is_bounded Seminorm.IsBounded
+-/
 
+/- warning: seminorm.is_bounded_const -> Seminorm.isBounded_const is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (ι' : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι'] {p : ι -> (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))} {q : Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))} (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u1, u2, u3, u4, u5, u6} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p (fun (_x : ι') => q) f) (Exists.{succ u5} (Finset.{u5} ι) (fun (s : Finset.{u5} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.partialOrder.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 q f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (Finset.sup.{u3, u5} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {𝕜₂ : Type.{u3}} {E : Type.{u4}} {F : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : AddCommGroup.{u4} E] [_inst_3 : Module.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2)] [_inst_4 : NormedField.{u3} 𝕜₂] [_inst_5 : AddCommGroup.{u2} F] [_inst_6 : Module.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)] {σ₁₂ : RingHom.{u5, u3} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u5, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u5} 𝕜 _inst_1) (NormedField.toNorm.{u3} 𝕜₂ _inst_4) σ₁₂] (ι' : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι'] {p : ι -> (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3)))))} {q : Seminorm.{u3, u2} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u2} F _inst_5) (SMulZeroClass.toSMul.{u3, u2} 𝕜₂ F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜₂ F (CommMonoidWithZero.toZero.{u3} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜₂ (Semifield.toCommGroupWithZero.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (Module.toMulActionWithZero.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6))))} (f : LinearMap.{u5, u3, u4, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u5, u3, u4, u2, u1, u6} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p (fun (_x : ι') => q) f) (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Preorder.toLE.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instPartialOrder.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))))) (Seminorm.comp.{u5, u3, u4, u2} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 q f) (HSMul.hSMul.{0, u4, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (instHSMul.{0, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instSMul.{0, u5, u4} NNReal 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (Finset.sup.{u4, u1} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
+Case conversion may be inaccurate. Consider using '#align seminorm.is_bounded_const Seminorm.isBounded_constₓ'. -/
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
     IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι)(C : ℝ≥0), q.comp f ≤ C • s.sup p := by
   simp only [is_bounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
+/- warning: seminorm.const_is_bounded -> Seminorm.const_isBounded is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι' : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (ι : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι] {p : Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))} {q : ι' -> (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6)))))} (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u1, u2, u3, u4, u6, u5} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 (fun (_x : ι) => p) q f) (forall (i : ι'), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.partialOrder.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C p)))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {𝕜₂ : Type.{u3}} {E : Type.{u4}} {F : Type.{u2}} {ι' : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : AddCommGroup.{u4} E] [_inst_3 : Module.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2)] [_inst_4 : NormedField.{u3} 𝕜₂] [_inst_5 : AddCommGroup.{u2} F] [_inst_6 : Module.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)] {σ₁₂ : RingHom.{u5, u3} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u5, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u5} 𝕜 _inst_1) (NormedField.toNorm.{u3} 𝕜₂ _inst_4) σ₁₂] (ι : Type.{u6}) [_inst_8 : Nonempty.{succ u6} ι] {p : Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))} {q : ι' -> (Seminorm.{u3, u2} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u2} F _inst_5) (SMulZeroClass.toSMul.{u3, u2} 𝕜₂ F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜₂ F (CommMonoidWithZero.toZero.{u3} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜₂ (Semifield.toCommGroupWithZero.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_5))))) (Module.toMulActionWithZero.{u3, u2} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6)))))} (f : LinearMap.{u5, u3, u4, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (Semifield.toDivisionSemiring.{u3} 𝕜₂ (Field.toSemifield.{u3} 𝕜₂ (NormedField.toField.{u3} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_3 _inst_6), Iff (Seminorm.IsBounded.{u5, u3, u4, u2, u6, u1} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 (fun (_x : ι) => p) q f) (forall (i : ι'), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Preorder.toLE.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u4} (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instPartialOrder.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (MonoidWithZero.toZero.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (Ring.toSemiring.{u5} 𝕜 (SeminormedRing.toRing.{u5} 𝕜 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))))) (Seminorm.comp.{u5, u3, u4, u2} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u3} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u3} 𝕜₂ (NormedField.toNormedCommRing.{u3} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f) (HSMul.hSMul.{0, u4, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (instHSMul.{0, u4} NNReal (Seminorm.{u5, u4} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3))))) (Seminorm.instSMul.{0, u5, u4} NNReal 𝕜 E (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u4} E _inst_2) (SMulZeroClass.toSMul.{u5, u4} 𝕜 E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜 E (CommMonoidWithZero.toZero.{u5} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜 (Semifield.toCommGroupWithZero.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜 E (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E _inst_2))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 E (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_2) _inst_3)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C p)))
+Case conversion may be inaccurate. Consider using '#align seminorm.const_is_bounded Seminorm.const_isBoundedₓ'. -/
 theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) : IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, (q i).comp f ≤ C • p :=
   by
@@ -253,6 +343,12 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
   simp only [h, Finset.sup_singleton]
 #align seminorm.const_is_bounded Seminorm.const_isBounded
 
+/- warning: seminorm.is_bounded_sup -> Seminorm.isBounded_sup is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} {ι' : Type.{u6}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] {p : ι -> (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))} {q : ι' -> (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6)))))} {f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6}, (Seminorm.IsBounded.{u1, u2, u3, u4, u5, u6} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p q f) -> (forall (s' : Finset.{u6} ι'), Exists.{1} NNReal (fun (C : NNReal) => Exists.{succ u5} (Finset.{u5} ι) (fun (s : Finset.{u5} ι) => LE.le.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.partialOrder.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u4, u6} (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) ι' (Seminorm.semilatticeSup.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) (Seminorm.orderBot.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) _inst_5 _inst_6) s' q) f) (SMul.smul.{0, u3} NNReal (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.hasSmul.{0, u1, u3} NNReal 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (Finset.sup.{u3, u5} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
+but is expected to have type
+  forall {𝕜 : Type.{u6}} {𝕜₂ : Type.{u4}} {E : Type.{u5}} {F : Type.{u3}} {ι : Type.{u2}} {ι' : Type.{u1}} [_inst_1 : NormedField.{u6} 𝕜] [_inst_2 : AddCommGroup.{u5} E] [_inst_3 : Module.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2)] [_inst_4 : NormedField.{u4} 𝕜₂] [_inst_5 : AddCommGroup.{u3} F] [_inst_6 : Module.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5)] {σ₁₂ : RingHom.{u6, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u6, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u6} 𝕜 _inst_1) (NormedField.toNorm.{u4} 𝕜₂ _inst_4) σ₁₂] {p : ι -> (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3)))))} {q : ι' -> (Seminorm.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u3} F _inst_5) (SMulZeroClass.toSMul.{u4, u3} 𝕜₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜₂ F (CommMonoidWithZero.toZero.{u4} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜₂ (Semifield.toCommGroupWithZero.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (Module.toMulActionWithZero.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_6)))))} {f : LinearMap.{u6, u4, u5, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6}, (Seminorm.IsBounded.{u6, u4, u5, u3, u2, u1} 𝕜 𝕜₂ E F ι ι' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 p q f) -> (forall (s' : Finset.{u1} ι'), Exists.{1} NNReal (fun (C : NNReal) => Exists.{succ u2} (Finset.{u2} ι) (fun (s : Finset.{u2} ι) => LE.le.{u5} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Preorder.toLE.{u5} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (PartialOrder.toPreorder.{u5} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.instPartialOrder.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (MonoidWithZero.toZero.{u6} 𝕜 (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (Ring.toSemiring.{u6} 𝕜 (SeminormedRing.toRing.{u6} 𝕜 (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))))) (Seminorm.comp.{u6, u4, u5, u3} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u3, u1} (Seminorm.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u3} F _inst_5) (SMulZeroClass.toSMul.{u4, u3} 𝕜₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜₂ F (CommMonoidWithZero.toZero.{u4} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜₂ (Semifield.toCommGroupWithZero.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (Module.toMulActionWithZero.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_6))))) ι' (Seminorm.instSemilatticeSup.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u3} F _inst_5) (SMulZeroClass.toSMul.{u4, u3} 𝕜₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜₂ F (CommMonoidWithZero.toZero.{u4} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜₂ (Semifield.toCommGroupWithZero.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_5))))) (Module.toMulActionWithZero.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_6))))) (Seminorm.instOrderBot.{u4, u3} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u4} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ _inst_4))) _inst_5 _inst_6) s' q) f) (HSMul.hSMul.{0, u5, u5} NNReal (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (instHSMul.{0, u5} NNReal (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.instSMul.{0, u6, u5} NNReal 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (Finset.sup.{u5, u2} (Seminorm.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u5} E _inst_2) (SMulZeroClass.toSMul.{u6, u5} 𝕜 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u6, u5} 𝕜 E (CommMonoidWithZero.toZero.{u6} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u6} 𝕜 (Semifield.toCommGroupWithZero.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u6, u5} 𝕜 E (Semiring.toMonoidWithZero.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E _inst_2))))) (Module.toMulActionWithZero.{u6, u5} 𝕜 E (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u6, u5} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u6} 𝕜 (NormedCommRing.toSeminormedCommRing.{u6} 𝕜 (NormedField.toNormedCommRing.{u6} 𝕜 _inst_1))) _inst_2 _inst_3) s p)))))
+Case conversion may be inaccurate. Consider using '#align seminorm.is_bounded_sup Seminorm.isBounded_supₓ'. -/
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
     ∃ (C : ℝ≥0)(s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
@@ -281,11 +377,19 @@ section Topology
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι]
 
+#print WithSeminorms /-
 /-- The proposition that the topology of `E` is induced by a family of seminorms `p`. -/
 structure WithSeminorms (p : SeminormFamily 𝕜 E ι) [t : TopologicalSpace E] : Prop where
   topology_eq_withSeminorms : t = p.ModuleFilterBasis.topology
 #align with_seminorms WithSeminorms
+-/
 
+/- warning: with_seminorms.with_seminorms_eq -> WithSeminorms.withSeminorms_eq is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3} [t : TopologicalSpace.{u2} E], (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p t) -> (Eq.{succ u2} (TopologicalSpace.{u2} E) t (ModuleFilterBasis.topology.{u1, u2} 𝕜 E (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (SeminormFamily.moduleFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3} [t : TopologicalSpace.{u2} E], (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p t) -> (Eq.{succ u2} (TopologicalSpace.{u2} E) t (ModuleFilterBasis.topology.{u3, u2} 𝕜 E (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) _inst_2 _inst_3 (SeminormFamily.moduleFilterBasis.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_4)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.with_seminorms_eq WithSeminorms.withSeminorms_eqₓ'. -/
 theorem WithSeminorms.withSeminorms_eq {p : SeminormFamily 𝕜 E ι} [t : TopologicalSpace E]
     (hp : WithSeminorms p) : t = p.ModuleFilterBasis.topology :=
   hp.1
@@ -295,12 +399,24 @@ variable [TopologicalSpace E]
 
 variable {p : SeminormFamily 𝕜 E ι}
 
+/- warning: with_seminorms.topological_add_group -> WithSeminorms.topologicalAddGroup is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (TopologicalAddGroup.{u2} E _inst_5 (AddCommGroup.toAddGroup.{u2} E _inst_2))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (TopologicalAddGroup.{u2} E _inst_5 (AddCommGroup.toAddGroup.{u2} E _inst_2))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroupₓ'. -/
 theorem WithSeminorms.topologicalAddGroup (hp : WithSeminorms p) : TopologicalAddGroup E :=
   by
   rw [hp.with_seminorms_eq]
   exact AddGroupFilterBasis.isTopologicalAddGroup _
 #align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroup
 
+/- warning: with_seminorms.has_basis -> WithSeminorms.hasBasis is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_5 (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (fun (s : Set.{u2} E) => Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) s (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (id.{succ u2} (Set.{u2} E)))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_5 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) (fun (s : Set.{u2} E) => Membership.mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.instMembershipSet.{u2} (Set.{u2} E)) s (SeminormFamily.basisSets.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (id.{succ u2} (Set.{u2} E)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis WithSeminorms.hasBasisₓ'. -/
 theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id :=
   by
@@ -308,6 +424,12 @@ theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
   exact AddGroupFilterBasis.nhds_zero_hasBasis _
 #align with_seminorms.has_basis WithSeminorms.hasBasis
 
+/- warning: with_seminorms.has_basis_zero_ball -> WithSeminorms.hasBasis_zero_ball is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Filter.HasBasis.{u2, succ u3} E (Prod.{u3, 0} (Finset.{u3} ι) Real) (nhds.{u2} E _inst_5 (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (fun (sr : Prod.{u3, 0} (Finset.{u3} ι) Real) => LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.snd.{u3, 0} (Finset.{u3} ι) Real sr)) (fun (sr : Prod.{u3, 0} (Finset.{u3} ι) Real) => Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, 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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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u3, 0} (Finset.{u3} ι) Real sr) p) (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 (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) (Prod.snd.{u3, 0} (Finset.{u3} ι) Real sr)))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Filter.HasBasis.{u2, succ u1} E (Prod.{u1, 0} (Finset.{u1} ι) Real) (nhds.{u2} E _inst_5 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) (fun (sr : Prod.{u1, 0} (Finset.{u1} ι) Real) => LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)) (fun (sr : Prod.{u1, 0} (Finset.{u1} ι) Real) => Seminorm.ball.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u1, 0} (Finset.{u1} ι) Real sr) p) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))))) (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ballₓ'. -/
 theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball 0 sr.2 :=
   by
@@ -320,6 +442,12 @@ theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
     exact ⟨_, ⟨s, r, hr, rfl⟩, hV⟩
 #align with_seminorms.has_basis_zero_ball WithSeminorms.hasBasis_zero_ball
 
+/- warning: with_seminorms.has_basis_ball -> WithSeminorms.hasBasis_ball is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall {x : E}, Filter.HasBasis.{u2, succ u3} E (Prod.{u3, 0} (Finset.{u3} ι) Real) (nhds.{u2} E _inst_5 x) (fun (sr : Prod.{u3, 0} (Finset.{u3} ι) Real) => LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.snd.{u3, 0} (Finset.{u3} ι) Real sr)) (fun (sr : Prod.{u3, 0} (Finset.{u3} ι) Real) => Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u3, 0} (Finset.{u3} ι) Real sr) p) x (Prod.snd.{u3, 0} (Finset.{u3} ι) Real sr)))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall {x : E}, Filter.HasBasis.{u2, succ u1} E (Prod.{u1, 0} (Finset.{u1} ι) Real) (nhds.{u2} E _inst_5 x) (fun (sr : Prod.{u1, 0} (Finset.{u1} ι) Real) => LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)) (fun (sr : Prod.{u1, 0} (Finset.{u1} ι) Real) => Seminorm.ball.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 _inst_3) (Prod.fst.{u1, 0} (Finset.{u1} ι) Real sr) p) x (Prod.snd.{u1, 0} (Finset.{u1} ι) Real sr)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ballₓ'. -/
 theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (𝓝 (x : E)).HasBasis (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 :=
   by
@@ -332,6 +460,12 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
   rwa [vadd_eq_add, add_zero] at this
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
 
+/- warning: with_seminorms.mem_nhds_iff -> WithSeminorms.mem_nhds_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (x : E) (U : Set.{u2} E), Iff (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) U (nhds.{u2} E _inst_5 x)) (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Exists.{1} Real (fun (r : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Seminorm.ball.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E 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(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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p) x r) U)))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (x : E) (U : Set.{u2} E), Iff (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) U (nhds.{u2} E _inst_5 x)) (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Seminorm.ball.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Finset.sup.{u2, u1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E 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(SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 _inst_3) s p) x r) U)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iffₓ'. -/
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around `x`.-/
 theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
@@ -339,6 +473,12 @@ theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
   rw [hp.has_basis_ball.mem_iff, Prod.exists]
 #align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iff
 
+/- warning: with_seminorms.is_open_iff_mem_balls -> WithSeminorms.isOpen_iff_mem_balls is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (U : Set.{u2} E), Iff (IsOpen.{u2} E _inst_5 U) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x U) -> (Exists.{succ u3} (Finset.{u3} ι) (fun (s : Finset.{u3} ι) => Exists.{1} Real (fun (r : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p) x r) U))))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (U : Set.{u2} E), Iff (IsOpen.{u2} E _inst_5 U) (forall (x : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x U) -> (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Seminorm.ball.{u3, u2} 𝕜 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(AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 _inst_3) s p) x r) U))))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_ballsₓ'. -/
 /-- The open sets of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around all of their points.-/
 theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
@@ -346,12 +486,18 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
   simp_rw [← WithSeminorms.mem_nhds_iff hp _ U, isOpen_iff_mem_nhds]
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 
+/- warning: with_seminorms.t1_of_separating -> WithSeminorms.T1_of_separating is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (x : E), (Ne.{succ u2} E x (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) -> (Exists.{succ u3} ι (fun (i : ι) => Ne.{1} Real (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 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_inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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} 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(NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (T1Space.{u2} E _inst_5)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (x : E), (Ne.{succ u2} E x (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) -> (Exists.{succ u1} ι (fun (i : ι) => Ne.{1} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) (FunLike.coe.{succ u2, succ u2, 1} 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(NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i) x) (OfNat.ofNat.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) 0 (Zero.toOfNat0.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instZeroReal))))) -> (T1Space.{u2} E _inst_5)
+Case conversion may be inaccurate. Consider using '#align with_seminorms.t1_of_separating WithSeminorms.T1_of_separatingₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
 and `topological_add_group.t3_space` -/
 /-- A separating family of seminorms induces a T₁ topology. -/
-theorem WithSeminorms.t1_of_separating (hp : WithSeminorms p)
+theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
     (h : ∀ (x) (_ : x ≠ 0), ∃ i, p i x ≠ 0) : T1Space E :=
   by
   haveI := hp.topological_add_group
@@ -361,10 +507,16 @@ theorem WithSeminorms.t1_of_separating (hp : WithSeminorms p)
   cases' h x hx with i pi_nonzero
   refine' ⟨{i}, p i x, by positivity, subset_compl_singleton_iff.mpr _⟩
   rw [Finset.sup_singleton, mem_ball, zero_sub, map_neg_eq_map, not_lt]
-#align with_seminorms.t1_of_separating WithSeminorms.t1_of_separating
-
+#align with_seminorms.t1_of_separating WithSeminorms.T1_of_separating
+
+/- warning: with_seminorms.separating_of_t1 -> WithSeminorms.separating_of_T1 is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3} [_inst_6 : T1Space.{u2} E _inst_5], (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (x : E), (Ne.{succ u2} E x (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) -> (Exists.{succ u3} ι (fun (i : ι) => Ne.{1} Real (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 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_inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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} 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(NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u3} E] {p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3} [_inst_6 : T1Space.{u3} E _inst_5], (WithSeminorms.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (x : E), (Ne.{succ u3} E x (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2)))))))) -> (Exists.{succ u1} ι (fun (i : ι) => Ne.{1} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) 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(Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u2, u3} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E 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(SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))))) (p i) x) (OfNat.ofNat.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) 0 (Zero.toOfNat0.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instZeroReal)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1ₓ'. -/
 /-- A family of seminorms inducing a T₁ topology is separating. -/
-theorem WithSeminorms.separating_of_t1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
+theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
     ∃ i, p i x ≠ 0 := by
   have := ((t1Space_TFAE E).out 0 9).mp inferInstance
   by_contra' h
@@ -372,17 +524,23 @@ theorem WithSeminorms.separating_of_t1 [T1Space E] (hp : WithSeminorms p) (x : E
   rw [hp.has_basis_zero_ball.specializes_iff]
   rintro ⟨s, r⟩ (hr : 0 < r)
   simp only [ball_finset_sup_eq_Inter _ _ _ hr, mem_Inter₂, mem_ball_zero, h, hr, forall_true_iff]
-#align with_seminorms.separating_of_t1 WithSeminorms.separating_of_t1
-
+#align with_seminorms.separating_of_t1 WithSeminorms.separating_of_T1
+
+/- warning: with_seminorms.separating_iff_t1 -> WithSeminorms.separating_iff_T1 is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (forall (x : E), (Ne.{succ u2} E x (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) -> (Exists.{succ u3} ι (fun (i : ι) => Ne.{1} Real (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 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_inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) (T1Space.{u2} E _inst_5))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (forall (x : E), (Ne.{succ u2} E x (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) -> (Exists.{succ u1} ι (fun (i : ι) => Ne.{1} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i) x) (OfNat.ofNat.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) 0 (Zero.toOfNat0.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instZeroReal))))) (T1Space.{u2} E _inst_5))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.separating_iff_t1 WithSeminorms.separating_iff_T1ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
-theorem WithSeminorms.separating_iff_t1 (hp : WithSeminorms p) :
+theorem WithSeminorms.separating_iff_T1 (hp : WithSeminorms p) :
     (∀ (x) (_ : x ≠ 0), ∃ i, p i x ≠ 0) ↔ T1Space E :=
   by
-  refine' ⟨WithSeminorms.t1_of_separating hp, _⟩
+  refine' ⟨WithSeminorms.T1_of_separating hp, _⟩
   intro
-  exact WithSeminorms.separating_of_t1 hp
-#align with_seminorms.separating_iff_t1 WithSeminorms.separating_iff_t1
+  exact WithSeminorms.separating_of_T1 hp
+#align with_seminorms.separating_iff_t1 WithSeminorms.separating_iff_T1
 
 end Topology
 
@@ -392,6 +550,12 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [Topo
 
 variable {p : SeminormFamily 𝕜 E ι}
 
+/- warning: with_seminorms.tendsto_nhds' -> WithSeminorms.tendsto_nhds' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) {f : Filter.{u3} F} (y₀ : E), Iff (Filter.Tendsto.{u3, u2} F E u f (nhds.{u2} E _inst_5 y₀)) (forall (s : Finset.{u4} ι) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Filter.Eventually.{u3} F (fun (x : F) => LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Finset.sup.{u2, u4} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s p) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) (u x) y₀)) ε) f)))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {F : Type.{u1}} {ι : Type.{u2}} [_inst_1 : NormedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u2} ι] [_inst_5 : TopologicalSpace.{u3} E] {p : SeminormFamily.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) {f : Filter.{u1} F} (y₀ : E), Iff (Filter.Tendsto.{u1, u3} F E u f (nhds.{u3} E _inst_5 y₀)) (forall (s : Finset.{u2} ι) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Filter.Eventually.{u1} F (fun (x : F) => LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u4, u3} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))))) (Finset.sup.{u3, u2} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) _inst_2 _inst_3) s p) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) ε) f)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'ₓ'. -/
 /-- Convergence along filters for `with_seminorms`.
 
 Variant with `finset.sup`. -/
@@ -400,6 +564,12 @@ theorem WithSeminorms.tendsto_nhds' (hp : WithSeminorms p) (u : F → E) {f : Fi
   by simp [hp.has_basis_ball.tendsto_right_iff]
 #align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'
 
+/- warning: with_seminorms.tendsto_nhds -> WithSeminorms.tendsto_nhds is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) {f : Filter.{u3} F} (y₀ : E), Iff (Filter.Tendsto.{u3, u2} F E u f (nhds.{u2} E _inst_5 y₀)) (forall (i : ι) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Filter.Eventually.{u3} F (fun (x : F) => LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) (u x) y₀)) ε) f)))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {F : Type.{u1}} {ι : Type.{u2}} [_inst_1 : NormedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u2} ι] [_inst_5 : TopologicalSpace.{u3} E] {p : SeminormFamily.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3}, (WithSeminorms.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) {f : Filter.{u1} F} (y₀ : E), Iff (Filter.Tendsto.{u1, u3} F E u f (nhds.{u3} E _inst_5 y₀)) (forall (i : ι) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Filter.Eventually.{u1} F (fun (x : F) => LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E 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𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u4, u3} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))))) (p i) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) ε) f)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds WithSeminorms.tendsto_nhdsₓ'. -/
 /-- Convergence along filters for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
     Filter.Tendsto u f (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∀ᶠ x in f, p i (u x - y₀) < ε :=
@@ -412,6 +582,12 @@ theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Fil
 
 variable [SemilatticeSup F] [Nonempty F]
 
+/- warning: with_seminorms.tendsto_nhds_at_top -> WithSeminorms.tendsto_nhds_atTop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] [_inst_5 : TopologicalSpace.{u2} E] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3} [_inst_6 : SemilatticeSup.{u3} F] [_inst_7 : Nonempty.{succ u3} F], (WithSeminorms.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) (y₀ : E), Iff (Filter.Tendsto.{u3, u2} F E u (Filter.atTop.{u3} F (PartialOrder.toPreorder.{u3} F (SemilatticeSup.toPartialOrder.{u3} F _inst_6))) (nhds.{u2} E _inst_5 y₀)) (forall (i : ι) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u3} F (fun (x₀ : F) => forall (x : F), (LE.le.{u3} F (Preorder.toHasLe.{u3} F (PartialOrder.toPreorder.{u3} F (SemilatticeSup.toPartialOrder.{u3} F _inst_6))) x₀ x) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) (u x) y₀)) ε)))))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {F : Type.{u1}} {ι : Type.{u2}} [_inst_1 : NormedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u2} ι] [_inst_5 : TopologicalSpace.{u3} E] {p : SeminormFamily.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3} [_inst_6 : SemilatticeSup.{u1} F] [_inst_7 : Nonempty.{succ u1} F], (WithSeminorms.{u4, u3, u2} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_4 p _inst_5) -> (forall (u : F -> E) (y₀ : E), Iff (Filter.Tendsto.{u1, u3} F E u (Filter.atTop.{u1} F (PartialOrder.toPreorder.{u1} F (SemilatticeSup.toPartialOrder.{u1} F _inst_6))) (nhds.{u3} E _inst_5 y₀)) (forall (i : ι) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} F (fun (x₀ : F) => forall (x : F), (LE.le.{u1} F (Preorder.toLE.{u1} F (PartialOrder.toPreorder.{u1} F (SemilatticeSup.toPartialOrder.{u1} F _inst_6))) x₀ x) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u4, u3} (Seminorm.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u4, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))))))) (p i) (HSub.hSub.{u3, u3, u3} E E E (instHSub.{u3} E (SubNegMonoid.toSub.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2)))) (u x) y₀)) ε)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.tendsto_nhds_at_top WithSeminorms.tendsto_nhds_atTopₓ'. -/
 /-- Limit `→ ∞` for `with_seminorms`. -/
 theorem WithSeminorms.tendsto_nhds_atTop (hp : WithSeminorms p) (u : F → E) (y₀ : E) :
     Filter.Tendsto u Filter.atTop (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∃ x₀, ∀ x, x₀ ≤ x → p i (u x - y₀) < ε :=
@@ -432,6 +608,12 @@ variable [Nonempty ι]
 
 include t
 
+/- warning: seminorm_family.with_seminorms_of_nhds -> SeminormFamily.withSeminorms_of_nhds is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Filter.{u2} E) (nhds.{u2} E t (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (FilterBasis.filter.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (ModuleFilterBasis.toAddGroupFilterBasis.{u1, u2} 𝕜 E (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (SeminormFamily.moduleFilterBasis.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p _inst_5))))) -> (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p t)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Filter.{u2} E) (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) (FilterBasis.filter.{u2} E (AddGroupFilterBasis.toFilterBasis.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2) (ModuleFilterBasis.toAddGroupFilterBasis.{u3, u2} 𝕜 E (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) _inst_2 _inst_3 (SeminormFamily.moduleFilterBasis.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p t))))) -> (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 t p _inst_4)
+Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminorms_of_nhdsₓ'. -/
 theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
     (h : 𝓝 (0 : E) = p.ModuleFilterBasis.toFilterBasis.filterₓ) : WithSeminorms p :=
   by
@@ -441,12 +623,24 @@ theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
   exact h
 #align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminorms_of_nhds
 
+/- warning: seminorm_family.with_seminorms_of_has_basis -> SeminormFamily.withSeminorms_of_hasBasis is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), (Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E t (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (fun (s : Set.{u2} E) => Membership.Mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.hasMem.{u2} (Set.{u2} E)) s (SeminormFamily.basisSets.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (id.{succ u2} (Set.{u2} E))) -> (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p t)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), (Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) (fun (s : Set.{u2} E) => Membership.mem.{u2, u2} (Set.{u2} E) (Set.{u2} (Set.{u2} E)) (Set.instMembershipSet.{u2} (Set.{u2} E)) s (SeminormFamily.basisSets.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 p)) (id.{succ u2} (Set.{u2} E))) -> (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 t p _inst_4)
+Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasisₓ'. -/
 theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
     (h : (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id) : WithSeminorms p :=
   p.withSeminorms_of_nhds <|
     Filter.HasBasis.eq_of_same_basis h p.AddGroupFilterBasis.toFilterBasis.HasBasis
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
+/- warning: seminorm_family.with_seminorms_iff_nhds_eq_infi -> SeminormFamily.withSeminorms_iff_nhds_eq_iInf is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p t) (Eq.{succ u2} (Filter.{u2} E) (nhds.{u2} E t (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 (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (iInf.{u2, succ u3} (Filter.{u2} E) (ConditionallyCompleteLattice.toHasInf.{u2} (Filter.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Filter.{u2} E) (Filter.completeLattice.{u2} E))) ι (fun (i : ι) => Filter.comap.{u2, 0} E Real (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (p i)) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 t p _inst_4) (Eq.{succ u2} (Filter.{u2} E) (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) (iInf.{u2, succ u1} (Filter.{u2} E) (ConditionallyCompleteLattice.toInfSet.{u2} (Filter.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Filter.{u2} E) (Filter.instCompleteLatticeFilter.{u2} E))) ι (fun (i : ι) => Filter.comap.{u2, 0} E Real (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i)) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInfₓ'. -/
 theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 0 : Filter E) = ⨅ i, (𝓝 0).comap (p i) :=
   by
@@ -456,6 +650,12 @@ theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E
   exact AddGroupFilterBasis.nhds_zero_eq _
 #align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInf
 
+/- warning: with_seminorms.continuous_seminorm -> WithSeminorms.continuous_seminorm is a dubious translation:
+lean 3 declaration is
+  forall {𝕝 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_2 : AddCommGroup.{u2} E] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] [_inst_6 : NontriviallyNormedField.{u1} 𝕝] [_inst_7 : Module.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_8 : ContinuousConstSMul.{u1, u2} 𝕝 E t (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))] {p : SeminormFamily.{u1, u2, u3} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6) _inst_2 _inst_7}, (WithSeminorms.{u1, u2, u3} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6) _inst_2 _inst_7 _inst_5 p t) -> (forall (i : ι), Continuous.{u2, 0} E Real t (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) (fun (_x : Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕝 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 (NontriviallyNormedField.toNormedField.{u1} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) (p i)))
+but is expected to have type
+  forall {𝕝 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_2 : AddCommGroup.{u2} E] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : NontriviallyNormedField.{u3} 𝕝] [_inst_7 : Module.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_8 : ContinuousConstSMul.{u3, u2} 𝕝 E _inst_4 (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))] {p : SeminormFamily.{u3, u2, u1} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6) _inst_2 _inst_7}, (WithSeminorms.{u3, u2, u1} 𝕝 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6) _inst_2 _inst_7 t p _inst_4) -> (forall (i : ι), Continuous.{u2, 0} E Real _inst_4 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7))))) 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7)))) (Seminorm.instSeminormClass.{u3, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (CommMonoidWithZero.toZero.{u3} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕝 (Semifield.toCommGroupWithZero.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕝 E (DivisionSemiring.toSemiring.{u3} 𝕝 (Semifield.toDivisionSemiring.{u3} 𝕝 (Field.toSemifield.{u3} 𝕝 (NormedField.toField.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_7)))))))) (p i)))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminormₓ'. -/
 theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
     [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
     Continuous (p i) := by
@@ -464,6 +664,12 @@ theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module
   exact Filter.mem_iInf_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
 
+/- warning: seminorm_family.with_seminorms_iff_topological_space_eq_infi -> SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : TopologicalSpace.{u2} E] [_inst_4 : TopologicalAddGroup.{u2} E t (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p t) (Eq.{succ u2} (TopologicalSpace.{u2} E) t (iInf.{u2, succ u3} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toHasInf.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.completeLattice.{u2} E))) ι (fun (i : ι) => UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u2} E _inst_2 (Seminorm.toAddGroupSeminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [t : Nonempty.{succ u1} ι] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 t p _inst_4) (Eq.{succ u2} (TopologicalSpace.{u2} E) _inst_4 (iInf.{u2, succ u1} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toInfSet.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{u2} E))) ι (fun (i : ι) => UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u2} E _inst_2 (Seminorm.toAddGroupSeminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i))))))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
 each seminorm individually. We express this as a characterization of `with_seminorms p`. -/
@@ -483,6 +689,12 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormF
 
 omit t
 
+/- warning: seminorm_family.with_seminorms_iff_uniform_space_eq_infi -> SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Nonempty.{succ u3} ι] [u : UniformSpace.{u2} E] [_inst_6 : UniformAddGroup.{u2} E u (AddCommGroup.toAddGroup.{u2} E _inst_2)] (p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p (UniformSpace.toTopologicalSpace.{u2} E u)) (Eq.{succ u2} (UniformSpace.{u2} E) u (iInf.{u2, succ u3} (UniformSpace.{u2} E) (UniformSpace.hasInf.{u2} E) ι (fun (i : ι) => PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u2} E _inst_2 (Seminorm.toAddGroupSeminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (p i)))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Nonempty.{succ u1} ι] [u : UniformSpace.{u3} E] [_inst_6 : UniformAddGroup.{u3} E u (AddCommGroup.toAddGroup.{u3} E _inst_2)] (p : SeminormFamily.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3), Iff (WithSeminorms.{u2, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_3 _inst_5 p (UniformSpace.toTopologicalSpace.{u3} E u)) (Eq.{succ u3} (UniformSpace.{u3} E) u (iInf.{u3, succ u1} (UniformSpace.{u3} E) (instInfSetUniformSpace.{u3} E) ι (fun (i : ι) => PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (AddGroupSeminorm.toSeminormedAddCommGroup.{u3} E _inst_2 (Seminorm.toAddGroupSeminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (p i)))))))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
 induced by each seminorm individually. We express this as a characterization of
@@ -504,6 +716,12 @@ end TopologicalAddGroup
 
 section NormedSpace
 
+/- warning: norm_with_seminorms -> norm_withSeminorms is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2], WithSeminorms.{u1, u2, 0} 𝕜 E (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) _inst_1 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (instNonempty.{1} (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.inhabited (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) => normSeminorm.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)))
+but is expected to have type
+  forall (𝕜 : Type.{u2}) (E : Type.{u1}) [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2], WithSeminorms.{u2, u1, 0} 𝕜 E (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) _inst_1 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) (instNonempty.{1} (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instInhabitedFinSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) => normSeminorm.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2)))
+Case conversion may be inaccurate. Consider using '#align norm_with_seminorms norm_withSeminormsₓ'. -/
 /-- The topology of a `normed_space 𝕜 E` is induced by the seminorm `norm_seminorm 𝕜 E`. -/
 theorem norm_withSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E] [NormedSpace 𝕜 E] :
     WithSeminorms fun _ : Fin 1 => normSeminorm 𝕜 E :=
@@ -537,6 +755,12 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 variable [TopologicalSpace E]
 
+/- warning: with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded -> WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] {s : Set.{u2} E}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 s) (forall (I : Finset.{u3} ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Finset.sup.{u2, u3} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) x) r)))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 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.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u2, u3, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u3} E] {s : Set.{u3} E}, (WithSeminorms.{u2, u3, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) _inst_5 s) (forall (I : Finset.{u1} ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u2, u3} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))))))) (Finset.sup.{u3, u1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) x) r)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedₓ'. -/
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, I.sup p x < r :=
   by
@@ -562,6 +786,12 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   exact (Finset.sup I p).ball_zero_absorbs_ball_zero hr
 #align with_seminorms.is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded
 
+/- warning: with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded -> WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {G : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u3} G}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 (Set.image.{u3, u2} G E f s)) (forall (I : Finset.{u4} ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : G), (Membership.Mem.{u3, u3} G (Set.{u3} G) (Set.hasMem.{u3} G) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Finset.sup.{u2, u4} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) (f x)) r)))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {G : Type.{u4}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u4} G}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_5 (Set.image.{u4, u2} G E f s)) (forall (I : Finset.{u1} ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : G), (Membership.mem.{u4, u4} G (Set.{u4} G) (Set.instMembershipSet.{u4} G) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (f x)) Real.instLTReal (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (Finset.sup.{u2, u1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_3) I p) (f x)) r)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_boundedₓ'. -/
 theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔
@@ -569,6 +799,12 @@ theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G →
   by simp_rw [hp.is_vonN_bounded_iff_finset_seminorm_bounded, Set.ball_image_iff]
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
 
+/- warning: with_seminorms.is_vonN_bounded_iff_seminorm_bounded -> WithSeminorms.isVonNBounded_iff_seminorm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] {s : Set.{u2} E}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 s) (forall (i : ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (p i) x) r)))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} 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.{u3} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u2, u3, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u3} E] {s : Set.{u3} E}, (WithSeminorms.{u2, u3, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) _inst_5 s) (forall (i : ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u3, succ u3, 1} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u3, u3, 0} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u3} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u3, u2, u3} (Seminorm.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u2, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 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.{u3} E _inst_2) _inst_3)))))))) (p i) x) r)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_boundedₓ'. -/
 theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i x < r :=
   by
@@ -592,6 +828,12 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
   exact ⟨1, zero_lt_one, fun _ _ => zero_lt_one⟩
 #align with_seminorms.is_vonN_bounded_iff_seminorm_bounded WithSeminorms.isVonNBounded_iff_seminorm_bounded
 
+/- warning: with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded -> WithSeminorms.image_isVonNBounded_iff_seminorm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {G : Type.{u3}} {ι : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u4} ι] {p : SeminormFamily.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u3} G}, (WithSeminorms.{u1, u2, u4} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_5 (Set.image.{u3, u2} G E f s)) (forall (i : ι), Exists.{1} Real (fun (r : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (fun (hr : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) => forall (x : G), (Membership.Mem.{u3, u3} G (Set.{u3} G) (Set.hasMem.{u3} G) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u2, succ u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{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 _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 _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 _inst_2) _inst_3))))) (p i) (f x)) r)))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {G : Type.{u4}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_5 : TopologicalSpace.{u2} E] (f : G -> E) {s : Set.{u4} G}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p _inst_5) -> (Iff (Bornology.IsVonNBounded.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_5 (Set.image.{u4, u2} G E f s)) (forall (i : ι), Exists.{1} Real (fun (r : Real) => And (GT.gt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : G), (Membership.mem.{u4, u4} G (Set.{u4} G) (Set.instMembershipSet.{u4} G) x s) -> (LT.lt.{0} ((fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) (f x)) Real.instLTReal (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (a : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) a) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u3, u2} (Seminorm.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u3, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (p i) (f x)) r)))))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_boundedₓ'. -/
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ (r : _)(hr : 0 < r), ∀ x ∈ s, p i (f x) < r :=
@@ -618,6 +860,12 @@ variable {τ₁₂ : 𝕝 →+* 𝕝₂} [RingHomIsometric τ₁₂]
 
 variable [Nonempty ι] [Nonempty ι']
 
+/- warning: seminorm.continuous_of_continuous_comp -> Seminorm.continuous_of_continuous_comp is a dubious translation:
+lean 3 declaration is
+  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι' : Type.{u5}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_7 : AddCommGroup.{u4} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u4} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_14 : Nonempty.{succ u5} ι'] {q : SeminormFamily.{u2, u4, u5} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u3} E] [_inst_16 : TopologicalAddGroup.{u3} E _inst_15 (AddCommGroup.toAddGroup.{u3} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)], (WithSeminorms.{u2, u4, u5} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10), (forall (i : ι'), Continuous.{u3, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u3, succ u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (fun (_x : Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕝 𝕝₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 _inst_7 _inst_5 _inst_10 (q i) f))) -> (Continuous.{u3, u4} E F _inst_15 _inst_17 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10 τ₁₂) f)))
+but is expected to have type
+  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u5}} {E : Type.{u2}} {F : Type.{u4}} {ι' : Type.{u3}} [_inst_2 : AddCommGroup.{u2} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u2} 𝕝 E (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_7 : AddCommGroup.{u4} F] [_inst_9 : NormedField.{u5} 𝕝₂] [_inst_10 : Module.{u5, u4} 𝕝₂ F (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {τ₁₂ : RingHom.{u1, u5} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u1} 𝕝 (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u5} 𝕝₂ (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u5} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u1} 𝕝 _inst_4) (NormedField.toNorm.{u5} 𝕝₂ _inst_9) τ₁₂] [_inst_14 : Nonempty.{succ u3} ι'] {q : SeminormFamily.{u5, u4, u3} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u2} E] [_inst_16 : TopologicalAddGroup.{u2} E _inst_15 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)], (WithSeminorms.{u5, u4, u3} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u5, u2, u4} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10), (forall (i : ι'), Continuous.{u2, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u1, u2} (Seminorm.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (Seminorm.instSeminormClass.{u1, u2} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕝 E (MonoidWithZero.toZero.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))))))) (Seminorm.comp.{u1, u5, u2, u4} 𝕝 𝕝₂ E F (SeminormedCommRing.toSeminormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕝₂ (NormedField.toNormedCommRing.{u5} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 _inst_7 _inst_5 _inst_10 (q i) f))) -> (Continuous.{u2, u4} E F _inst_15 _inst_17 (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u5, u2, u4} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u1, u5, u2, u4} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u1} 𝕝 (Semifield.toDivisionSemiring.{u1} 𝕝 (Field.toSemifield.{u1} 𝕝 (NormedField.toField.{u1} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u5} 𝕝₂ (Semifield.toDivisionSemiring.{u5} 𝕝₂ (Field.toSemifield.{u5} 𝕝₂ (NormedField.toField.{u5} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10 τ₁₂) f)))
+Case conversion may be inaccurate. Consider using '#align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_compₓ'. -/
 theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i, Continuous ((q i).comp f)) : Continuous f :=
@@ -630,12 +878,24 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
   exact (map_zero _).symm
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
 
+/- warning: seminorm.continuous_iff_continuous_comp -> Seminorm.continuous_iff_continuous_comp is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι' : Type.{u5}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 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.{u3} E _inst_2)] [_inst_6 : NontriviallyNormedField.{u2} 𝕜₂] [_inst_7 : AddCommGroup.{u4} F] [_inst_8 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))))} [_inst_11 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (NormedField.toHasNorm.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) (NormedField.toHasNorm.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6)) σ₁₂] [_inst_14 : Nonempty.{succ u5} ι'] {q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6) _inst_7 _inst_8} [_inst_15 : TopologicalSpace.{u3} E] [_inst_16 : TopologicalAddGroup.{u3} E _inst_15 (AddCommGroup.toAddGroup.{u3} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)] [_inst_19 : ContinuousConstSMul.{u2, u4} 𝕜₂ F _inst_17 (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_8))))], (WithSeminorms.{u2, u4, u5} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6) _inst_7 _inst_8 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8), Iff (Continuous.{u3, u4} E F _inst_15 _inst_17 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕜 𝕜₂ 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.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8 σ₁₂) f)) (forall (i : ι'), Continuous.{u3, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (coeFn.{succ u3, succ u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (fun (_x : Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) => E -> Real) (Seminorm.hasCoeToFun.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_6)))) σ₁₂ _inst_11 _inst_2 _inst_7 _inst_3 _inst_8 (q i) f))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u5}} {E : Type.{u2}} {F : Type.{u4}} {ι' : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (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 _inst_2)] [_inst_6 : NontriviallyNormedField.{u5} 𝕜₂] [_inst_7 : AddCommGroup.{u4} F] [_inst_8 : Module.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {σ₁₂ : RingHom.{u1, u5} 𝕜 𝕜₂ (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)))))) (Semiring.toNonAssocSemiring.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))))} [_inst_11 : RingHomIsometric.{u1, u5} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (NormedField.toNorm.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) (NormedField.toNorm.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)) σ₁₂] [_inst_14 : Nonempty.{succ u3} ι'] {q : SeminormFamily.{u5, u4, u3} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6) _inst_7 _inst_8} [_inst_15 : TopologicalSpace.{u2} E] [_inst_16 : TopologicalAddGroup.{u2} E _inst_15 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)] [_inst_19 : ContinuousConstSMul.{u5, u4} 𝕜₂ F _inst_17 (SMulZeroClass.toSMul.{u5, u4} 𝕜₂ F (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_7))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜₂ F (CommMonoidWithZero.toZero.{u5} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜₂ (Semifield.toCommGroupWithZero.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_7))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_7))))) (Module.toMulActionWithZero.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_8))))], (WithSeminorms.{u5, u4, u3} 𝕜₂ F ι' (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6) _inst_7 _inst_8 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u5, u2, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8), Iff (Continuous.{u2, u4} E F _inst_15 _inst_17 (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u5, u2, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u1, u5, u2, u4} 𝕜 𝕜₂ 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.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_3 _inst_8 σ₁₂) f)) (forall (i : ι'), Continuous.{u2, 0} E Real _inst_15 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (FunLike.coe.{succ u2, succ u2, 1} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E (fun (_x : E) => (fun (a._@.Mathlib.Analysis.Seminorm._hyg.838 : E) => Real) _x) (SubadditiveHomClass.toFunLike.{u2, u2, 0} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real Real.orderedAddCommMonoid))) (AddGroupSeminormClass.toAddLEAddHomClass.{u2, u2, 0} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) E Real (AddCommGroup.toAddGroup.{u2} E _inst_2) Real.orderedAddCommMonoid (SeminormClass.toAddGroupSeminormClass.{u2, u1, u2} (Seminorm.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (Seminorm.instSeminormClass.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddGroup.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))))) (Seminorm.comp.{u1, u5, u2, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ (NontriviallyNormedField.toNormedField.{u5} 𝕜₂ _inst_6)))) σ₁₂ _inst_11 _inst_2 _inst_7 _inst_3 _inst_8 (q i) f))))
+Case conversion may be inaccurate. Consider using '#align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_compₓ'. -/
 theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [TopologicalSpace E]
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul 𝕜₂ F]
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) : Continuous f ↔ ∀ i, Continuous ((q i).comp f) :=
   ⟨fun h i => Continuous.comp (hq.continuous_seminorm i) h, continuous_of_continuous_comp hq f⟩
 #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp
 
+/- warning: seminorm.continuous_from_bounded -> Seminorm.continuous_from_bounded is a dubious translation:
+lean 3 declaration is
+  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} {ι' : Type.{u6}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_7 : AddCommGroup.{u4} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u4} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7)] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u5} ι] [_inst_14 : Nonempty.{succ u6} ι'] {p : SeminormFamily.{u1, u3, u5} 𝕝 E ι _inst_4 _inst_2 _inst_5} {q : SeminormFamily.{u2, u4, u6} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u3} E] [_inst_16 : TopologicalAddGroup.{u3} E _inst_15 (AddCommGroup.toAddGroup.{u3} E _inst_2)], (WithSeminorms.{u1, u3, u5} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p _inst_15) -> (forall [_inst_17 : TopologicalSpace.{u4} F] [_inst_18 : TopologicalAddGroup.{u4} F _inst_17 (AddCommGroup.toAddGroup.{u4} F _inst_7)], (WithSeminorms.{u2, u4, u6} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10), (Seminorm.IsBounded.{u1, u2, u3, u4, u5, u6} 𝕝 𝕝₂ E F ι ι' _inst_4 _inst_2 _inst_5 _inst_9 _inst_7 _inst_10 τ₁₂ _inst_12 p q f) -> (Continuous.{u3, u4} E F _inst_15 _inst_17 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_7) _inst_5 _inst_10 τ₁₂) f))))
+but is expected to have type
+  forall {𝕝 : Type.{u6}} {𝕝₂ : Type.{u3}} {E : Type.{u5}} {F : Type.{u2}} {ι : Type.{u4}} {ι' : Type.{u1}} [_inst_2 : AddCommGroup.{u5} E] [_inst_4 : NormedField.{u6} 𝕝] [_inst_5 : Module.{u6, u5} 𝕝 E (DivisionSemiring.toSemiring.{u6} 𝕝 (Semifield.toDivisionSemiring.{u6} 𝕝 (Field.toSemifield.{u6} 𝕝 (NormedField.toField.{u6} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2)] [_inst_7 : AddCommGroup.{u2} F] [_inst_9 : NormedField.{u3} 𝕝₂] [_inst_10 : Module.{u3, u2} 𝕝₂ F (DivisionSemiring.toSemiring.{u3} 𝕝₂ (Semifield.toDivisionSemiring.{u3} 𝕝₂ (Field.toSemifield.{u3} 𝕝₂ (NormedField.toField.{u3} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_7)] {τ₁₂ : RingHom.{u6, u3} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u6} 𝕝 (DivisionSemiring.toSemiring.{u6} 𝕝 (Semifield.toDivisionSemiring.{u6} 𝕝 (Field.toSemifield.{u6} 𝕝 (NormedField.toField.{u6} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u3} 𝕝₂ (DivisionSemiring.toSemiring.{u3} 𝕝₂ (Semifield.toDivisionSemiring.{u3} 𝕝₂ (Field.toSemifield.{u3} 𝕝₂ (NormedField.toField.{u3} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u6, u3} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u6} 𝕝 (Semifield.toDivisionSemiring.{u6} 𝕝 (Field.toSemifield.{u6} 𝕝 (NormedField.toField.{u6} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕝₂ (Semifield.toDivisionSemiring.{u3} 𝕝₂ (Field.toSemifield.{u3} 𝕝₂ (NormedField.toField.{u3} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u6} 𝕝 _inst_4) (NormedField.toNorm.{u3} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u4} ι] [_inst_14 : Nonempty.{succ u1} ι'] {p : SeminormFamily.{u6, u5, u4} 𝕝 E ι _inst_4 _inst_2 _inst_5} {q : SeminormFamily.{u3, u2, u1} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10} [_inst_15 : TopologicalSpace.{u5} E] [_inst_16 : TopologicalAddGroup.{u5} E _inst_15 (AddCommGroup.toAddGroup.{u5} E _inst_2)], (WithSeminorms.{u6, u5, u4} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p _inst_15) -> (forall [_inst_17 : TopologicalSpace.{u2} F] [_inst_18 : TopologicalAddGroup.{u2} F _inst_17 (AddCommGroup.toAddGroup.{u2} F _inst_7)], (WithSeminorms.{u3, u2, u1} 𝕝₂ F ι' _inst_9 _inst_7 _inst_10 _inst_14 q _inst_17) -> (forall (f : LinearMap.{u6, u3, u5, u2} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u6} 𝕝 (Semifield.toDivisionSemiring.{u6} 𝕝 (Field.toSemifield.{u6} 𝕝 (NormedField.toField.{u6} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕝₂ (Semifield.toDivisionSemiring.{u3} 𝕝₂ (Field.toSemifield.{u3} 𝕝₂ (NormedField.toField.{u3} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_7) _inst_5 _inst_10), (Seminorm.IsBounded.{u6, u3, u5, u2, u4, u1} 𝕝 𝕝₂ E F ι ι' _inst_4 _inst_2 _inst_5 _inst_9 _inst_7 _inst_10 τ₁₂ _inst_12 p q f) -> (Continuous.{u5, u2} E F _inst_15 _inst_17 (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (LinearMap.{u6, u3, u5, u2} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u6} 𝕝 (Semifield.toDivisionSemiring.{u6} 𝕝 (Field.toSemifield.{u6} 𝕝 (NormedField.toField.{u6} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕝₂ (Semifield.toDivisionSemiring.{u3} 𝕝₂ (Field.toSemifield.{u3} 𝕝₂ (NormedField.toField.{u3} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_7) _inst_5 _inst_10) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u6, u3, u5, u2} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u6} 𝕝 (Semifield.toDivisionSemiring.{u6} 𝕝 (Field.toSemifield.{u6} 𝕝 (NormedField.toField.{u6} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕝₂ (Semifield.toDivisionSemiring.{u3} 𝕝₂ (Field.toSemifield.{u3} 𝕝₂ (NormedField.toField.{u3} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_7) _inst_5 _inst_10 τ₁₂) f))))
+Case conversion may be inaccurate. Consider using '#align seminorm.continuous_from_bounded Seminorm.continuous_from_boundedₓ'. -/
 theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'}
     [TopologicalSpace E] [TopologicalAddGroup E] (hp : WithSeminorms p) [TopologicalSpace F]
     [TopologicalAddGroup F] (hq : WithSeminorms q) (f : E →ₛₗ[τ₁₂] F)
@@ -656,6 +916,12 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
   simp only [le_add_iff_nonneg_right, zero_le']
 #align seminorm.continuous_from_bounded Seminorm.continuous_from_bounded
 
+/- warning: seminorm.cont_with_seminorms_normed_space -> Seminorm.cont_withSeminorms_normedSpace is a dubious translation:
+lean 3 declaration is
+  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {E : Type.{u3}} {ι : Type.{u4}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u1} 𝕝] [_inst_5 : Module.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_9 : NormedField.{u2} 𝕝₂] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u4} ι] (F : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} F] [_inst_16 : NormedSpace.{u2, u5} 𝕝₂ F _inst_9 _inst_15] [_inst_17 : UniformSpace.{u3} E] [_inst_18 : UniformAddGroup.{u3} E _inst_17 (AddCommGroup.toAddGroup.{u3} E _inst_2)] {p : ι -> (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))))}, (WithSeminorms.{u1, u3, u4} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p (UniformSpace.toTopologicalSpace.{u3} E _inst_17)) -> (forall (f : LinearMap.{u1, u2, u3, u5} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)), (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E 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(AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Preorder.toHasLe.{u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 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(NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E 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_inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))))) (Seminorm.comp.{u1, u2, u3, u5} 𝕝 𝕝₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) (normSeminorm.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) f) (SMul.smul.{0, u3} NNReal 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(AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (Finset.sup.{u3, u4} (Seminorm.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.orderBot.{u1, u3} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) _inst_2 _inst_5) s p))))) -> (Continuous.{u3, u5} E F (UniformSpace.toTopologicalSpace.{u3} E _inst_17) (UniformSpace.toTopologicalSpace.{u5} F (PseudoMetricSpace.toUniformSpace.{u5} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F _inst_15))) (coeFn.{max (succ u3) (succ u5), max (succ u3) (succ u5)} (LinearMap.{u1, u2, u3, u5} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)) (fun (_x : LinearMap.{u1, u2, u3, u5} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u5} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u2, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) τ₁₂) f)))
+but is expected to have type
+  forall {𝕝 : Type.{u2}} {𝕝₂ : Type.{u4}} {E : Type.{u3}} {ι : Type.{u1}} [_inst_2 : AddCommGroup.{u3} E] [_inst_4 : NormedField.{u2} 𝕝] [_inst_5 : Module.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_9 : NormedField.{u4} 𝕝₂] {τ₁₂ : RingHom.{u2, u4} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u4} 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u2, u4} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u2} 𝕝 _inst_4) (NormedField.toNorm.{u4} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u1} ι] (F : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} F] [_inst_16 : NormedSpace.{u4, u5} 𝕝₂ F _inst_9 _inst_15] [_inst_17 : UniformSpace.{u3} E] [_inst_18 : UniformAddGroup.{u3} E _inst_17 (AddCommGroup.toAddGroup.{u3} E _inst_2)] {p : ι -> (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))))}, (WithSeminorms.{u2, u3, u1} 𝕝 E ι _inst_4 _inst_2 _inst_5 _inst_13 p (UniformSpace.toTopologicalSpace.{u3} E _inst_17)) -> (forall (f : LinearMap.{u2, u4, u3, u5} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)), (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u3} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Preorder.toLE.{u3} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (PartialOrder.toPreorder.{u3} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.instPartialOrder.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (MonoidWithZero.toZero.{u2} 𝕝 (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (Ring.toSemiring.{u2} 𝕝 (SeminormedRing.toRing.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))))) (Seminorm.comp.{u2, u4, u3, u5} 𝕝 𝕝₂ E F (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (SeminormedCommRing.toSeminormedRing.{u4} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u4} 𝕝₂ (NormedField.toNormedCommRing.{u4} 𝕝₂ _inst_9))) τ₁₂ _inst_12 _inst_2 (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) (normSeminorm.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) f) (HSMul.hSMul.{0, u3, u3} NNReal (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (instHSMul.{0, u3} NNReal (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.instSMul.{0, u2, u3} NNReal 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (Finset.sup.{u3, u1} (Seminorm.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) ι (Seminorm.instSemilatticeSup.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toSMul.{u2, u3} 𝕝 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5))))) (Seminorm.instOrderBot.{u2, u3} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 _inst_4))) _inst_2 _inst_5) s p))))) -> (Continuous.{u3, u5} E F (UniformSpace.toTopologicalSpace.{u3} E _inst_17) (UniformSpace.toTopologicalSpace.{u5} F (PseudoMetricSpace.toUniformSpace.{u5} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F _inst_15))) (FunLike.coe.{max (succ u3) (succ u5), succ u3, succ u5} (LinearMap.{u2, u4, u3, u5} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u4, u3, u5} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕝₂ (Semifield.toDivisionSemiring.{u4} 𝕝₂ (Field.toSemifield.{u4} 𝕝₂ (NormedField.toField.{u4} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u5} F (SeminormedAddCommGroup.toAddCommGroup.{u5} F _inst_15)) _inst_5 (NormedSpace.toModule.{u4, u5} 𝕝₂ F _inst_9 _inst_15 _inst_16) τ₁₂) f)))
+Case conversion may be inaccurate. Consider using '#align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpaceₓ'. -/
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι)(C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
@@ -664,6 +930,12 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
   exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 
+/- warning: seminorm.cont_normed_space_to_with_seminorms -> Seminorm.cont_normedSpace_to_withSeminorms is a dubious translation:
+lean 3 declaration is
+  forall {𝕝 : Type.{u1}} {𝕝₂ : Type.{u2}} {F : Type.{u3}} {ι : Type.{u4}} [_inst_4 : NormedField.{u1} 𝕝] [_inst_7 : AddCommGroup.{u3} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u3} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)] {τ₁₂ : RingHom.{u1, u2} 𝕝 𝕝₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕝 (Ring.toNonAssocRing.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕝₂ (Ring.toNonAssocRing.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u1, u2} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (NormedField.toHasNorm.{u1} 𝕝 _inst_4) (NormedField.toHasNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u4} ι] (E : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} E] [_inst_16 : NormedSpace.{u1, u5} 𝕝 E _inst_4 _inst_15] [_inst_17 : UniformSpace.{u3} F] [_inst_18 : UniformAddGroup.{u3} F _inst_17 (AddCommGroup.toAddGroup.{u3} F _inst_7)] {q : ι -> (Seminorm.{u2, u3} 𝕝₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) (AddCommGroup.toAddGroup.{u3} F _inst_7) (SMulZeroClass.toHasSmul.{u2, u3} 𝕝₂ F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝₂ F (MulZeroClass.toHasZero.{u2} 𝕝₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕝₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕝₂ (Semiring.toMonoidWithZero.{u2} 𝕝₂ (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝₂ F (Semiring.toMonoidWithZero.{u2} 𝕝₂ (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)))) (Module.toMulActionWithZero.{u2, u3} 𝕝₂ F (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) _inst_10)))))}, (WithSeminorms.{u2, u3, u4} 𝕝₂ F ι _inst_9 _inst_7 _inst_10 _inst_13 q (UniformSpace.toTopologicalSpace.{u3} F _inst_17)) -> (forall (f : LinearMap.{u1, u2, u5, u3} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10), (forall (i : ι), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u5} (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Preorder.toHasLe.{u5} (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E 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𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (PartialOrder.toPreorder.{u5} (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.partialOrder.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))))) (Seminorm.comp.{u1, u2, u5, u3} 𝕝 𝕝₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15) _inst_7 (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 (q i) f) (SMul.smul.{0, u5} NNReal (Seminorm.{u1, u5} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.hasSmul.{0, u1, u5} NNReal 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toHasSmul.{u1, u5} 𝕝 E (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (SMulWithZero.toSmulZeroClass.{u1, u5} 𝕝 E (MulZeroClass.toHasZero.{u1} 𝕝 (MulZeroOneClass.toMulZeroClass.{u1} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (MulActionWithZero.toSMulWithZero.{u1, u5} 𝕝 E (Semiring.toMonoidWithZero.{u1} 𝕝 (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))))) (AddZeroClass.toHasZero.{u5} E (AddMonoid.toAddZeroClass.{u5} E (AddCommMonoid.toAddMonoid.{u5} E (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15))))) (Module.toMulActionWithZero.{u1, u5} 𝕝 E (Ring.toSemiring.{u1} 𝕝 (SeminormedRing.toRing.{u1} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕝 (NormedCommRing.toSeminormedCommRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16))))) (MulAction.toHasSmul.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid))) (Mul.toSMul.{0} NNReal (MulOneClass.toHasMul.{0} NNReal (Monoid.toMulOneClass.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring))))) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{0} Real (Monoid.toMulAction.{0} Real Real.monoid)))) C (normSeminorm.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))) -> (Continuous.{u5, u3} E F (UniformSpace.toTopologicalSpace.{u5} E (PseudoMetricSpace.toUniformSpace.{u5} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} E _inst_15))) (UniformSpace.toTopologicalSpace.{u3} F _inst_17) (coeFn.{max (succ u5) (succ u3), max (succ u5) (succ u3)} (LinearMap.{u1, u2, u5, u3} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10) (fun (_x : LinearMap.{u1, u2, u5, u3} 𝕝 𝕝₂ (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u5, u3} 𝕝 𝕝₂ E F (Ring.toSemiring.{u1} 𝕝 (NormedRing.toRing.{u1} 𝕝 (NormedCommRing.toNormedRing.{u1} 𝕝 (NormedField.toNormedCommRing.{u1} 𝕝 _inst_4)))) (Ring.toSemiring.{u2} 𝕝₂ (NormedRing.toRing.{u2} 𝕝₂ (NormedCommRing.toNormedRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u1, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 τ₁₂) f)))
+but is expected to have type
+  forall {𝕝 : Type.{u4}} {𝕝₂ : Type.{u2}} {F : Type.{u3}} {ι : Type.{u1}} [_inst_4 : NormedField.{u4} 𝕝] [_inst_7 : AddCommGroup.{u3} F] [_inst_9 : NormedField.{u2} 𝕝₂] [_inst_10 : Module.{u2, u3} 𝕝₂ F (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7)] {τ₁₂ : RingHom.{u4, u2} 𝕝 𝕝₂ (Semiring.toNonAssocSemiring.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (Semiring.toNonAssocSemiring.{u2} 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))))} [_inst_12 : RingHomIsometric.{u4, u2} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (NormedField.toNorm.{u4} 𝕝 _inst_4) (NormedField.toNorm.{u2} 𝕝₂ _inst_9) τ₁₂] [_inst_13 : Nonempty.{succ u1} ι] (E : Type.{u5}) [_inst_15 : SeminormedAddCommGroup.{u5} E] [_inst_16 : NormedSpace.{u4, u5} 𝕝 E _inst_4 _inst_15] [_inst_17 : UniformSpace.{u3} F] [_inst_18 : UniformAddGroup.{u3} F _inst_17 (AddCommGroup.toAddGroup.{u3} F _inst_7)] {q : ι -> (Seminorm.{u2, u3} 𝕝₂ F (SeminormedCommRing.toSeminormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) (AddCommGroup.toAddGroup.{u3} F _inst_7) (SMulZeroClass.toSMul.{u2, u3} 𝕝₂ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_7))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕝₂ F (CommMonoidWithZero.toZero.{u2} 𝕝₂ (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝₂ (Semifield.toCommGroupWithZero.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_7))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕝₂ F (Semiring.toMonoidWithZero.{u2} 𝕝₂ (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_7))))) (Module.toMulActionWithZero.{u2, u3} 𝕝₂ F (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) _inst_10)))))}, (WithSeminorms.{u2, u3, u1} 𝕝₂ F ι _inst_9 _inst_7 _inst_10 _inst_13 q (UniformSpace.toTopologicalSpace.{u3} F _inst_17)) -> (forall (f : LinearMap.{u4, u2, u5, u3} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10), (forall (i : ι), Exists.{1} NNReal (fun (C : NNReal) => LE.le.{u5} (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Preorder.toLE.{u5} (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (PartialOrder.toPreorder.{u5} (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.instPartialOrder.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (AddCommGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (MonoidWithZero.toZero.{u4} 𝕝 (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4)))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (Ring.toSemiring.{u4} 𝕝 (SeminormedRing.toRing.{u4} 𝕝 (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))))) (Seminorm.comp.{u4, u2, u5, u3} 𝕝 𝕝₂ E F (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedCommRing.toSeminormedRing.{u2} 𝕝₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕝₂ (NormedField.toNormedCommRing.{u2} 𝕝₂ _inst_9))) τ₁₂ _inst_12 (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15) _inst_7 (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 (q i) f) (HSMul.hSMul.{0, u5, u5} NNReal (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (instHSMul.{0, u5} NNReal (Seminorm.{u4, u5} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))))) (Seminorm.instSMul.{0, u4, u5} NNReal 𝕝 E (SeminormedCommRing.toSeminormedRing.{u4} 𝕝 (NormedCommRing.toSeminormedCommRing.{u4} 𝕝 (NormedField.toNormedCommRing.{u4} 𝕝 _inst_4))) (SeminormedAddGroup.toAddGroup.{u5} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} E _inst_15)) (SMulZeroClass.toSMul.{u4, u5} 𝕝 E (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (SMulWithZero.toSMulZeroClass.{u4, u5} 𝕝 E (CommMonoidWithZero.toZero.{u4} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕝 (Semifield.toCommGroupWithZero.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (MulActionWithZero.toSMulWithZero.{u4, u5} 𝕝 E (Semiring.toMonoidWithZero.{u4} 𝕝 (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4))))) (NegZeroClass.toZero.{u5} E (SubNegZeroMonoid.toNegZeroClass.{u5} E (SubtractionMonoid.toSubNegZeroMonoid.{u5} E (SubtractionCommMonoid.toSubtractionMonoid.{u5} E (AddCommGroup.toDivisionAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)))))) (Module.toMulActionWithZero.{u4, u5} 𝕝 E (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16))))) Seminorm.smul_nnreal_real (Algebra.toSMul.{0, 0} NNReal NNReal instNNRealCommSemiring instNNRealSemiring (Algebra.id.{0} NNReal instNNRealCommSemiring)) (IsScalarTower.left.{0, 0} NNReal Real (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{0} Real (MulActionWithZero.toMulAction.{0, 0} Real Real Real.instMonoidWithZeroReal Real.instZeroReal (MonoidWithZero.toMulActionWithZero.{0} Real Real.instMonoidWithZeroReal)))))) C (normSeminorm.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16)))) -> (Continuous.{u5, u3} E F (UniformSpace.toTopologicalSpace.{u5} E (PseudoMetricSpace.toUniformSpace.{u5} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} E _inst_15))) (UniformSpace.toTopologicalSpace.{u3} F _inst_17) (FunLike.coe.{max (succ u3) (succ u5), succ u5, succ u3} (LinearMap.{u4, u2, u5, u3} 𝕝 𝕝₂ (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) τ₁₂ E F (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u4, u2, u5, u3} 𝕝 𝕝₂ E F (DivisionSemiring.toSemiring.{u4} 𝕝 (Semifield.toDivisionSemiring.{u4} 𝕝 (Field.toSemifield.{u4} 𝕝 (NormedField.toField.{u4} 𝕝 _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕝₂ (Semifield.toDivisionSemiring.{u2} 𝕝₂ (Field.toSemifield.{u2} 𝕝₂ (NormedField.toField.{u2} 𝕝₂ _inst_9)))) (AddCommGroup.toAddCommMonoid.{u5} E (SeminormedAddCommGroup.toAddCommGroup.{u5} E _inst_15)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_7) (NormedSpace.toModule.{u4, u5} 𝕝 E _inst_4 _inst_15 _inst_16) _inst_10 τ₁₂) f)))
+Case conversion may be inaccurate. Consider using '#align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminormsₓ'. -/
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
@@ -683,7 +955,13 @@ open LocallyConvexSpace
 variable [Nonempty ι] [NormedField 𝕜] [NormedSpace ℝ 𝕜] [AddCommGroup E] [Module 𝕜 E] [Module ℝ E]
   [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E] [TopologicalAddGroup E]
 
-theorem WithSeminorms.to_locallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
+/- warning: with_seminorms.to_locally_convex_space -> WithSeminorms.toLocallyConvexSpace is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : Nonempty.{succ u3} ι] [_inst_2 : NormedField.{u1} 𝕜] [_inst_3 : NormedSpace.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_6 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_7 : IsScalarTower.{0, u1, u2} Real 𝕜 E (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2))))))) (NormedSpace.toModule.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2))))) _inst_3))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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 _inst_2)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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 _inst_2))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_5)))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6))))] [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : TopologicalAddGroup.{u2} E _inst_8 (AddCommGroup.toAddGroup.{u2} E _inst_4)] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι _inst_2 _inst_4 _inst_5}, (WithSeminorms.{u1, u2, u3} 𝕜 E ι _inst_2 _inst_4 _inst_5 _inst_1 p _inst_8) -> (LocallyConvexSpace.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6 _inst_8)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : Nonempty.{succ u1} ι] [_inst_2 : NormedField.{u3} 𝕜] [_inst_3 : NormedSpace.{0, u3} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕜 (NormedRing.toNonUnitalNormedRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_2)))))] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_6 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)] [_inst_7 : IsScalarTower.{0, u3, u2} Real 𝕜 E (SMulZeroClass.toSMul.{0, u3} Real 𝕜 (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u3} Real 𝕜 Real.instZeroReal (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u3} Real 𝕜 Real.instMonoidWithZeroReal (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (Module.toMulActionWithZero.{0, u3} Real 𝕜 Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_2))))))) (NormedSpace.toModule.{0, u3} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕜 (NormedRing.toNonUnitalNormedRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_2))))) _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{0, u2} Real E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{0, u2} Real E Real.instZeroReal (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6))))] [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : TopologicalAddGroup.{u2} E _inst_8 (AddCommGroup.toAddGroup.{u2} E _inst_4)] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι _inst_2 _inst_4 _inst_5}, (WithSeminorms.{u3, u2, u1} 𝕜 E ι _inst_2 _inst_4 _inst_5 _inst_1 p _inst_8) -> (LocallyConvexSpace.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_4) _inst_6 _inst_8)
+Case conversion may be inaccurate. Consider using '#align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpaceₓ'. -/
+theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
     LocallyConvexSpace ℝ E :=
   by
   apply of_basis_zero ℝ E id fun s => s ∈ p.basis_sets
@@ -694,7 +972,7 @@ theorem WithSeminorms.to_locallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
     simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs
     rcases hs with ⟨I, r, hr, rfl⟩
     exact convex_ball _ _ _
-#align with_seminorms.to_locally_convex_space WithSeminorms.to_locallyConvexSpace
+#align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpace
 
 end LocallyConvexSpace
 
@@ -702,18 +980,26 @@ section NormedSpace
 
 variable (𝕜) [NormedField 𝕜] [NormedSpace ℝ 𝕜] [SeminormedAddCommGroup E]
 
+/- warning: normed_space.to_locally_convex_space' -> NormedSpace.toLocallyConvexSpace' is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedSpace.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_3] [_inst_5 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_6 : IsScalarTower.{0, u1, u2} Real 𝕜 E (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (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} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (SeminormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (NormedSpace.toModule.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) _inst_2))))) (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 _inst_3))))) (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 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (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 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_5))))], LocallyConvexSpace.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_5 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3)))
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : NormedSpace.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_3] [_inst_5 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3))] [_inst_6 : IsScalarTower.{0, u2, u1} Real 𝕜 E (SMulZeroClass.toSMul.{0, u2} Real 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u2} Real 𝕜 Real.instZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real 𝕜 Real.instMonoidWithZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Module.toMulActionWithZero.{0, u2} Real 𝕜 Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))))) (NormedSpace.toModule.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) _inst_2))))) (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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)) _inst_5))))], LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)) _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3)))
+Case conversion may be inaccurate. Consider using '#align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'ₓ'. -/
 /-- Not an instance since `𝕜` can't be inferred. See `normed_space.to_locally_convex_space` for a
 slightly weaker instance version. -/
-theorem NormedSpace.to_locally_convex_space' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
+theorem NormedSpace.toLocallyConvexSpace' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
     LocallyConvexSpace ℝ E :=
-  (norm_withSeminorms 𝕜 E).to_locallyConvexSpace
-#align normed_space.to_locally_convex_space' NormedSpace.to_locally_convex_space'
+  (norm_withSeminorms 𝕜 E).toLocallyConvexSpace
+#align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'
 
+#print NormedSpace.toLocallyConvexSpace /-
 /-- See `normed_space.to_locally_convex_space'` for a slightly stronger version which is not an
 instance. -/
-instance NormedSpace.to_locallyConvexSpace [NormedSpace ℝ E] : LocallyConvexSpace ℝ E :=
-  NormedSpace.to_locally_convex_space' ℝ
-#align normed_space.to_locally_convex_space NormedSpace.to_locallyConvexSpace
+instance NormedSpace.toLocallyConvexSpace [NormedSpace ℝ E] : LocallyConvexSpace ℝ E :=
+  NormedSpace.toLocallyConvexSpace' ℝ
+#align normed_space.to_locally_convex_space NormedSpace.toLocallyConvexSpace
+-/
 
 end NormedSpace
 
@@ -725,16 +1011,30 @@ variable [NormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F]
 
 variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
+#print SeminormFamily.comp /-
 /-- The family of seminorms obtained by composing each seminorm by a linear map. -/
 def SeminormFamily.comp (q : SeminormFamily 𝕜₂ F ι) (f : E →ₛₗ[σ₁₂] F) : SeminormFamily 𝕜 E ι :=
   fun i => (q i).comp f
 #align seminorm_family.comp SeminormFamily.comp
+-/
 
+/- warning: seminorm_family.comp_apply -> SeminormFamily.comp_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (i : ι) (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f i) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {𝕜₂ : Type.{u5}} {E : Type.{u1}} {F : Type.{u4}} {ι : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormedField.{u5} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u2, u5} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u2, u5} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u2} 𝕜 _inst_1) (NormedField.toNorm.{u5} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u5, u4, u3} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (i : ι) (f : LinearMap.{u2, u5, u1, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u1} (Seminorm.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) (SeminormFamily.comp.{u2, u5, u1, u4, u3} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f i) (Seminorm.comp.{u2, u5, u1, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (q i) f)
+Case conversion may be inaccurate. Consider using '#align seminorm_family.comp_apply SeminormFamily.comp_applyₓ'. -/
 theorem SeminormFamily.comp_apply (q : SeminormFamily 𝕜₂ F ι) (i : ι) (f : E →ₛₗ[σ₁₂] F) :
     q.comp f i = (q i).comp f :=
   rfl
 #align seminorm_family.comp_apply SeminormFamily.comp_apply
 
+/- warning: seminorm_family.finset_sup_comp -> SeminormFamily.finset_sup_comp is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (s : Finset.{u5} ι) (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u3} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.comp.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u4, u5} (Seminorm.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) ι (Seminorm.semilatticeSup.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜₂ F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜₂ F (MulZeroClass.toHasZero.{u2} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u2} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜₂ (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u2} 𝕜₂ (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)))) (Module.toMulActionWithZero.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) (Seminorm.orderBot.{u2, u4} 𝕜₂ F (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4))) _inst_5 _inst_6) s q) f) (Finset.sup.{u3, u5} (Seminorm.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) ι (Seminorm.semilatticeSup.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u3} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))))) (Seminorm.orderBot.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 _inst_3) s (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {𝕜₂ : Type.{u5}} {E : Type.{u1}} {F : Type.{u4}} {ι : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormedField.{u5} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u2, u5} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u2, u5} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u2} 𝕜 _inst_1) (NormedField.toNorm.{u5} 𝕜₂ _inst_4) σ₁₂] (q : SeminormFamily.{u5, u4, u3} 𝕜₂ F ι _inst_4 _inst_5 _inst_6) (s : Finset.{u3} ι) (f : LinearMap.{u2, u5, u1, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), Eq.{succ u1} (Seminorm.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) (Seminorm.comp.{u2, u5, u1, u4} 𝕜 𝕜₂ E F (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) σ₁₂ _inst_7 _inst_2 _inst_5 _inst_3 _inst_6 (Finset.sup.{u4, u3} (Seminorm.{u5, u4} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toSMul.{u5, u4} 𝕜₂ F (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜₂ F (CommMonoidWithZero.toZero.{u5} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜₂ (Semifield.toCommGroupWithZero.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (Module.toMulActionWithZero.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) ι (Seminorm.instSemilatticeSup.{u5, u4} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) (AddCommGroup.toAddGroup.{u4} F _inst_5) (SMulZeroClass.toSMul.{u5, u4} 𝕜₂ F (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u5, u4} 𝕜₂ F (CommMonoidWithZero.toZero.{u5} 𝕜₂ (CommGroupWithZero.toCommMonoidWithZero.{u5} 𝕜₂ (Semifield.toCommGroupWithZero.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u5, u4} 𝕜₂ F (Semiring.toMonoidWithZero.{u5} 𝕜₂ (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4))))) (NegZeroClass.toZero.{u4} F (SubNegZeroMonoid.toNegZeroClass.{u4} F (SubtractionMonoid.toSubNegZeroMonoid.{u4} F (SubtractionCommMonoid.toSubtractionMonoid.{u4} F (AddCommGroup.toDivisionAddCommMonoid.{u4} F _inst_5))))) (Module.toMulActionWithZero.{u5, u4} 𝕜₂ F (DivisionSemiring.toSemiring.{u5} 𝕜₂ (Semifield.toDivisionSemiring.{u5} 𝕜₂ (Field.toSemifield.{u5} 𝕜₂ (NormedField.toField.{u5} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_6))))) (Seminorm.instOrderBot.{u5, u4} 𝕜₂ F (SeminormedCommRing.toSeminormedRing.{u5} 𝕜₂ (NormedCommRing.toSeminormedCommRing.{u5} 𝕜₂ (NormedField.toNormedCommRing.{u5} 𝕜₂ _inst_4))) _inst_5 _inst_6) s q) f) (Finset.sup.{u1, u3} (Seminorm.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) ι (Seminorm.instSemilatticeSup.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddGroup.{u1} E _inst_2) (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 _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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) (Seminorm.instOrderBot.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) _inst_2 _inst_3) s (SeminormFamily.comp.{u2, u5, u1, u4, u3} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f))
+Case conversion may be inaccurate. Consider using '#align seminorm_family.finset_sup_comp SeminormFamily.finset_sup_compₓ'. -/
 theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Finset ι)
     (f : E →ₛₗ[σ₁₂] F) : (s.sup q).comp f = s.sup (q.comp f) :=
   by
@@ -745,6 +1045,12 @@ theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Fi
 
 variable [TopologicalSpace F] [TopologicalAddGroup F]
 
+/- warning: linear_map.with_seminorms_induced -> LinearMap.withSeminorms_induced is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u4} F] [_inst_9 : TopologicalAddGroup.{u4} F _inst_8 (AddCommGroup.toAddGroup.{u4} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall (f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6), WithSeminorms.{u1, u3, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) (TopologicalSpace.induced.{u3, u4} E F (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6 σ₁₂) f) (inferInstance.{succ u4} (TopologicalSpace.{u4} F) _inst_8)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {𝕜₂ : Type.{u4}} {E : Type.{u1}} {F : Type.{u3}} {ι : Type.{u5}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormedField.{u4} 𝕜₂] [_inst_5 : AddCommGroup.{u3} F] [_inst_6 : Module.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5)] {σ₁₂ : RingHom.{u2, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u2, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u2} 𝕜 _inst_1) (NormedField.toNorm.{u4} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u3} F] [_inst_9 : TopologicalAddGroup.{u3} F _inst_8 (AddCommGroup.toAddGroup.{u3} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u4, u3, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u4, u3, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall (f : LinearMap.{u2, u4, u1, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6), WithSeminorms.{u2, u1, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u2, u4, u1, u3, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) (TopologicalSpace.induced.{u1, u3} E F (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u4, u1, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u4, u1, u3} 𝕜 𝕜₂ E F (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6 σ₁₂) f) (inferInstance.{succ u3} (TopologicalSpace.{u3} F) _inst_8)))
+Case conversion may be inaccurate. Consider using '#align linear_map.with_seminorms_induced LinearMap.withSeminorms_inducedₓ'. -/
 theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
     @WithSeminorms 𝕜 E ι _ _ _ _ (q.comp f) (induced f inferInstance) :=
@@ -757,6 +1063,12 @@ theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily
   exact Filter.comap_comap
 #align linear_map.with_seminorms_induced LinearMap.withSeminorms_induced
 
+/- warning: inducing.with_seminorms -> Inducing.withSeminorms is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u2}} {E : Type.{u3}} {F : Type.{u4}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_4 : NormedField.{u2} 𝕜₂] [_inst_5 : AddCommGroup.{u4} F] [_inst_6 : Module.{u2, u4} 𝕜₂ F (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5)] {σ₁₂ : RingHom.{u1, u2} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (NonAssocRing.toNonAssocSemiring.{u2} 𝕜₂ (Ring.toNonAssocRing.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedField.toHasNorm.{u2} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u4} F] [_inst_9 : TopologicalAddGroup.{u4} F _inst_8 (AddCommGroup.toAddGroup.{u4} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u2, u4, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall [_inst_10 : TopologicalSpace.{u3} E] {f : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6}, (Inducing.{u3, u4} E F _inst_10 _inst_8 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6) => E -> F) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} 𝕜 𝕜₂ E F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u2} 𝕜₂ (NormedRing.toRing.{u2} 𝕜₂ (NormedCommRing.toNormedRing.{u2} 𝕜₂ (NormedField.toNormedCommRing.{u2} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} F _inst_5) _inst_3 _inst_6 σ₁₂) f)) -> (WithSeminorms.{u1, u3, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u1, u2, u3, u4, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) _inst_10))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {𝕜₂ : Type.{u4}} {E : Type.{u2}} {F : Type.{u3}} {ι : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : NormedField.{u4} 𝕜₂] [_inst_5 : AddCommGroup.{u3} F] [_inst_6 : Module.{u4, u3} 𝕜₂ F (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5)] {σ₁₂ : RingHom.{u1, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))))} [_inst_7 : RingHomIsometric.{u1, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (NormedField.toNorm.{u1} 𝕜 _inst_1) (NormedField.toNorm.{u4} 𝕜₂ _inst_4) σ₁₂] [_inst_8 : TopologicalSpace.{u3} F] [_inst_9 : TopologicalAddGroup.{u3} F _inst_8 (AddCommGroup.toAddGroup.{u3} F _inst_5)] [hι : Nonempty.{succ u5} ι] {q : SeminormFamily.{u4, u3, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6}, (WithSeminorms.{u4, u3, u5} 𝕜₂ F ι _inst_4 _inst_5 _inst_6 hι q _inst_8) -> (forall [_inst_10 : TopologicalSpace.{u2} E] {f : LinearMap.{u1, u4, u2, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6}, (Inducing.{u2, u3} E F _inst_10 _inst_8 (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u4, u2, u3} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) σ₁₂ E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u1, u4, u2, u3} 𝕜 𝕜₂ E F (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_5) _inst_3 _inst_6 σ₁₂) f)) -> (WithSeminorms.{u1, u2, u5} 𝕜 E ι _inst_1 _inst_2 _inst_3 hι (SeminormFamily.comp.{u1, u4, u2, u3, u5} 𝕜 𝕜₂ E F ι _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7 q f) _inst_10))
+Case conversion may be inaccurate. Consider using '#align inducing.with_seminorms Inducing.withSeminormsₓ'. -/
 theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι} (hq : WithSeminorms q)
     [TopologicalSpace E] {f : E →ₛₗ[σ₁₂] F} (hf : Inducing f) : WithSeminorms (q.comp f) :=
   by
@@ -774,6 +1086,12 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 variable [UniformSpace E] [UniformAddGroup E]
 
+/- warning: with_seminorms.first_countable -> WithSeminorms.first_countable is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{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 _inst_2)] [_inst_4 : Nonempty.{succ u3} ι] [_inst_5 : Countable.{succ u3} ι] {p : SeminormFamily.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_6 : UniformSpace.{u2} E] [_inst_7 : UniformAddGroup.{u2} E _inst_6 (AddCommGroup.toAddGroup.{u2} E _inst_2)], (WithSeminorms.{u1, u2, u3} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p (UniformSpace.toTopologicalSpace.{u2} E _inst_6)) -> (TopologicalSpace.FirstCountableTopology.{u2} E (UniformSpace.toTopologicalSpace.{u2} E _inst_6))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {ι : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Nonempty.{succ u1} ι] [_inst_5 : Countable.{succ u1} ι] {p : SeminormFamily.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3} [_inst_6 : UniformSpace.{u2} E] [_inst_7 : UniformAddGroup.{u2} E _inst_6 (AddCommGroup.toAddGroup.{u2} E _inst_2)], (WithSeminorms.{u3, u2, u1} 𝕜 E ι (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1) _inst_2 _inst_3 _inst_4 p (UniformSpace.toTopologicalSpace.{u2} E _inst_6)) -> (TopologicalSpace.FirstCountableTopology.{u2} E (UniformSpace.toTopologicalSpace.{u2} E _inst_6))
+Case conversion may be inaccurate. Consider using '#align with_seminorms.first_countable WithSeminorms.first_countableₓ'. -/
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology
 is first countable. -/
 theorem WithSeminorms.first_countable (hp : WithSeminorms p) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -683,7 +683,7 @@ open LocallyConvexSpace
 variable [Nonempty ι] [NormedField 𝕜] [NormedSpace ℝ 𝕜] [AddCommGroup E] [Module 𝕜 E] [Module ℝ E]
   [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E] [TopologicalAddGroup E]
 
-theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
+theorem WithSeminorms.to_locallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
     LocallyConvexSpace ℝ E :=
   by
   apply of_basis_zero ℝ E id fun s => s ∈ p.basis_sets
@@ -694,7 +694,7 @@ theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
     simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs
     rcases hs with ⟨I, r, hr, rfl⟩
     exact convex_ball _ _ _
-#align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpace
+#align with_seminorms.to_locally_convex_space WithSeminorms.to_locallyConvexSpace
 
 end LocallyConvexSpace
 
@@ -704,16 +704,16 @@ variable (𝕜) [NormedField 𝕜] [NormedSpace ℝ 𝕜] [SeminormedAddCommGrou
 
 /-- Not an instance since `𝕜` can't be inferred. See `normed_space.to_locally_convex_space` for a
 slightly weaker instance version. -/
-theorem NormedSpace.toLocallyConvexSpace' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
+theorem NormedSpace.to_locally_convex_space' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
     LocallyConvexSpace ℝ E :=
-  (norm_withSeminorms 𝕜 E).toLocallyConvexSpace
-#align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'
+  (norm_withSeminorms 𝕜 E).to_locallyConvexSpace
+#align normed_space.to_locally_convex_space' NormedSpace.to_locally_convex_space'
 
 /-- See `normed_space.to_locally_convex_space'` for a slightly stronger version which is not an
 instance. -/
-instance NormedSpace.toLocallyConvexSpace [NormedSpace ℝ E] : LocallyConvexSpace ℝ E :=
-  NormedSpace.toLocallyConvexSpace' ℝ
-#align normed_space.to_locally_convex_space NormedSpace.toLocallyConvexSpace
+instance NormedSpace.to_locallyConvexSpace [NormedSpace ℝ E] : LocallyConvexSpace ℝ E :=
+  NormedSpace.to_locally_convex_space' ℝ
+#align normed_space.to_locally_convex_space NormedSpace.to_locallyConvexSpace
 
 end NormedSpace
 

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

@@ -110,9 +110,9 @@ theorem basisSets_intersect (U V : Set E) (hU : U ∈ p.basis_sets) (hV : V ∈
       ball_finset_sup_eq_Inter _ _ _ hr₁, ball_finset_sup_eq_Inter _ _ _ hr₂]
     exact
       Set.subset_inter
-        (Set.interᵢ₂_mono' fun i hi =>
+        (Set.iInter₂_mono' fun i hi =>
           ⟨i, Finset.subset_union_left _ _ hi, ball_mono <| min_le_left _ _⟩)
-        (Set.interᵢ₂_mono' fun i hi =>
+        (Set.iInter₂_mono' fun i hi =>
           ⟨i, Finset.subset_union_right _ _ hi, ball_mono <| min_le_right _ _⟩)
 #align seminorm_family.basis_sets_intersect SeminormFamily.basisSets_intersect
 
@@ -196,10 +196,10 @@ protected def moduleFilterBasis : ModuleFilterBasis 𝕜 E
   smul_right' := p.basisSets_smul_right
 #align seminorm_family.module_filter_basis SeminormFamily.moduleFilterBasis
 
-theorem filter_eq_infᵢ (p : SeminormFamily 𝕜 E ι) :
+theorem filter_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     p.ModuleFilterBasis.toFilterBasis.filterₓ = ⨅ i, (𝓝 0).comap (p i) :=
   by
-  refine' le_antisymm (le_infᵢ fun i => _) _
+  refine' le_antisymm (le_iInf fun i => _) _
   · rw [p.module_filter_basis.to_filter_basis.has_basis.le_basis_iff
         (metric.nhds_basis_ball.comap _)]
     intro ε hε
@@ -210,12 +210,12 @@ theorem filter_eq_infᵢ (p : SeminormFamily 𝕜 E ι) :
   · rw [p.module_filter_basis.to_filter_basis.has_basis.ge_iff]
     rintro U (hU : U ∈ p.basis_sets)
     rcases p.basis_sets_iff.mp hU with ⟨s, r, hr, rfl⟩
-    rw [id, Seminorm.ball_finset_sup_eq_interᵢ _ _ _ hr, s.Inter_mem_sets]
+    rw [id, Seminorm.ball_finset_sup_eq_iInter _ _ _ hr, s.Inter_mem_sets]
     exact fun i hi =>
-      Filter.mem_infᵢ_of_mem i
+      Filter.mem_iInf_of_mem i
         ⟨Metric.ball 0 r, Metric.ball_mem_nhds 0 hr,
           Eq.subset (p i).ball_zero_eq_preimage_ball.symm⟩
-#align seminorm_family.filter_eq_infi SeminormFamily.filter_eq_infᵢ
+#align seminorm_family.filter_eq_infi SeminormFamily.filter_eq_iInf
 
 end SeminormFamily
 
@@ -260,12 +260,12 @@ theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂
     obtain rfl | hs' := s'.eq_empty_or_nonempty
     · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
     choose fₛ fC hf using hf
-    use s'.card • s'.sup fC, Finset.bunionᵢ s' fₛ
-    have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.bunionᵢ s' fₛ).sup p :=
+    use s'.card • s'.sup fC, Finset.biUnion s' fₛ
+    have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.biUnion s' fₛ).sup p :=
       by
       intro i hi
       refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
-      exact Finset.sup_mono (Finset.subset_bunionᵢ_of_mem fₛ hi)
+      exact Finset.sup_mono (Finset.subset_biUnion_of_mem fₛ hi)
     refine' (comp_mono f (finset_sup_le_sum q s')).trans _
     simp_rw [← pullback_apply, AddMonoidHom.map_sum, pullback_apply]
     refine' (Finset.sum_le_sum hs).trans _
@@ -447,39 +447,39 @@ theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
     Filter.HasBasis.eq_of_same_basis h p.AddGroupFilterBasis.toFilterBasis.HasBasis
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
-theorem SeminormFamily.withSeminorms_iff_nhds_eq_infᵢ (p : SeminormFamily 𝕜 E ι) :
+theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 0 : Filter E) = ⨅ i, (𝓝 0).comap (p i) :=
   by
   rw [← p.filter_eq_infi]
   refine' ⟨fun h => _, p.with_seminorms_of_nhds⟩
   rw [h.topology_eq_with_seminorms]
   exact AddGroupFilterBasis.nhds_zero_eq _
-#align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_infᵢ
+#align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInf
 
 theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
     [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
     Continuous (p i) := by
   refine' Seminorm.continuous one_pos _
   rw [p.with_seminorms_iff_nhds_eq_infi.mp hp, ball_zero_eq_preimage_ball]
-  exact Filter.mem_infᵢ_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
+  exact Filter.mem_iInf_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
 each seminorm individually. We express this as a characterization of `with_seminorms p`. -/
-theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_infᵢ (p : SeminormFamily 𝕜 E ι) :
+theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔
       t =
         ⨅ i, (p i).toAddGroupSeminorm.toSeminormedAddCommGroup.toUniformSpace.toTopologicalSpace :=
   by
   rw [p.with_seminorms_iff_nhds_eq_infi,
-    TopologicalAddGroup.ext_iff inferInstance (topologicalAddGroup_infᵢ fun i => inferInstance),
-    nhds_infᵢ]
+    TopologicalAddGroup.ext_iff inferInstance (topologicalAddGroup_iInf fun i => inferInstance),
+    nhds_iInf]
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
   all_goals infer_instance
-#align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_infᵢ
+#align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf
 
 omit t
 
@@ -487,18 +487,18 @@ omit t
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
 induced by each seminorm individually. We express this as a characterization of
 `with_seminorms p`. -/
-theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_infᵢ [u : UniformSpace E]
+theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf [u : UniformSpace E]
     [UniformAddGroup E] (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ u = ⨅ i, (p i).toAddGroupSeminorm.toSeminormedAddCommGroup.toUniformSpace :=
   by
   rw [p.with_seminorms_iff_nhds_eq_infi,
-    UniformAddGroup.ext_iff inferInstance (uniformAddGroup_infᵢ fun i => inferInstance),
-    toTopologicalSpace_infᵢ, nhds_infᵢ]
+    UniformAddGroup.ext_iff inferInstance (uniformAddGroup_iInf fun i => inferInstance),
+    toTopologicalSpace_iInf, nhds_iInf]
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
   all_goals infer_instance
-#align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_infᵢ
+#align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf
 
 end TopologicalAddGroup
 
@@ -623,7 +623,7 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i, Continuous ((q i).comp f)) : Continuous f :=
   by
   refine' continuous_of_continuousAt_zero f _
-  simp_rw [ContinuousAt, f.map_zero, q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.tendsto_infᵢ,
+  simp_rw [ContinuousAt, f.map_zero, q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.tendsto_iInf,
     Filter.tendsto_comap_iff]
   intro i
   convert(hf i).ContinuousAt
@@ -690,8 +690,8 @@ theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
   · rw [hp.1, AddGroupFilterBasis.nhds_eq _, AddGroupFilterBasis.N_zero]
     exact FilterBasis.hasBasis _
   · intro s hs
-    change s ∈ Set.unionᵢ _ at hs
-    simp_rw [Set.mem_unionᵢ, Set.mem_singleton_iff] at hs
+    change s ∈ Set.iUnion _ at hs
+    simp_rw [Set.mem_iUnion, Set.mem_singleton_iff] at hs
     rcases hs with ⟨I, r, hr, rfl⟩
     exact convex_ball _ _ _
 #align with_seminorms.to_locally_convex_space WithSeminorms.toLocallyConvexSpace
@@ -751,9 +751,9 @@ theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily
   by
   letI : TopologicalSpace E := induced f inferInstance
   letI : TopologicalAddGroup E := topologicalAddGroup_induced f
-  rw [(q.comp f).withSeminorms_iff_nhds_eq_infᵢ, nhds_induced, map_zero,
-    q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.comap_infᵢ]
-  refine' infᵢ_congr fun i => _
+  rw [(q.comp f).withSeminorms_iff_nhds_eq_iInf, nhds_induced, map_zero,
+    q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.comap_iInf]
+  refine' iInf_congr fun i => _
   exact Filter.comap_comap
 #align linear_map.with_seminorms_induced LinearMap.withSeminorms_induced
 
@@ -782,7 +782,7 @@ theorem WithSeminorms.first_countable (hp : WithSeminorms p) :
   have : (𝓝 (0 : E)).IsCountablyGenerated :=
     by
     rw [p.with_seminorms_iff_nhds_eq_infi.mp hp]
-    exact Filter.infᵢ.isCountablyGenerated _
+    exact Filter.iInf.isCountablyGenerated _
   haveI : (uniformity E).IsCountablyGenerated := UniformAddGroup.uniformity_countably_generated
   exact UniformSpace.firstCountableTopology E
 #align with_seminorms.first_countable WithSeminorms.first_countable

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -298,7 +298,7 @@ variable {p : SeminormFamily 𝕜 E ι}
 theorem WithSeminorms.topologicalAddGroup (hp : WithSeminorms p) : TopologicalAddGroup E :=
   by
   rw [hp.with_seminorms_eq]
-  exact AddGroupFilterBasis.is_topological_add_group _
+  exact AddGroupFilterBasis.isTopologicalAddGroup _
 #align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroup
 
 theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
@@ -432,20 +432,20 @@ variable [Nonempty ι]
 
 include t
 
-theorem SeminormFamily.withSeminormsOfNhds (p : SeminormFamily 𝕜 E ι)
+theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
     (h : 𝓝 (0 : E) = p.ModuleFilterBasis.toFilterBasis.filterₓ) : WithSeminorms p :=
   by
   refine'
     ⟨TopologicalAddGroup.ext inferInstance p.add_group_filter_basis.is_topological_add_group _⟩
   rw [AddGroupFilterBasis.nhds_zero_eq]
   exact h
-#align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminormsOfNhds
+#align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminorms_of_nhds
 
-theorem SeminormFamily.withSeminormsOfHasBasis (p : SeminormFamily 𝕜 E ι)
+theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
     (h : (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basis_sets) id) : WithSeminorms p :=
-  p.withSeminormsOfNhds <|
+  p.withSeminorms_of_nhds <|
     Filter.HasBasis.eq_of_same_basis h p.AddGroupFilterBasis.toFilterBasis.HasBasis
-#align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminormsOfHasBasis
+#align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
 theorem SeminormFamily.withSeminorms_iff_nhds_eq_infᵢ (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 0 : Filter E) = ⨅ i, (𝓝 0).comap (p i) :=
@@ -505,7 +505,7 @@ end TopologicalAddGroup
 section NormedSpace
 
 /-- The topology of a `normed_space 𝕜 E` is induced by the seminorm `norm_seminorm 𝕜 E`. -/
-theorem normWithSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E] [NormedSpace 𝕜 E] :
+theorem norm_withSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E] [NormedSpace 𝕜 E] :
     WithSeminorms fun _ : Fin 1 => normSeminorm 𝕜 E :=
   by
   let p : SeminormFamily 𝕜 E (Fin 1) := fun _ => normSeminorm 𝕜 E
@@ -525,7 +525,7 @@ theorem normWithSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E]
   · rw [Finset.sup_const h]
   rw [finset.not_nonempty_iff_eq_empty.mp h, Finset.sup_empty, ball_bot _ hr]
   exact Set.subset_univ _
-#align norm_with_seminorms normWithSeminorms
+#align norm_with_seminorms norm_withSeminorms
 
 end NormedSpace
 
@@ -661,7 +661,7 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
     (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι)(C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
     Continuous f := by
   rw [← Seminorm.isBounded_const (Fin 1)] at hf
-  exact continuous_from_bounded hp (normWithSeminorms 𝕝₂ F) f hf
+  exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
@@ -669,7 +669,7 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
     Continuous f := by
   rw [← Seminorm.const_isBounded (Fin 1)] at hf
-  exact continuous_from_bounded (normWithSeminorms 𝕝 E) hq f hf
+  exact continuous_from_bounded (norm_withSeminorms 𝕝 E) hq f hf
 #align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminorms
 
 end Seminorm
@@ -687,7 +687,7 @@ theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp :
     LocallyConvexSpace ℝ E :=
   by
   apply of_basis_zero ℝ E id fun s => s ∈ p.basis_sets
-  · rw [hp.1, AddGroupFilterBasis.nhds_eq _, AddGroupFilterBasis.n_zero]
+  · rw [hp.1, AddGroupFilterBasis.nhds_eq _, AddGroupFilterBasis.N_zero]
     exact FilterBasis.hasBasis _
   · intro s hs
     change s ∈ Set.unionᵢ _ at hs
@@ -706,7 +706,7 @@ variable (𝕜) [NormedField 𝕜] [NormedSpace ℝ 𝕜] [SeminormedAddCommGrou
 slightly weaker instance version. -/
 theorem NormedSpace.toLocallyConvexSpace' [NormedSpace 𝕜 E] [Module ℝ E] [IsScalarTower ℝ 𝕜 E] :
     LocallyConvexSpace ℝ E :=
-  (normWithSeminorms 𝕜 E).toLocallyConvexSpace
+  (norm_withSeminorms 𝕜 E).toLocallyConvexSpace
 #align normed_space.to_locally_convex_space' NormedSpace.toLocallyConvexSpace'
 
 /-- See `normed_space.to_locally_convex_space'` for a slightly stronger version which is not an
@@ -745,7 +745,7 @@ theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Fi
 
 variable [TopologicalSpace F] [TopologicalAddGroup F]
 
-theorem LinearMap.withSeminormsInduced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
+theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
     @WithSeminorms 𝕜 E ι _ _ _ _ (q.comp f) (induced f inferInstance) :=
   by
@@ -755,7 +755,7 @@ theorem LinearMap.withSeminormsInduced [hι : Nonempty ι] {q : SeminormFamily 
     q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.comap_infᵢ]
   refine' infᵢ_congr fun i => _
   exact Filter.comap_comap
-#align linear_map.with_seminorms_induced LinearMap.withSeminormsInduced
+#align linear_map.with_seminorms_induced LinearMap.withSeminorms_induced
 
 theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι} (hq : WithSeminorms q)
     [TopologicalSpace E] {f : E →ₛₗ[σ₁₂] F} (hf : Inducing f) : WithSeminorms (q.comp f) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.with_seminorms
-! leanprover-community/mathlib commit ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
+! leanprover-community/mathlib commit b31173ee05c911d61ad6a05bd2196835c932e0ec
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -234,46 +234,41 @@ variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 -- Todo: This should be phrased entirely in terms of the von Neumann bornology.
 /-- The proposition that a linear map is bounded between spaces with families of seminorms. -/
 def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f : E →ₛₗ[σ₁₂] F) : Prop :=
-  ∀ i, ∃ s : Finset ι, ∃ C : ℝ≥0, C ≠ 0 ∧ (q i).comp f ≤ C • s.sup p
+  ∀ i, ∃ s : Finset ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • s.sup p
 #align seminorm.is_bounded Seminorm.IsBounded
 
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
-    IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι)(C : ℝ≥0), C ≠ 0 ∧ q.comp f ≤ C • s.sup p :=
-  by simp only [is_bounded, forall_const]
+    IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι)(C : ℝ≥0), q.comp f ≤ C • s.sup p := by
+  simp only [is_bounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
 theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
-    (f : E →ₛₗ[σ₁₂] F) :
-    IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, C ≠ 0 ∧ (q i).comp f ≤ C • p :=
+    (f : E →ₛₗ[σ₁₂] F) : IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, (q i).comp f ≤ C • p :=
   by
   constructor <;> intro h i
-  · rcases h i with ⟨s, C, hC, h⟩
-    exact ⟨C, hC, le_trans h (smul_le_smul (Finset.sup_le fun _ _ => le_rfl) le_rfl)⟩
+  · rcases h i with ⟨s, C, h⟩
+    exact ⟨C, le_trans h (smul_le_smul (Finset.sup_le fun _ _ => le_rfl) le_rfl)⟩
   use {Classical.arbitrary ι}
   simp only [h, Finset.sup_singleton]
 #align seminorm.const_is_bounded Seminorm.const_isBounded
 
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
-    ∃ (C : ℝ≥0)(s : Finset ι), 0 < C ∧ (s'.sup q).comp f ≤ C • s.sup p := by
+    ∃ (C : ℝ≥0)(s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
   classical
     obtain rfl | hs' := s'.eq_empty_or_nonempty
-    · exact ⟨1, ∅, zero_lt_one, by simp [Seminorm.bot_eq_zero]⟩
+    · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
     choose fₛ fC hf using hf
     use s'.card • s'.sup fC, Finset.bunionᵢ s' fₛ
-    constructor
-    · refine' nsmul_pos _ (ne_of_gt (Finset.Nonempty.card_pos hs'))
-      cases' Finset.Nonempty.bex hs' with j hj
-      exact lt_of_lt_of_le (zero_lt_iff.mpr (And.left (hf j))) (Finset.le_sup hj)
     have hs : ∀ i : ι', i ∈ s' → (q i).comp f ≤ s'.sup fC • (Finset.bunionᵢ s' fₛ).sup p :=
       by
       intro i hi
-      refine' le_trans (And.right (hf i)) (smul_le_smul _ (Finset.le_sup hi))
+      refine' (hf i).trans (smul_le_smul _ (Finset.le_sup hi))
       exact Finset.sup_mono (Finset.subset_bunionᵢ_of_mem fₛ hi)
-    refine' le_trans (comp_mono f (finset_sup_le_sum q s')) _
+    refine' (comp_mono f (finset_sup_le_sum q s')).trans _
     simp_rw [← pullback_apply, AddMonoidHom.map_sum, pullback_apply]
-    refine' le_trans (Finset.sum_le_sum hs) _
+    refine' (Finset.sum_le_sum hs).trans _
     rw [Finset.sum_const, smul_assoc]
     exact le_rfl
 #align seminorm.is_bounded_sup Seminorm.isBounded_sup
@@ -649,20 +644,21 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
   refine' continuous_of_continuous_comp hq _ fun i => Seminorm.continuous_of_continuousAt_zero _
   rw [Metric.continuousAt_iff', map_zero]
   intro r hr
-  rcases hf i with ⟨s₁, C, hC, hf⟩
-  have hC' : 0 < C := hC.bot_lt
+  rcases hf i with ⟨s₁, C, hf⟩
+  have hC' : 0 < C + 1 := by positivity
   rw [hp.has_basis.eventually_iff]
-  refine' ⟨(s₁.sup p).ball 0 (r / C), p.basis_sets_mem _ (by positivity), _⟩
+  refine' ⟨(s₁.sup p).ball 0 (r / (C + 1)), p.basis_sets_mem _ (by positivity), _⟩
   simp_rw [← Metric.mem_ball, ← mem_preimage, ← ball_zero_eq_preimage_ball]
   refine' subset.trans _ (ball_antitone hf)
-  rw [ball_smul (s₁.sup p) hC']
-  rfl
+  norm_cast
+  rw [← ball_smul (s₁.sup p) hC']
+  refine' ball_antitone (smul_le_smul le_rfl _)
+  simp only [le_add_iff_nonneg_right, zero_le']
 #align seminorm.continuous_from_bounded Seminorm.continuous_from_bounded
 
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
-    (f : E →ₛₗ[τ₁₂] F)
-    (hf : ∃ (s : Finset ι)(C : ℝ≥0), C ≠ 0 ∧ (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
+    (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι)(C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
     Continuous f := by
   rw [← Seminorm.isBounded_const (Fin 1)] at hf
   exact continuous_from_bounded hp (normWithSeminorms 𝕝₂ F) f hf
@@ -670,7 +666,7 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
 
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
     [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
-    (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, C ≠ 0 ∧ (q i).comp f ≤ C • normSeminorm 𝕝 E) :
+    (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
     Continuous f := by
   rw [← Seminorm.const_isBounded (Fin 1)] at hf
   exact continuous_from_bounded (normWithSeminorms 𝕝 E) hq f hf

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.with_seminorms
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -391,6 +391,42 @@ theorem WithSeminorms.separating_iff_t1 (hp : WithSeminorms p) :
 
 end Topology
 
+section Tendsto
+
+variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [TopologicalSpace E]
+
+variable {p : SeminormFamily 𝕜 E ι}
+
+/-- Convergence along filters for `with_seminorms`.
+
+Variant with `finset.sup`. -/
+theorem WithSeminorms.tendsto_nhds' (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
+    Filter.Tendsto u f (𝓝 y₀) ↔ ∀ (s : Finset ι) (ε), 0 < ε → ∀ᶠ x in f, s.sup p (u x - y₀) < ε :=
+  by simp [hp.has_basis_ball.tendsto_right_iff]
+#align with_seminorms.tendsto_nhds' WithSeminorms.tendsto_nhds'
+
+/-- Convergence along filters for `with_seminorms`. -/
+theorem WithSeminorms.tendsto_nhds (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
+    Filter.Tendsto u f (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∀ᶠ x in f, p i (u x - y₀) < ε :=
+  by
+  rw [hp.tendsto_nhds' u y₀]
+  exact
+    ⟨fun h i => by simpa only [Finset.sup_singleton] using h {i}, fun h s ε hε =>
+      (s.eventually_all.2 fun i _ => h i ε hε).mono fun _ => finset_sup_apply_lt hε⟩
+#align with_seminorms.tendsto_nhds WithSeminorms.tendsto_nhds
+
+variable [SemilatticeSup F] [Nonempty F]
+
+/-- Limit `→ ∞` for `with_seminorms`. -/
+theorem WithSeminorms.tendsto_nhds_atTop (hp : WithSeminorms p) (u : F → E) (y₀ : E) :
+    Filter.Tendsto u Filter.atTop (𝓝 y₀) ↔ ∀ i ε, 0 < ε → ∃ x₀, ∀ x, x₀ ≤ x → p i (u x - y₀) < ε :=
+  by
+  rw [hp.tendsto_nhds u y₀]
+  exact forall₃_congr fun _ _ _ => Filter.eventually_atTop
+#align with_seminorms.tendsto_nhds_at_top WithSeminorms.tendsto_nhds_atTop
+
+end Tendsto
+
 section TopologicalAddGroup
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -595,7 +595,7 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
   simp_rw [ContinuousAt, f.map_zero, q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.tendsto_infᵢ,
     Filter.tendsto_comap_iff]
   intro i
-  convert (hf i).ContinuousAt
+  convert(hf i).ContinuousAt
   exact (map_zero _).symm
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
 

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

@@ -157,7 +157,7 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basis_sets) :
   · simp_rw [(lt_div_iff h).symm]
     rw [← _root_.ball_zero_eq]
     exact Metric.ball_mem_nhds 0 (div_pos hr h)
-  simp_rw [le_antisymm (not_lt.mp h) (map_nonneg _ v), mul_zero, hr]
+  simp_rw [le_antisymm (not_lt.mp h) (map_nonneg _ v), MulZeroClass.mul_zero, hr]
   exact IsOpen.mem_nhds isOpen_univ (mem_univ 0)
 #align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_right
 

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

@@ -351,7 +351,7 @@ theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
   simp_rw [← WithSeminorms.mem_nhds_iff hp _ U, isOpen_iff_mem_nhds]
 #align with_seminorms.is_open_iff_mem_balls WithSeminorms.isOpen_iff_mem_balls
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /- Note that through the following lemmas, one also immediately has that separating families
 of seminorms induce T₂ and T₃ topologies by `topological_add_group.t2_space`
 and `topological_add_group.t3_space` -/
@@ -379,7 +379,7 @@ theorem WithSeminorms.separating_of_t1 [T1Space E] (hp : WithSeminorms p) (x : E
   simp only [ball_finset_sup_eq_Inter _ _ _ hr, mem_Inter₂, mem_ball_zero, h, hr, forall_true_iff]
 #align with_seminorms.separating_of_t1 WithSeminorms.separating_of_t1
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /-- A family of seminorms is separating iff it induces a T₁ topology. -/
 theorem WithSeminorms.separating_iff_t1 (hp : WithSeminorms p) :
     (∀ (x) (_ : x ≠ 0), ∃ i, p i x ≠ 0) ↔ T1Space E :=
@@ -433,7 +433,7 @@ theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module
   exact Filter.mem_infᵢ_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
 each seminorm individually. We express this as a characterization of `with_seminorms p`. -/
 theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_infᵢ (p : SeminormFamily 𝕜 E ι) :
@@ -445,14 +445,14 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_infᵢ (p : Seminor
     TopologicalAddGroup.ext_iff inferInstance (topologicalAddGroup_infᵢ fun i => inferInstance),
     nhds_infᵢ]
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
   all_goals infer_instance
 #align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_infᵢ
 
 omit t
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]] -/
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
 induced by each seminorm individually. We express this as a characterization of
 `with_seminorms p`. -/
@@ -464,7 +464,7 @@ theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_infᵢ [u : UniformSpac
     UniformAddGroup.ext_iff inferInstance (uniformAddGroup_infᵢ fun i => inferInstance),
     toTopologicalSpace_infᵢ, nhds_infᵢ]
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
   all_goals infer_instance
 #align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_infᵢ

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

@@ -461,7 +461,7 @@ theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_infᵢ [u : UniformSpac
     WithSeminorms p ↔ u = ⨅ i, (p i).toAddGroupSeminorm.toSeminormedAddCommGroup.toUniformSpace :=
   by
   rw [p.with_seminorms_iff_nhds_eq_infi,
-    UniformAddGroup.ext_iff inferInstance (uniform_add_group_infᵢ fun i => inferInstance),
+    UniformAddGroup.ext_iff inferInstance (uniformAddGroup_infᵢ fun i => inferInstance),
     toTopologicalSpace_infᵢ, nhds_infᵢ]
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"

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

@@ -442,7 +442,7 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_infᵢ (p : Seminor
         ⨅ i, (p i).toAddGroupSeminorm.toSeminormedAddCommGroup.toUniformSpace.toTopologicalSpace :=
   by
   rw [p.with_seminorms_iff_nhds_eq_infi,
-    TopologicalAddGroup.ext_iff inferInstance (topological_add_group_infᵢ fun i => inferInstance),
+    TopologicalAddGroup.ext_iff inferInstance (topologicalAddGroup_infᵢ fun i => inferInstance),
     nhds_infᵢ]
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr = »(_, «expr⨅ , »((i), _))]]"
@@ -591,7 +591,7 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
     [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i, Continuous ((q i).comp f)) : Continuous f :=
   by
-  refine' continuous_of_continuous_at_zero f _
+  refine' continuous_of_continuousAt_zero f _
   simp_rw [ContinuousAt, f.map_zero, q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.tendsto_infᵢ,
     Filter.tendsto_comap_iff]
   intro i
@@ -718,7 +718,7 @@ theorem LinearMap.withSeminormsInduced [hι : Nonempty ι] {q : SeminormFamily 
     @WithSeminorms 𝕜 E ι _ _ _ _ (q.comp f) (induced f inferInstance) :=
   by
   letI : TopologicalSpace E := induced f inferInstance
-  letI : TopologicalAddGroup E := topological_add_group_induced f
+  letI : TopologicalAddGroup E := topologicalAddGroup_induced f
   rw [(q.comp f).withSeminorms_iff_nhds_eq_infᵢ, nhds_induced, map_zero,
     q.with_seminorms_iff_nhds_eq_infi.mp hq, Filter.comap_infᵢ]
   refine' infᵢ_congr fun i => _

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

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -486,7 +486,7 @@ theorem norm_withSeminorms (𝕜 E) [NormedField 𝕜] [SeminormedAddCommGroup E
   rintro U (hU : U ∈ p.basisSets)
   rcases p.basisSets_iff.mp hU with ⟨s, r, hr, hU⟩
   use r, hr
-  rw [hU, id.def]
+  rw [hU, id]
   by_cases h : s.Nonempty
   · rw [Finset.sup_const h]
   rw [Finset.not_nonempty_iff_eq_empty.mp h, Finset.sup_empty, ball_bot _ hr]
@@ -506,7 +506,7 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   rw [hp.hasBasis.isVonNBounded_iff]
   constructor
   · intro h I
-    simp only [id.def] at h
+    simp only [id] at h
     specialize h ((I.sup p).ball 0 1) (p.basisSets_mem I zero_lt_one)
     rcases h.exists_pos with ⟨r, hr, h⟩
     cases' NormedField.exists_lt_norm 𝕜 r with a ha
@@ -518,7 +518,7 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
     exact (Finset.sup I p).mem_ball_zero.mp h
   intro h s' hs'
   rcases p.basisSets_iff.mp hs' with ⟨I, r, hr, hs'⟩
-  rw [id.def, hs']
+  rw [id, hs']
   rcases h I with ⟨r', _, h'⟩
   simp_rw [← (I.sup p).mem_ball_zero] at h'
   refine' Absorbs.mono_right _ h'

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -158,9 +158,9 @@ variable [Nonempty ι]
 theorem basisSets_smul (U) (hU : U ∈ p.basisSets) :
     ∃ V ∈ 𝓝 (0 : 𝕜), ∃ W ∈ p.addGroupFilterBasis.sets, V • W ⊆ U := by
   rcases p.basisSets_iff.mp hU with ⟨s, r, hr, hU⟩
-  refine' ⟨Metric.ball 0 r.sqrt, Metric.ball_mem_nhds 0 (Real.sqrt_pos.mpr hr), _⟩
-  refine' ⟨(s.sup p).ball 0 r.sqrt, p.basisSets_mem s (Real.sqrt_pos.mpr hr), _⟩
-  refine' Set.Subset.trans (ball_smul_ball (s.sup p) r.sqrt r.sqrt) _
+  refine' ⟨Metric.ball 0 √r, Metric.ball_mem_nhds 0 (Real.sqrt_pos.mpr hr), _⟩
+  refine' ⟨(s.sup p).ball 0 √r, p.basisSets_mem s (Real.sqrt_pos.mpr hr), _⟩
+  refine' Set.Subset.trans (ball_smul_ball (s.sup p) √r √r) _
   rw [hU, Real.mul_self_sqrt (le_of_lt hr)]
 #align seminorm_family.basis_sets_smul SeminormFamily.basisSets_smul
 

Follow-up to #10816.

Remaining places containing such lemmas are

• Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
• Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
• bef_def is still used in a number of places and could be renamed
• BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -547,7 +547,7 @@ theorem WithSeminorms.isVonNBounded_iff_seminorm_bounded {s : Set E} (hp : WithS
   by_cases hI : I.Nonempty
   · choose r hr h using hi
     have h' : 0 < I.sup' hI r := by
-      rcases hI.bex with ⟨i, hi⟩
+      rcases hI with ⟨i, hi⟩
       exact lt_of_lt_of_le (hr i) (Finset.le_sup' r hi)
     refine' ⟨I.sup' hI r, h', fun x hx => finset_sup_apply_lt h' fun i hi => _⟩
     refine' lt_of_lt_of_le (h i x hx) _

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -318,14 +318,14 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
 #align with_seminorms.has_basis_ball WithSeminorms.hasBasis_ball
 
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
-are exactly the sets which contain seminorm balls around `x`.-/
+are exactly the sets which contain seminorm balls around `x`. -/
 theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
     U ∈ 𝓝 x ↔ ∃ s : Finset ι, ∃ r > 0, (s.sup p).ball x r ⊆ U := by
   rw [hp.hasBasis_ball.mem_iff, Prod.exists]
 #align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iff
 
 /-- The open sets of a space whose topology is induced by a family of seminorms
-are exactly the sets which contain seminorm balls around all of their points.-/
+are exactly the sets which contain seminorm balls around all of their points. -/
 theorem WithSeminorms.isOpen_iff_mem_balls (hp : WithSeminorms p) (U : Set E) :
     IsOpen U ↔ ∀ x ∈ U, ∃ s : Finset ι, ∃ r > 0, (s.sup p).ball x r ⊆ U := by
   simp_rw [← WithSeminorms.mem_nhds_iff hp _ U, isOpen_iff_mem_nhds]

@@ -830,7 +830,7 @@ lemma bound_of_continuous [Nonempty ι] [t : TopologicalSpace E] (hp : WithSemin
   -- The inclusion `hε` tells us exactly that `q` is *still* continuous for this new topology
   have : Continuous q :=
     Seminorm.continuous (r := 1) (mem_of_superset (Metric.ball_mem_nhds _ ε_pos) hε)
-  -- Hence we can conclude by applying `bound_of_continuous_normed_space`.
+  -- Hence we can conclude by applying `bound_of_continuous_normedSpace`.
   rcases bound_of_continuous_normedSpace q this with ⟨C, C_pos, hC⟩
   exact ⟨s, ⟨C, C_pos.le⟩, fun H ↦ C_pos.ne.symm (congr_arg NNReal.toReal H), hC⟩
   -- Note that the key ingredient for this proof is that, by scaling arguments hidden in

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)

@@ -58,7 +58,6 @@ variable {𝕜 𝕜₂ 𝕝 𝕝₂ E F G ι ι' : Type*}
 section FilterBasis
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable (𝕜 E ι)
 
 /-- An abbreviation for indexed families of seminorms. This is mainly to allow for dot-notation. -/
@@ -215,9 +214,7 @@ section Bounded
 namespace Seminorm
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [NormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F]
-
 variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
 -- Todo: This should be phrased entirely in terms of the von Neumann bornology.
@@ -278,7 +275,6 @@ theorem WithSeminorms.withSeminorms_eq {p : SeminormFamily 𝕜 E ι} [t : Topol
 #align with_seminorms.with_seminorms_eq WithSeminorms.withSeminorms_eq
 
 variable [TopologicalSpace E]
-
 variable {p : SeminormFamily 𝕜 E ι}
 
 theorem WithSeminorms.topologicalAddGroup (hp : WithSeminorms p) : TopologicalAddGroup E := by
@@ -374,7 +370,6 @@ end Topology
 section Tendsto
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [TopologicalSpace E]
-
 variable {p : SeminormFamily 𝕜 E ι}
 
 /-- Convergence along filters for `WithSeminorms`.
@@ -409,7 +404,6 @@ end Tendsto
 section TopologicalAddGroup
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [Nonempty ι]
 
 section TopologicalSpace
@@ -504,9 +498,7 @@ end NormedSpace
 section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι]
-
 variable {p : SeminormFamily 𝕜 E ι}
-
 variable [TopologicalSpace E]
 
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
@@ -584,17 +576,11 @@ section continuous_of_bounded
 namespace Seminorm
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [NormedField 𝕝] [Module 𝕝 E]
-
 variable [NontriviallyNormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F]
-
 variable [NormedField 𝕝₂] [Module 𝕝₂ F]
-
 variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
-
 variable {τ₁₂ : 𝕝 →+* 𝕝₂} [RingHomIsometric τ₁₂]
-
 variable [Nonempty ι] [Nonempty ι']
 
 theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [TopologicalSpace E]
@@ -899,9 +885,7 @@ end NormedSpace
 section TopologicalConstructions
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [NormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F]
-
 variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
 /-- The family of seminorms obtained by composing each seminorm by a linear map. -/
@@ -960,9 +944,7 @@ end TopologicalConstructions
 section TopologicalProperties
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι] [Countable ι]
-
 variable {p : SeminormFamily 𝕜 E ι}
-
 variable [TopologicalSpace E]
 
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -539,7 +539,7 @@ theorem WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded (f : G →
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔
       ∀ I : Finset ι, ∃ r > 0, ∀ x ∈ s, I.sup p (f x) < r := by
-  simp_rw [hp.isVonNBounded_iff_finset_seminorm_bounded, Set.ball_image_iff]
+  simp_rw [hp.isVonNBounded_iff_finset_seminorm_bounded, Set.forall_mem_image]
 
 set_option linter.uppercaseLean3 false in
 #align with_seminorms.image_is_vonN_bounded_iff_finset_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded
@@ -571,7 +571,7 @@ set_option linter.uppercaseLean3 false in
 theorem WithSeminorms.image_isVonNBounded_iff_seminorm_bounded (f : G → E) {s : Set G}
     (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∀ i : ι, ∃ r > 0, ∀ x ∈ s, p i (f x) < r := by
-  simp_rw [hp.isVonNBounded_iff_seminorm_bounded, Set.ball_image_iff]
+  simp_rw [hp.isVonNBounded_iff_seminorm_bounded, Set.forall_mem_image]
 
 set_option linter.uppercaseLean3 false in
 #align with_seminorms.image_is_vonN_bounded_iff_seminorm_bounded WithSeminorms.image_isVonNBounded_iff_seminorm_bounded
@@ -694,7 +694,7 @@ protected theorem _root_.WithSeminorms.equicontinuous_TFAE {κ : Type*}
       simpa using (hx k).le
     have bdd : BddAbove (range fun k ↦ (q i).comp (f k)) :=
       Seminorm.bddAbove_of_absorbent (absorbent_nhds_zero this)
-        (fun x hx ↦ ⟨1, forall_range_iff.mpr hx⟩)
+        (fun x hx ↦ ⟨1, forall_mem_range.mpr hx⟩)
     rw [← Seminorm.coe_iSup_eq bdd]
     refine ⟨bdd, Seminorm.continuous' (r := 1) ?_⟩
     filter_upwards [this] with x hx

... to avoid conflict with _root_.map_nonneg, see Zulip.

@@ -150,7 +150,7 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basisSets) :
   · simp_rw [(lt_div_iff h).symm]
     rw [← _root_.ball_zero_eq]
     exact Metric.ball_mem_nhds 0 (div_pos hr h)
-  simp_rw [le_antisymm (not_lt.mp h) (map_nonneg _ v), mul_zero, hr]
+  simp_rw [le_antisymm (not_lt.mp h) (apply_nonneg _ v), mul_zero, hr]
   exact IsOpen.mem_nhds isOpen_univ (mem_univ 0)
 #align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_right
 

Also fix GeneralizedContinuedFraction.of_convergence: it worked for the Preorder.topology only.

@@ -324,7 +324,7 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
 /-- The `x`-neighbourhoods of a space whose topology is induced by a family of seminorms
 are exactly the sets which contain seminorm balls around `x`.-/
 theorem WithSeminorms.mem_nhds_iff (hp : WithSeminorms p) (x : E) (U : Set E) :
-    U ∈ nhds x ↔ ∃ s : Finset ι, ∃ r > 0, (s.sup p).ball x r ⊆ U := by
+    U ∈ 𝓝 x ↔ ∃ s : Finset ι, ∃ r > 0, (s.sup p).ball x r ⊆ U := by
   rw [hp.hasBasis_ball.mem_iff, Prod.exists]
 #align with_seminorms.mem_nhds_iff WithSeminorms.mem_nhds_iff
 

Redefine Absorbs and Absorbent in terms of the cobounded filter.

@@ -516,7 +516,7 @@ theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp
   · intro h I
     simp only [id.def] at h
     specialize h ((I.sup p).ball 0 1) (p.basisSets_mem I zero_lt_one)
-    rcases h with ⟨r, hr, h⟩
+    rcases h.exists_pos with ⟨r, hr, h⟩
     cases' NormedField.exists_lt_norm 𝕜 r with a ha
     specialize h a (le_of_lt ha)
     rw [Seminorm.smul_ball_zero (norm_pos_iff.1 <| hr.trans ha), mul_one] at h

Rename Filter.HasBasis.isVonNBounded_basis_iff to Filter.HasBasis.isVonNBounded_iff. It already has basis in the namespace.

@@ -511,7 +511,7 @@ variable [TopologicalSpace E]
 
 theorem WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded {s : Set E} (hp : WithSeminorms p) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∀ I : Finset ι, ∃ r > 0, ∀ x ∈ s, I.sup p x < r := by
-  rw [hp.hasBasis.isVonNBounded_basis_iff]
+  rw [hp.hasBasis.isVonNBounded_iff]
   constructor
   · intro h I
     simp only [id.def] at h

See Zulip thread for the discussion.

@@ -802,7 +802,7 @@ variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 lemma map_eq_zero_of_norm_zero (q : Seminorm 𝕜 F)
     (hq : Continuous q) {x : F} (hx : ‖x‖ = 0) : q x = 0 :=
   (map_zero q) ▸
-    ((specializes_iff_mem_closure.mpr $ mem_closure_zero_iff_norm.mpr hx).map hq).eq.symm
+    ((specializes_iff_mem_closure.mpr <| mem_closure_zero_iff_norm.mpr hx).map hq).eq.symm
 
 /-- Let `F` be a semi-`NormedSpace` over a `NontriviallyNormedField`, and let `q` be a
 seminorm on `F`. If `q` is continuous, then it is uniformly controlled by the norm, that is there
@@ -813,7 +813,7 @@ controlled image by `q`. The control of `q` at the original element follows by r
 lemma bound_of_continuous_normedSpace (q : Seminorm 𝕜 F)
     (hq : Continuous q) : ∃ C, 0 < C ∧ (∀ x : F, q x ≤ C * ‖x‖) := by
   have hq' : Tendsto q (𝓝 0) (𝓝 0) := map_zero q ▸ hq.tendsto 0
-  rcases NormedAddCommGroup.nhds_zero_basis_norm_lt.mem_iff.mp (hq' $ Iio_mem_nhds one_pos)
+  rcases NormedAddCommGroup.nhds_zero_basis_norm_lt.mem_iff.mp (hq' <| Iio_mem_nhds one_pos)
     with ⟨ε, ε_pos, hε⟩
   rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
   have : 0 < ‖c‖ / ε := by positivity

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -78,8 +78,8 @@ def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
 variable (p : SeminormFamily 𝕜 E ι)
 
 theorem basisSets_iff {U : Set E} :
-    U ∈ p.basisSets ↔ ∃ (i : Finset ι) (r : _) (_ : 0 < r), U = ball (i.sup p) 0 r := by
-  simp only [basisSets, mem_iUnion, mem_singleton_iff]
+    U ∈ p.basisSets ↔ ∃ (i : Finset ι) (r : ℝ), 0 < r ∧ U = ball (i.sup p) 0 r := by
+  simp only [basisSets, mem_iUnion, exists_prop, mem_singleton_iff]
 #align seminorm_family.basis_sets_iff SeminormFamily.basisSets_iff
 
 theorem basisSets_mem (i : Finset ι) {r : ℝ} (hr : 0 < r) : (i.sup p).ball 0 r ∈ p.basisSets :=

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -313,7 +313,7 @@ theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 := by
   have : TopologicalAddGroup E := hp.topologicalAddGroup
   rw [← map_add_left_nhds_zero]
-  convert hp.hasBasis_zero_ball.map ((· + ·) x) using 1
+  convert hp.hasBasis_zero_ball.map (x + ·) using 1
   ext sr : 1
   -- Porting note: extra type ascriptions needed on `0`
   have : (sr.fst.sup p).ball (x +ᵥ (0 : E)) sr.snd = x +ᵥ (sr.fst.sup p).ball 0 sr.snd :=

To fit with the "please try harder" convention of ! tactics.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -354,7 +354,7 @@ theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
 theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E) (hx : x ≠ 0) :
     ∃ i, p i x ≠ 0 := by
   have := ((t1Space_TFAE E).out 0 9).mp (inferInstanceAs <| T1Space E)
-  by_contra' h
+  by_contra! h
   refine' hx (this _)
   rw [hp.hasBasis_zero_ball.specializes_iff]
   rintro ⟨s, r⟩ (hr : 0 < r)

Make toTopologicalSpace_top a rfl. Also move some lemmas to the UniformSpace namespace.

@@ -468,7 +468,7 @@ theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf [u : UniformSpace
     WithSeminorms p ↔ u = ⨅ i, (p i).toSeminormedAddCommGroup.toUniformSpace := by
   rw [p.withSeminorms_iff_nhds_eq_iInf,
     UniformAddGroup.ext_iff inferInstance (uniformAddGroup_iInf fun i => inferInstance),
-    toTopologicalSpace_iInf, nhds_iInf]
+    UniformSpace.toTopologicalSpace_iInf, nhds_iInf]
   congrm _ = ⨅ i, ?_
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
 #align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf

All the other properties of topological spaces like T0Space or RegularSpace are in the root namespace. Many files were opening TopologicalSpace just for the sake of shortening TopologicalSpace.SecondCountableTopology...

@@ -968,7 +968,7 @@ variable [TopologicalSpace E]
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology
 is first countable. -/
 theorem WithSeminorms.first_countable (hp : WithSeminorms p) :
-    TopologicalSpace.FirstCountableTopology E := by
+    FirstCountableTopology E := by
   have := hp.topologicalAddGroup
   let _ : UniformSpace E := TopologicalAddGroup.toUniformSpace E
   have : UniformAddGroup E := comm_topologicalAddGroup_is_uniform

And fix some names in comments where this revealed issues

@@ -848,7 +848,7 @@ lemma bound_of_continuous [Nonempty ι] [t : TopologicalSpace E] (hp : WithSemin
   rcases bound_of_continuous_normedSpace q this with ⟨C, C_pos, hC⟩
   exact ⟨s, ⟨C, C_pos.le⟩, fun H ↦ C_pos.ne.symm (congr_arg NNReal.toReal H), hC⟩
   -- Note that the key ingredient for this proof is that, by scaling arguments hidden in
-  -- `seminorm.continuous`, we only have to look at the `q`-ball of radius one, and the `s` we get
+  -- `Seminorm.continuous`, we only have to look at the `q`-ball of radius one, and the `s` we get
   -- from that will automatically work for all other radii.
 
 end Seminorm

Adds a term elaborator for congr(...) "congruence quotations". For example, if hf : f = f' and hx : x = x', then we have congr($hf $x) : f x = f' x'. This supports the functions having implicit arguments, and it has support for subsingleton instance arguments. So for example, if s t : Set X are sets with Fintype instances and h : s = t then congr(Fintype.card $h) : Fintype.card s = Fintype.card t works.

Ports the congrm tactic as a convenient frontend for applying a congruence quotation to the goal. Holes are turned into congruence holes. For example, congrm 1 + ?_ uses congr(1 + $(?_)). Placeholders (_) do not turn into congruence holes; that's not to say they have to be identical on the LHS and RHS, but congrm itself is responsible for finding a congruence lemma for such arguments.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>

@@ -447,10 +447,7 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf [TopologicalAd
   rw [p.withSeminorms_iff_nhds_eq_iInf,
     TopologicalAddGroup.ext_iff inferInstance (topologicalAddGroup_iInf fun i => inferInstance),
     nhds_iInf]
-  -- Porting note: next three lines was `congrm (_ = ⨅ i, _)`
-  refine Eq.to_iff ?_
-  congr
-  funext i
+  congrm _ = ⨅ i, ?_
   exact @comap_norm_nhds_zero _ (p i).toSeminormedAddGroup
 #align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf
 
@@ -472,10 +469,7 @@ theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf [u : UniformSpace
   rw [p.withSeminorms_iff_nhds_eq_iInf,
     UniformAddGroup.ext_iff inferInstance (uniformAddGroup_iInf fun i => inferInstance),
     toTopologicalSpace_iInf, nhds_iInf]
-  -- Porting note: next three lines was `congrm (_ = ⨅ i, _)`
-  refine Eq.to_iff ?_
-  congr
-  funext i
+  congrm _ = ⨅ i, ?_
   exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
 #align seminorm_family.with_seminorms_iff_uniform_space_eq_infi SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf
 

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -150,7 +150,7 @@ theorem basisSets_smul_right (v : E) (U : Set E) (hU : U ∈ p.basisSets) :
   · simp_rw [(lt_div_iff h).symm]
     rw [← _root_.ball_zero_eq]
     exact Metric.ball_mem_nhds 0 (div_pos hr h)
-  simp_rw [le_antisymm (not_lt.mp h) (map_nonneg _ v), MulZeroClass.mul_zero, hr]
+  simp_rw [le_antisymm (not_lt.mp h) (map_nonneg _ v), mul_zero, hr]
   exact IsOpen.mem_nhds isOpen_univ (mem_univ 0)
 #align seminorm_family.basis_sets_smul_right SeminormFamily.basisSets_smul_right
 

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

This has nice performance benefits.

@@ -53,7 +53,7 @@ open NormedField Set Seminorm TopologicalSpace Filter List
 
 open BigOperators NNReal Pointwise Topology Uniformity
 
-variable {𝕜 𝕜₂ 𝕝 𝕝₂ E F G ι ι' : Type _}
+variable {𝕜 𝕜₂ 𝕝 𝕝₂ E F G ι ι' : Type*}
 
 section FilterBasis
 
@@ -226,13 +226,13 @@ def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f :
   ∀ i, ∃ s : Finset ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • s.sup p
 #align seminorm.is_bounded Seminorm.IsBounded
 
-theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
+theorem isBounded_const (ι' : Type*) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
     IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι) (C : ℝ≥0), q.comp f ≤ C • s.sup p := by
   simp only [IsBounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
-theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
+theorem const_isBounded (ι : Type*) [Nonempty ι] {p : Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) : IsBounded (fun _ : ι => p) q f ↔ ∀ i, ∃ C : ℝ≥0, (q i).comp f ≤ C • p := by
   constructor <;> intro h i
   · rcases h i with ⟨s, C, h⟩
@@ -669,7 +669,7 @@ maps from `E` to `F`, the following are equivalent:
 In particular, if you can determine all continuous seminorms on `E`, that gives you a complete
 characterization of equicontinuity for linear maps from `E` to `F`. For example `E` and `F` are
 both normed spaces, you get `NormedSpace.equicontinuous_TFAE`. -/
-protected theorem _root_.WithSeminorms.equicontinuous_TFAE {κ : Type _}
+protected theorem _root_.WithSeminorms.equicontinuous_TFAE {κ : Type*}
     {q : SeminormFamily 𝕜₂ F ι'} [UniformSpace E] [UniformAddGroup E] [u : UniformSpace F]
     [hu : UniformAddGroup F] (hq : WithSeminorms q) [ContinuousSMul 𝕜 E]
     (f : κ → E →ₛₗ[σ₁₂] F) : TFAE
@@ -713,7 +713,7 @@ protected theorem _root_.WithSeminorms.equicontinuous_TFAE {κ : Type _}
       eventually_of_forall fun x k ↦ by simpa using hfp k x
   tfae_finish
 
-theorem _root_.WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm {κ : Type _}
+theorem _root_.WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm {κ : Type*}
     {q : SeminormFamily 𝕜₂ F ι'} [UniformSpace E] [UniformAddGroup E] [u : UniformSpace F]
     [hu : UniformAddGroup F] (hq : WithSeminorms q) [ContinuousSMul 𝕜 E]
     (f : κ → E →ₛₗ[σ₁₂] F) :
@@ -721,7 +721,7 @@ theorem _root_.WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminor
     ∀ i, ∃ p : Seminorm 𝕜 E, Continuous p ∧ ∀ k, (q i).comp (f k) ≤ p :=
   (hq.equicontinuous_TFAE f).out 2 3
 
-theorem _root_.WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup {κ : Type _}
+theorem _root_.WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup {κ : Type*}
     {q : SeminormFamily 𝕜₂ F ι'} [UniformSpace E] [UniformAddGroup E] [u : UniformSpace F]
     [hu : UniformAddGroup F] (hq : WithSeminorms q) [ContinuousSMul 𝕜 E]
     (f : κ → E →ₛₗ[σ₁₂] F) :
@@ -948,11 +948,11 @@ theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F
 #align inducing.with_seminorms Inducing.withSeminorms
 
 /-- (Disjoint) union of seminorm families. -/
-protected def SeminormFamily.sigma {κ : ι → Type _} (p : (i : ι) → SeminormFamily 𝕜 E (κ i)) :
+protected def SeminormFamily.sigma {κ : ι → Type*} (p : (i : ι) → SeminormFamily 𝕜 E (κ i)) :
     SeminormFamily 𝕜 E ((i : ι) × κ i) :=
   fun ⟨i, k⟩ => p i k
 
-theorem withSeminorms_iInf {κ : ι → Type _} [Nonempty ((i : ι) × κ i)] [∀ i, Nonempty (κ i)]
+theorem withSeminorms_iInf {κ : ι → Type*} [Nonempty ((i : ι) × κ i)] [∀ i, Nonempty (κ i)]
     {p : (i : ι) → SeminormFamily 𝕜 E (κ i)} {t : ι → TopologicalSpace E}
     [∀ i, @TopologicalAddGroup E (t i) _] (hp : ∀ i, WithSeminorms (topology := t i) (p i)) :
     WithSeminorms (topology := ⨅ i, t i) (SeminormFamily.sigma p) := by

@@ -4,7 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
 -/
 import Mathlib.Analysis.Seminorm
-import Mathlib.Analysis.LocallyConvex.Bounded
+import Mathlib.Topology.Algebra.Equicontinuity
+import Mathlib.Topology.MetricSpace.Equicontinuity
 import Mathlib.Topology.Algebra.FilterBasis
 import Mathlib.Topology.Algebra.Module.LocallyConvex
 
@@ -48,9 +49,9 @@ seminorm, locally convex
 -/
 
 
-open NormedField Set Seminorm TopologicalSpace Filter
+open NormedField Set Seminorm TopologicalSpace Filter List
 
-open BigOperators NNReal Pointwise Topology
+open BigOperators NNReal Pointwise Topology Uniformity
 
 variable {𝕜 𝕜₂ 𝕝 𝕝₂ E F G ι ι' : Type _}
 
@@ -173,7 +174,7 @@ theorem basisSets_smul_left (x : 𝕜) (U : Set E) (hU : U ∈ p.basisSets) :
     use (s.sup p).ball 0 (r / ‖x‖)
     exact ⟨p.basisSets_mem s (div_pos hr (norm_pos_iff.mpr h)), Subset.rfl⟩
   refine' ⟨(s.sup p).ball 0 r, p.basisSets_mem s hr, _⟩
-  simp only [not_ne_iff.mp h, subset_def, mem_ball_zero, hr, mem_univ, map_zero, imp_true_iff,
+  simp only [not_ne_iff.mp h, Set.subset_def, mem_ball_zero, hr, mem_univ, map_zero, imp_true_iff,
     preimage_const_of_mem, zero_smul]
 #align seminorm_family.basis_sets_smul_left SeminormFamily.basisSets_smul_left
 
@@ -655,6 +656,80 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
   exact continuous_from_bounded (norm_withSeminorms 𝕝 E) hq f hf
 #align seminorm.cont_normed_space_to_with_seminorms Seminorm.cont_normedSpace_to_withSeminorms
 
+/-- Let `E` and `F` be two topological vector spaces over a `NontriviallyNormedField`, and assume
+that the topology of `F` is generated by some family of seminorms `q`. For a family `f` of linear
+maps from `E` to `F`, the following are equivalent:
+* `f` is equicontinuous at `0`.
+* `f` is equicontinuous.
+* `f` is uniformly equicontinuous.
+* For each `q i`, the family of seminorms `k ↦ (q i) ∘ (f k)` is bounded by some continuous
+  seminorm `p` on `E`.
+* For each `q i`, the seminorm `⊔ k, (q i) ∘ (f k)` is well-defined and continuous.
+
+In particular, if you can determine all continuous seminorms on `E`, that gives you a complete
+characterization of equicontinuity for linear maps from `E` to `F`. For example `E` and `F` are
+both normed spaces, you get `NormedSpace.equicontinuous_TFAE`. -/
+protected theorem _root_.WithSeminorms.equicontinuous_TFAE {κ : Type _}
+    {q : SeminormFamily 𝕜₂ F ι'} [UniformSpace E] [UniformAddGroup E] [u : UniformSpace F]
+    [hu : UniformAddGroup F] (hq : WithSeminorms q) [ContinuousSMul 𝕜 E]
+    (f : κ → E →ₛₗ[σ₁₂] F) : TFAE
+    [ EquicontinuousAt ((↑) ∘ f) 0,
+      Equicontinuous ((↑) ∘ f),
+      UniformEquicontinuous ((↑) ∘ f),
+      ∀ i, ∃ p : Seminorm 𝕜 E, Continuous p ∧ ∀ k, (q i).comp (f k) ≤ p,
+      ∀ i, BddAbove (range fun k ↦ (q i).comp (f k)) ∧ Continuous (⨆ k, (q i).comp (f k)) ] := by
+  -- We start by reducing to the case where the target is a seminormed space
+  rw [q.withSeminorms_iff_uniformSpace_eq_iInf.mp hq, uniformEquicontinuous_iInf_rng,
+      equicontinuous_iInf_rng, equicontinuousAt_iInf_rng]
+  refine forall_tfae [_, _, _, _, _] fun i ↦ ?_
+  let _ : SeminormedAddCommGroup F := (q i).toSeminormedAddCommGroup
+  clear u hu hq
+  -- Now we can prove the equivalence in this setting
+  simp only [List.map]
+  tfae_have 1 → 3
+  · exact uniformEquicontinuous_of_equicontinuousAt_zero f
+  tfae_have 3 → 2
+  · exact UniformEquicontinuous.equicontinuous
+  tfae_have 2 → 1
+  · exact fun H ↦ H 0
+  tfae_have 3 → 5
+  · intro H
+    have : ∀ᶠ x in 𝓝 0, ∀ k, q i (f k x) ≤ 1 := by
+      filter_upwards [Metric.equicontinuousAt_iff_right.mp (H.equicontinuous 0) 1 one_pos]
+        with x hx k
+      simpa using (hx k).le
+    have bdd : BddAbove (range fun k ↦ (q i).comp (f k)) :=
+      Seminorm.bddAbove_of_absorbent (absorbent_nhds_zero this)
+        (fun x hx ↦ ⟨1, forall_range_iff.mpr hx⟩)
+    rw [← Seminorm.coe_iSup_eq bdd]
+    refine ⟨bdd, Seminorm.continuous' (r := 1) ?_⟩
+    filter_upwards [this] with x hx
+    simpa only [closedBall_iSup bdd _ one_pos, mem_iInter, mem_closedBall_zero] using hx
+  tfae_have 5 → 4
+  · exact fun H ↦ ⟨⨆ k, (q i).comp (f k), Seminorm.coe_iSup_eq H.1 ▸ H.2, le_ciSup H.1⟩
+  tfae_have 4 → 1 -- This would work over any `NormedField`
+  · intro ⟨p, hp, hfp⟩
+    exact Metric.equicontinuousAt_of_continuity_modulus p (map_zero p ▸ hp.tendsto 0) _ <|
+      eventually_of_forall fun x k ↦ by simpa using hfp k x
+  tfae_finish
+
+theorem _root_.WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm {κ : Type _}
+    {q : SeminormFamily 𝕜₂ F ι'} [UniformSpace E] [UniformAddGroup E] [u : UniformSpace F]
+    [hu : UniformAddGroup F] (hq : WithSeminorms q) [ContinuousSMul 𝕜 E]
+    (f : κ → E →ₛₗ[σ₁₂] F) :
+    UniformEquicontinuous ((↑) ∘ f) ↔
+    ∀ i, ∃ p : Seminorm 𝕜 E, Continuous p ∧ ∀ k, (q i).comp (f k) ≤ p :=
+  (hq.equicontinuous_TFAE f).out 2 3
+
+theorem _root_.WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup {κ : Type _}
+    {q : SeminormFamily 𝕜₂ F ι'} [UniformSpace E] [UniformAddGroup E] [u : UniformSpace F]
+    [hu : UniformAddGroup F] (hq : WithSeminorms q) [ContinuousSMul 𝕜 E]
+    (f : κ → E →ₛₗ[σ₁₂] F) :
+    UniformEquicontinuous ((↑) ∘ f) ↔ ∀ i,
+    BddAbove (range fun k ↦ (q i).comp (f k)) ∧
+      Continuous (⨆ k, (q i).comp (f k)) :=
+  (hq.equicontinuous_TFAE f).out 2 4
+
 end Seminorm
 
 section Congr
@@ -770,8 +845,7 @@ lemma bound_of_continuous [Nonempty ι] [t : TopologicalSpace E] (hp : WithSemin
   -- Now forget that `E` already had a topology and view it as the (semi)normed space
   -- `(E, s.sup p)`.
   clear hp hq t
-  let _ : SeminormedAddCommGroup E :=
-    (s.sup p).toAddGroupSeminorm.toSeminormedAddCommGroup
+  let _ : SeminormedAddCommGroup E := (s.sup p).toSeminormedAddCommGroup
   let _ : NormedSpace 𝕜 E := { norm_smul_le := fun a b ↦ le_of_eq (map_smul_eq_mul (s.sup p) a b) }
   -- The inclusion `hε` tells us exactly that `q` is *still* continuous for this new topology
   have : Continuous q :=

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.locally_convex.with_seminorms
-! leanprover-community/mathlib commit b31173ee05c911d61ad6a05bd2196835c932e0ec
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Seminorm
 import Mathlib.Analysis.LocallyConvex.Bounded
 import Mathlib.Topology.Algebra.FilterBasis
 import Mathlib.Topology.Algebra.Module.LocallyConvex
 
+#align_import analysis.locally_convex.with_seminorms from "leanprover-community/mathlib"@"b31173ee05c911d61ad6a05bd2196835c932e0ec"
+
 /-!
 # Topology induced by a family of seminorms
 

This adds WithSeminorms.congr which allows to replace a family of seminorm by an equivalent one. We use that to prove that one can always replace the family by a directed family (and a nice one if the indexing set is a LocallyFiniteOrderBot).

@@ -433,8 +433,7 @@ theorem SeminormFamily.withSeminorms_of_hasBasis [TopologicalAddGroup E] (p : Se
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
 theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf [TopologicalAddGroup E]
-    (p : SeminormFamily 𝕜 E ι) :
-    WithSeminorms p ↔ (𝓝 (0 : E)) = ⨅ i, (𝓝 0).comap (p i) := by
+    (p : SeminormFamily 𝕜 E ι) : WithSeminorms p ↔ (𝓝 (0 : E)) = ⨅ i, (𝓝 0).comap (p i) := by
   rw [← p.filter_eq_iInf]
   refine' ⟨fun h => _, p.withSeminorms_of_nhds⟩
   rw [h.topology_eq_withSeminorms]
@@ -628,7 +627,7 @@ theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [Topol
 #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp
 
 theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'}
-    [TopologicalSpace E] (hp : WithSeminorms p) [TopologicalSpace F] (hq : WithSeminorms q)
+    {_ : TopologicalSpace E} (hp : WithSeminorms p) {_ : TopologicalSpace F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : Seminorm.IsBounded p q f) : Continuous f := by
   have : TopologicalAddGroup E := hp.topologicalAddGroup
   refine continuous_of_continuous_comp hq _ fun i => ?_
@@ -661,6 +660,68 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
 
 end Seminorm
 
+section Congr
+
+namespace WithSeminorms
+
+variable [Nonempty ι] [Nonempty ι']
+variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
+variable [NormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F]
+variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
+
+/-- Two families of seminorms `p` and `q` on the same space generate the same topology
+if each `p i` is bounded by some `C • Finset.sup s q` and vice-versa.
+
+We formulate these boundedness assumptions as `Seminorm.IsBounded q p LinearMap.id` (and
+vice-versa) to reuse the API. Furthermore, we don't actually state it as an equality of topologies
+but as a way to deduce `WithSeminorms q` from `WithSeminorms p`, since this should be more
+useful in practice. -/
+protected theorem congr {p : SeminormFamily 𝕜 E ι} {q : SeminormFamily 𝕜 E ι'}
+    [t : TopologicalSpace E] (hp : WithSeminorms p) (hpq : Seminorm.IsBounded p q LinearMap.id)
+    (hqp : Seminorm.IsBounded q p LinearMap.id) : WithSeminorms q := by
+  constructor
+  rw [hp.topology_eq_withSeminorms]
+  clear hp t
+  refine le_antisymm ?_ ?_ <;>
+  rw [← continuous_id_iff_le] <;>
+  refine continuous_from_bounded (.mk (topology := _) rfl) (.mk (topology := _) rfl)
+    LinearMap.id (by assumption)
+
+protected theorem finset_sups {p : SeminormFamily 𝕜 E ι} [TopologicalSpace E]
+    (hp : WithSeminorms p) : WithSeminorms (fun s : Finset ι ↦ s.sup p) := by
+  refine hp.congr ?_ ?_
+  · intro s
+    refine ⟨s, 1, ?_⟩
+    rw [one_smul]
+    rfl
+  · intro i
+    refine ⟨{{i}}, 1, ?_⟩
+    rw [Finset.sup_singleton, Finset.sup_singleton, one_smul]
+    rfl
+
+protected theorem partial_sups [Preorder ι] [LocallyFiniteOrderBot ι] {p : SeminormFamily 𝕜 E ι}
+    [TopologicalSpace E] (hp : WithSeminorms p) : WithSeminorms (fun i ↦ (Finset.Iic i).sup p) := by
+  refine hp.congr ?_ ?_
+  · intro i
+    refine ⟨Finset.Iic i, 1, ?_⟩
+    rw [one_smul]
+    rfl
+  · intro i
+    refine ⟨{i}, 1, ?_⟩
+    rw [Finset.sup_singleton, one_smul]
+    exact (Finset.le_sup (Finset.mem_Iic.mpr le_rfl) : p i ≤ (Finset.Iic i).sup p)
+
+protected theorem congr_equiv {p : SeminormFamily 𝕜 E ι} [t : TopologicalSpace E]
+    (hp : WithSeminorms p) (e : ι' ≃ ι) : WithSeminorms (p ∘ e) := by
+  refine hp.congr ?_ ?_ <;>
+  intro i <;>
+  [use {e i}, 1; use {e.symm i}, 1] <;>
+  simp
+
+end WithSeminorms
+
+end Congr
+
 end continuous_of_bounded
 
 section bounded_of_continuous

@@ -288,6 +288,10 @@ theorem WithSeminorms.topologicalAddGroup (hp : WithSeminorms p) : TopologicalAd
   exact AddGroupFilterBasis.isTopologicalAddGroup _
 #align with_seminorms.topological_add_group WithSeminorms.topologicalAddGroup
 
+theorem WithSeminorms.continuousSMul (hp : WithSeminorms p) : ContinuousSMul 𝕜 E := by
+  rw [hp.withSeminorms_eq]
+  exact ModuleFilterBasis.continuousSMul _
+
 theorem WithSeminorms.hasBasis (hp : WithSeminorms p) :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basisSets) id := by
   rw [congr_fun (congr_arg (@nhds E) hp.1) 0]
@@ -309,7 +313,7 @@ theorem WithSeminorms.hasBasis_zero_ball (hp : WithSeminorms p) :
 theorem WithSeminorms.hasBasis_ball (hp : WithSeminorms p) {x : E} :
     (𝓝 (x : E)).HasBasis
     (fun sr : Finset ι × ℝ => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2 := by
-  haveI : TopologicalAddGroup E := hp.topologicalAddGroup
+  have : TopologicalAddGroup E := hp.topologicalAddGroup
   rw [← map_add_left_nhds_zero]
   convert hp.hasBasis_zero_ball.map ((· + ·) x) using 1
   ext sr : 1
@@ -339,7 +343,7 @@ and `TopologicalAddGroup.t3Space` -/
 /-- A separating family of seminorms induces a T₁ topology. -/
 theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
     (h : ∀ x, x ≠ 0 → ∃ i, p i x ≠ 0) : T1Space E := by
-  haveI := hp.topologicalAddGroup
+  have := hp.topologicalAddGroup
   refine' TopologicalAddGroup.t1Space _ _
   rw [← isOpen_compl_iff, hp.isOpen_iff_mem_balls]
   rintro x (hx : x ≠ 0)
@@ -412,9 +416,9 @@ variable [Nonempty ι]
 
 section TopologicalSpace
 
-variable [t : TopologicalSpace E] [TopologicalAddGroup E]
+variable [t : TopologicalSpace E]
 
-theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
+theorem SeminormFamily.withSeminorms_of_nhds [TopologicalAddGroup E] (p : SeminormFamily 𝕜 E ι)
     (h : 𝓝 (0 : E) = p.moduleFilterBasis.toFilterBasis.filter) : WithSeminorms p := by
   refine'
     ⟨TopologicalAddGroup.ext inferInstance p.addGroupFilterBasis.isTopologicalAddGroup _⟩
@@ -422,13 +426,14 @@ theorem SeminormFamily.withSeminorms_of_nhds (p : SeminormFamily 𝕜 E ι)
   exact h
 #align seminorm_family.with_seminorms_of_nhds SeminormFamily.withSeminorms_of_nhds
 
-theorem SeminormFamily.withSeminorms_of_hasBasis (p : SeminormFamily 𝕜 E ι)
+theorem SeminormFamily.withSeminorms_of_hasBasis [TopologicalAddGroup E] (p : SeminormFamily 𝕜 E ι)
     (h : (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ p.basisSets) id) : WithSeminorms p :=
   p.withSeminorms_of_nhds <|
     Filter.HasBasis.eq_of_same_basis h p.addGroupFilterBasis.toFilterBasis.hasBasis
 #align seminorm_family.with_seminorms_of_has_basis SeminormFamily.withSeminorms_of_hasBasis
 
-theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E ι) :
+theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf [TopologicalAddGroup E]
+    (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔ (𝓝 (0 : E)) = ⨅ i, (𝓝 0).comap (p i) := by
   rw [← p.filter_eq_iInf]
   refine' ⟨fun h => _, p.withSeminorms_of_nhds⟩
@@ -436,17 +441,10 @@ theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E
   exact AddGroupFilterBasis.nhds_zero_eq _
 #align seminorm_family.with_seminorms_iff_nhds_eq_infi SeminormFamily.withSeminorms_iff_nhds_eq_iInf
 
-theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
-    [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
-    Continuous (p i) := by
-  refine' Seminorm.continuous (r := 1) _
-  rw [p.withSeminorms_iff_nhds_eq_iInf.mp hp, ball_zero_eq_preimage_ball]
-  exact Filter.mem_iInf_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
-#align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
-
 /-- The topology induced by a family of seminorms is exactly the infimum of the ones induced by
 each seminorm individually. We express this as a characterization of `WithSeminorms p`. -/
-theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormFamily 𝕜 E ι) :
+theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf [TopologicalAddGroup E]
+    (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔
       t = ⨅ i, (p i).toSeminormedAddCommGroup.toUniformSpace.toTopologicalSpace := by
   rw [p.withSeminorms_iff_nhds_eq_iInf,
@@ -459,6 +457,13 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormF
   exact @comap_norm_nhds_zero _ (p i).toSeminormedAddGroup
 #align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf
 
+theorem WithSeminorms.continuous_seminorm {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p)
+    (i : ι) : Continuous (p i) := by
+  have := hp.topologicalAddGroup
+  rw [p.withSeminorms_iff_topologicalSpace_eq_iInf.mp hp]
+  exact continuous_iInf_dom (@continuous_norm _ (p i).toSeminormedAddGroup)
+#align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
+
 end TopologicalSpace
 
 /-- The uniform structure induced by a family of seminorms is exactly the infimum of the ones
@@ -602,8 +607,9 @@ variable {τ₁₂ : 𝕝 →+* 𝕝₂} [RingHomIsometric τ₁₂]
 variable [Nonempty ι] [Nonempty ι']
 
 theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [TopologicalSpace E]
-    [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] (hq : WithSeminorms q)
+    [TopologicalAddGroup E] [TopologicalSpace F] (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i, Continuous ((q i).comp f)) : Continuous f := by
+  have : TopologicalAddGroup F := hq.topologicalAddGroup
   refine' continuous_of_continuousAt_zero f _
   simp_rw [ContinuousAt, f.map_zero, q.withSeminorms_iff_nhds_eq_iInf.mp hq, Filter.tendsto_iInf,
     Filter.tendsto_comap_iff]
@@ -613,8 +619,8 @@ theorem continuous_of_continuous_comp {q : SeminormFamily 𝕝₂ F ι'} [Topolo
 #align seminorm.continuous_of_continuous_comp Seminorm.continuous_of_continuous_comp
 
 theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [TopologicalSpace E]
-    [TopologicalAddGroup E] [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul 𝕜₂ F]
-    (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) : Continuous f ↔ ∀ i, Continuous ((q i).comp f) :=
+    [TopologicalAddGroup E] [TopologicalSpace F] (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
+    Continuous f ↔ ∀ i, Continuous ((q i).comp f) :=
     -- Porting note: if we *don't* use dot notation for `Continuous.comp`, Lean tries to show
     -- continuity of `((q i).comp f) ∘ id` because it doesn't see that `((q i).comp f)` is
     -- actually a composition of functions.
@@ -622,27 +628,23 @@ theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [Topol
 #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp
 
 theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'}
-    [TopologicalSpace E] [TopologicalAddGroup E] (hp : WithSeminorms p) [TopologicalSpace F]
-    [TopologicalAddGroup F] (hq : WithSeminorms q) (f : E →ₛₗ[τ₁₂] F)
-    (hf : Seminorm.IsBounded p q f) : Continuous f := by
-  refine' continuous_of_continuous_comp hq _ fun i => Seminorm.continuous_of_continuousAt_zero _
-  rw [Metric.continuousAt_iff', map_zero]
-  intro r hr
-  rcases hf i with ⟨s₁, C, hf⟩
-  have hC' : 0 < C + 1 := by positivity
-  rw [hp.hasBasis.eventually_iff]
-  -- Porting note: `div_pos hr (by norm_cast)` was `by positivity`
-  refine' ⟨(s₁.sup p).ball 0 (r / (C + 1)), p.basisSets_mem _ (div_pos hr (by norm_cast)), _⟩
-  simp_rw [← Metric.mem_ball, ← mem_preimage, ← ball_zero_eq_preimage_ball]
-  refine' Subset.trans _ (ball_antitone hf)
-  norm_cast
-  rw [← ball_smul (s₁.sup p) hC']
-  refine' ball_antitone (smul_le_smul le_rfl _)
-  simp only [le_add_iff_nonneg_right, zero_le']
+    [TopologicalSpace E] (hp : WithSeminorms p) [TopologicalSpace F] (hq : WithSeminorms q)
+    (f : E →ₛₗ[τ₁₂] F) (hf : Seminorm.IsBounded p q f) : Continuous f := by
+  have : TopologicalAddGroup E := hp.topologicalAddGroup
+  refine continuous_of_continuous_comp hq _ fun i => ?_
+  rcases hf i with ⟨s, C, hC⟩
+  rw [← Seminorm.finset_sup_smul] at hC
+  -- Note: we deduce continuouty of `s.sup (C • p)` from that of `∑ i in s, C • p i`.
+  -- The reason is that there is no `continuous_finset_sup`, and even if it were we couldn't
+  -- really use it since `ℝ` is not an `OrderBot`.
+  refine Seminorm.continuous_of_le ?_ (hC.trans <| Seminorm.finset_sup_le_sum _ _)
+  change Continuous (fun x ↦ Seminorm.coeFnAddMonoidHom _ _ (∑ i in s, C • p i) x)
+  simp_rw [map_sum, Finset.sum_apply]
+  exact (continuous_finset_sum _ fun i _ ↦ (hp.continuous_seminorm i).const_smul (C : ℝ))
 #align seminorm.continuous_from_bounded Seminorm.continuous_from_bounded
 
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
-    [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
+    [TopologicalSpace E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι) (C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
     Continuous f := by
   rw [← Seminorm.isBounded_const (Fin 1)] at hf
@@ -650,7 +652,7 @@ theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpa
 #align seminorm.cont_with_seminorms_normed_space Seminorm.cont_withSeminorms_normedSpace
 
 theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [NormedSpace 𝕝 E]
-    [UniformSpace F] [UniformAddGroup F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
+    [TopologicalSpace F] {q : ι → Seminorm 𝕝₂ F} (hq : WithSeminorms q)
     (f : E →ₛₗ[τ₁₂] F) (hf : ∀ i : ι, ∃ C : ℝ≥0, (q i).comp f ≤ C • normSeminorm 𝕝 E) :
     Continuous f := by
   rw [← Seminorm.const_isBounded (Fin 1)] at hf
@@ -710,9 +712,9 @@ lemma bound_of_continuous [Nonempty ι] [t : TopologicalSpace E] (hp : WithSemin
   -- Now forget that `E` already had a topology and view it as the (semi)normed space
   -- `(E, s.sup p)`.
   clear hp hq t
-  letI : SeminormedAddCommGroup E :=
+  let _ : SeminormedAddCommGroup E :=
     (s.sup p).toAddGroupSeminorm.toSeminormedAddCommGroup
-  letI : NormedSpace 𝕜 E := { norm_smul_le := fun a b ↦ le_of_eq (map_smul_eq_mul (s.sup p) a b) }
+  let _ : NormedSpace 𝕜 E := { norm_smul_le := fun a b ↦ le_of_eq (map_smul_eq_mul (s.sup p) a b) }
   -- The inclusion `hε` tells us exactly that `q` is *still* continuous for this new topology
   have : Continuous q :=
     Seminorm.continuous (r := 1) (mem_of_superset (Metric.ball_mem_nhds _ ε_pos) hε)
@@ -732,10 +734,11 @@ section LocallyConvexSpace
 open LocallyConvexSpace
 
 variable [Nonempty ι] [NormedField 𝕜] [NormedSpace ℝ 𝕜] [AddCommGroup E] [Module 𝕜 E] [Module ℝ E]
-  [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E] [TopologicalAddGroup E]
+  [IsScalarTower ℝ 𝕜 E] [TopologicalSpace E]
 
 theorem WithSeminorms.toLocallyConvexSpace {p : SeminormFamily 𝕜 E ι} (hp : WithSeminorms p) :
     LocallyConvexSpace ℝ E := by
+  have := hp.topologicalAddGroup
   apply ofBasisZero ℝ E id fun s => s ∈ p.basisSets
   · rw [hp.1, AddGroupFilterBasis.nhds_eq _, AddGroupFilterBasis.N_zero]
     exact FilterBasis.hasBasis _
@@ -792,13 +795,14 @@ theorem SeminormFamily.finset_sup_comp (q : SeminormFamily 𝕜₂ F ι) (s : Fi
   rfl
 #align seminorm_family.finset_sup_comp SeminormFamily.finset_sup_comp
 
-variable [TopologicalSpace F] [TopologicalAddGroup F]
+variable [TopologicalSpace F]
 
 theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
     WithSeminorms (topology := induced f inferInstance) (q.comp f) := by
-  letI : TopologicalSpace E := induced f inferInstance
-  letI : TopologicalAddGroup E := topologicalAddGroup_induced f
+  have := hq.topologicalAddGroup
+  let _ : TopologicalSpace E := induced f inferInstance
+  have : TopologicalAddGroup E := topologicalAddGroup_induced f
   rw [(q.comp f).withSeminorms_iff_nhds_eq_iInf, nhds_induced, map_zero,
     q.withSeminorms_iff_nhds_eq_iInf.mp hq, Filter.comap_iInf]
   refine' iInf_congr fun i => _
@@ -820,7 +824,7 @@ theorem withSeminorms_iInf {κ : ι → Type _} [Nonempty ((i : ι) × κ i)] [
     {p : (i : ι) → SeminormFamily 𝕜 E (κ i)} {t : ι → TopologicalSpace E}
     [∀ i, @TopologicalAddGroup E (t i) _] (hp : ∀ i, WithSeminorms (topology := t i) (p i)) :
     WithSeminorms (topology := ⨅ i, t i) (SeminormFamily.sigma p) := by
-  haveI : @TopologicalAddGroup E (⨅ i, t i) _ := topologicalAddGroup_iInf (fun i ↦ inferInstance)
+  have : @TopologicalAddGroup E (⨅ i, t i) _ := topologicalAddGroup_iInf (fun i ↦ inferInstance)
   simp_rw [@SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf _ _ _ _ _ _ _ (_)] at hp ⊢
   rw [iInf_sigma]
   exact iInf_congr hp
@@ -833,16 +837,19 @@ variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonemp
 
 variable {p : SeminormFamily 𝕜 E ι}
 
-variable [UniformSpace E] [UniformAddGroup E]
+variable [TopologicalSpace E]
 
 /-- If the topology of a space is induced by a countable family of seminorms, then the topology
 is first countable. -/
 theorem WithSeminorms.first_countable (hp : WithSeminorms p) :
     TopologicalSpace.FirstCountableTopology E := by
+  have := hp.topologicalAddGroup
+  let _ : UniformSpace E := TopologicalAddGroup.toUniformSpace E
+  have : UniformAddGroup E := comm_topologicalAddGroup_is_uniform
   have : (𝓝 (0 : E)).IsCountablyGenerated := by
     rw [p.withSeminorms_iff_nhds_eq_iInf.mp hp]
     exact Filter.iInf.isCountablyGenerated _
-  haveI : (uniformity E).IsCountablyGenerated := UniformAddGroup.uniformity_countably_generated
+  have : (uniformity E).IsCountablyGenerated := UniformAddGroup.uniformity_countably_generated
   exact UniformSpace.firstCountableTopology E
 #align with_seminorms.first_countable WithSeminorms.first_countable
 

@@ -270,8 +270,8 @@ section Topology
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Nonempty ι]
 
 /-- The proposition that the topology of `E` is induced by a family of seminorms `p`. -/
-structure WithSeminorms (p : SeminormFamily 𝕜 E ι) [t : TopologicalSpace E] : Prop where
-  topology_eq_withSeminorms : t = p.moduleFilterBasis.topology
+structure WithSeminorms (p : SeminormFamily 𝕜 E ι) [topology : TopologicalSpace E] : Prop where
+  topology_eq_withSeminorms : topology = p.moduleFilterBasis.topology
 #align with_seminorms WithSeminorms
 
 theorem WithSeminorms.withSeminorms_eq {p : SeminormFamily 𝕜 E ι} [t : TopologicalSpace E]
@@ -448,8 +448,7 @@ theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module
 each seminorm individually. We express this as a characterization of `WithSeminorms p`. -/
 theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormFamily 𝕜 E ι) :
     WithSeminorms p ↔
-      t = ⨅ i,
-        (p i).toAddGroupSeminorm.toSeminormedAddCommGroup.toUniformSpace.toTopologicalSpace := by
+      t = ⨅ i, (p i).toSeminormedAddCommGroup.toUniformSpace.toTopologicalSpace := by
   rw [p.withSeminorms_iff_nhds_eq_iInf,
     TopologicalAddGroup.ext_iff inferInstance (topologicalAddGroup_iInf fun i => inferInstance),
     nhds_iInf]
@@ -457,7 +456,7 @@ theorem SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf (p : SeminormF
   refine Eq.to_iff ?_
   congr
   funext i
-  exact @comap_norm_nhds_zero _ (p i).toAddGroupSeminorm.toSeminormedAddGroup
+  exact @comap_norm_nhds_zero _ (p i).toSeminormedAddGroup
 #align seminorm_family.with_seminorms_iff_topological_space_eq_infi SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf
 
 end TopologicalSpace
@@ -467,8 +466,7 @@ induced by each seminorm individually. We express this as a characterization of
 `WithSeminorms p`. -/
 theorem SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf [u : UniformSpace E]
     [UniformAddGroup E] (p : SeminormFamily 𝕜 E ι) :
-    WithSeminorms p ↔
-    u = ⨅ i, (p i).toAddGroupSeminorm.toSeminormedAddCommGroup.toUniformSpace := by
+    WithSeminorms p ↔ u = ⨅ i, (p i).toSeminormedAddCommGroup.toUniformSpace := by
   rw [p.withSeminorms_iff_nhds_eq_iInf,
     UniformAddGroup.ext_iff inferInstance (uniformAddGroup_iInf fun i => inferInstance),
     toTopologicalSpace_iInf, nhds_iInf]
@@ -798,7 +796,7 @@ variable [TopologicalSpace F] [TopologicalAddGroup F]
 
 theorem LinearMap.withSeminorms_induced [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F ι}
     (hq : WithSeminorms q) (f : E →ₛₗ[σ₁₂] F) :
-    @WithSeminorms 𝕜 E ι _ _ _ _ (q.comp f) (induced f inferInstance) := by
+    WithSeminorms (topology := induced f inferInstance) (q.comp f) := by
   letI : TopologicalSpace E := induced f inferInstance
   letI : TopologicalAddGroup E := topologicalAddGroup_induced f
   rw [(q.comp f).withSeminorms_iff_nhds_eq_iInf, nhds_induced, map_zero,
@@ -813,6 +811,20 @@ theorem Inducing.withSeminorms [hι : Nonempty ι] {q : SeminormFamily 𝕜₂ F
   exact f.withSeminorms_induced hq
 #align inducing.with_seminorms Inducing.withSeminorms
 
+/-- (Disjoint) union of seminorm families. -/
+protected def SeminormFamily.sigma {κ : ι → Type _} (p : (i : ι) → SeminormFamily 𝕜 E (κ i)) :
+    SeminormFamily 𝕜 E ((i : ι) × κ i) :=
+  fun ⟨i, k⟩ => p i k
+
+theorem withSeminorms_iInf {κ : ι → Type _} [Nonempty ((i : ι) × κ i)] [∀ i, Nonempty (κ i)]
+    {p : (i : ι) → SeminormFamily 𝕜 E (κ i)} {t : ι → TopologicalSpace E}
+    [∀ i, @TopologicalAddGroup E (t i) _] (hp : ∀ i, WithSeminorms (topology := t i) (p i)) :
+    WithSeminorms (topology := ⨅ i, t i) (SeminormFamily.sigma p) := by
+  haveI : @TopologicalAddGroup E (⨅ i, t i) _ := topologicalAddGroup_iInf (fun i ↦ inferInstance)
+  simp_rw [@SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf _ _ _ _ _ _ _ (_)] at hp ⊢
+  rw [iInf_sigma]
+  exact iInf_congr hp
+
 end TopologicalConstructions
 
 section TopologicalProperties

This removes a chance to infer an argument, but I think that's a fairly good use case for using the new named arguments, because adding (r := _) to specify a radius feels completely right.

@@ -439,7 +439,7 @@ theorem SeminormFamily.withSeminorms_iff_nhds_eq_iInf (p : SeminormFamily 𝕜 E
 theorem WithSeminorms.continuous_seminorm [NontriviallyNormedField 𝕝] [Module 𝕝 E]
     [ContinuousConstSMul 𝕝 E] {p : SeminormFamily 𝕝 E ι} (hp : WithSeminorms p) (i : ι) :
     Continuous (p i) := by
-  refine' Seminorm.continuous one_pos _
+  refine' Seminorm.continuous (r := 1) _
   rw [p.withSeminorms_iff_nhds_eq_iInf.mp hp, ball_zero_eq_preimage_ball]
   exact Filter.mem_iInf_of_mem i (Filter.preimage_mem_comap <| Metric.ball_mem_nhds _ one_pos)
 #align with_seminorms.continuous_seminorm WithSeminorms.continuous_seminorm
@@ -717,7 +717,7 @@ lemma bound_of_continuous [Nonempty ι] [t : TopologicalSpace E] (hp : WithSemin
   letI : NormedSpace 𝕜 E := { norm_smul_le := fun a b ↦ le_of_eq (map_smul_eq_mul (s.sup p) a b) }
   -- The inclusion `hε` tells us exactly that `q` is *still* continuous for this new topology
   have : Continuous q :=
-    Seminorm.continuous one_pos (mem_of_superset (Metric.ball_mem_nhds _ ε_pos) hε)
+    Seminorm.continuous (r := 1) (mem_of_superset (Metric.ball_mem_nhds _ ε_pos) hε)
   -- Hence we can conclude by applying `bound_of_continuous_normed_space`.
   rcases bound_of_continuous_normedSpace q this with ⟨C, C_pos, hC⟩
   exact ⟨s, ⟨C, C_pos.le⟩, fun H ↦ C_pos.ne.symm (congr_arg NNReal.toReal H), hC⟩

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -692,9 +692,9 @@ lemma bound_of_continuous_normedSpace (q : Seminorm 𝕜 F)
   have : 0 < ‖c‖ / ε := by positivity
   refine ⟨‖c‖ / ε, this, fun x ↦ ?_⟩
   by_cases hx : ‖x‖ = 0
-  . rw [hx, mul_zero]
+  · rw [hx, mul_zero]
     exact le_of_eq (map_eq_zero_of_norm_zero q hq hx)
-  . refine (normSeminorm 𝕜 F).bound_of_shell q ε_pos hc (fun x hle hlt ↦ ?_) hx
+  · refine (normSeminorm 𝕜 F).bound_of_shell q ε_pos hc (fun x hle hlt ↦ ?_) hx
     refine (le_of_lt <| show q x < _ from hε hlt).trans ?_
     rwa [← div_le_iff' this, one_div_div]
 

@@ -74,7 +74,7 @@ namespace SeminormFamily
 
 /-- The sets of a filter basis for the neighborhood filter of 0. -/
 def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
-  ⋃ (s : Finset ι) (r) (_ : 0 < r), singleton <| ball (s.sup p) (0 : E) r
+  ⋃ (s : Finset ι) (r) (_ : 0 < r), singleton (ball (s.sup p) (0 : E) r)
 #align seminorm_family.basis_sets SeminormFamily.basisSets
 
 variable (p : SeminormFamily 𝕜 E ι)

This shows that, if the topology of E is defined by some family of seminorms p, then a seminorm q is continuous iff ∃ s : Finset ι, ∃ C : ℝ≥0, C ≠ 0 ∧ q ≤ C • s.sup p. Via Seminorm.continuous_iff_continuous_comp this gives the converse of Seminorm.continuous_from_bounded and hence a characterization of continuous linear maps between such spaces.

To do that, we restate all of the "bound of shell" lemmas in terms of seminorms, which needs changing some imports, but I've checked the current state of the port and this should not cause too much trouble since most of the touched files are already ported so we can changes the imports in mathlib4 too.

The WithSeminorms file needs a naming/dot notation refactor at some point, because the naming scheme is neither predictable nor convenient to use, but this PR is already large enough.

@@ -51,7 +51,7 @@ seminorm, locally convex
 -/
 
 
-open NormedField Set Seminorm TopologicalSpace
+open NormedField Set Seminorm TopologicalSpace Filter
 
 open BigOperators NNReal Pointwise Topology
 
@@ -584,7 +584,8 @@ set_option linter.uppercaseLean3 false in
 
 end NontriviallyNormedField
 
-section ContinuousBounded
+-- TODO: the names in this section are not very predictable
+section continuous_of_bounded
 
 namespace Seminorm
 
@@ -660,7 +661,73 @@ theorem cont_normedSpace_to_withSeminorms (E) [SeminormedAddCommGroup E] [Normed
 
 end Seminorm
 
-end ContinuousBounded
+end continuous_of_bounded
+
+section bounded_of_continuous
+
+namespace Seminorm
+
+variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
+  [SeminormedAddCommGroup F] [NormedSpace 𝕜 F]
+  {p : SeminormFamily 𝕜 E ι}
+
+/-- In a semi-`NormedSpace`, a continuous seminorm is zero on elements of norm `0`. -/
+lemma map_eq_zero_of_norm_zero (q : Seminorm 𝕜 F)
+    (hq : Continuous q) {x : F} (hx : ‖x‖ = 0) : q x = 0 :=
+  (map_zero q) ▸
+    ((specializes_iff_mem_closure.mpr $ mem_closure_zero_iff_norm.mpr hx).map hq).eq.symm
+
+/-- Let `F` be a semi-`NormedSpace` over a `NontriviallyNormedField`, and let `q` be a
+seminorm on `F`. If `q` is continuous, then it is uniformly controlled by the norm, that is there
+is some `C > 0` such that `∀ x, q x ≤ C * ‖x‖`.
+The continuity ensures boundedness on a ball of some radius `ε`. The nontriviality of the
+norm is then used to rescale any element into an element of norm in `[ε/C, ε[`, thus with a
+controlled image by `q`. The control of `q` at the original element follows by rescaling. -/
+lemma bound_of_continuous_normedSpace (q : Seminorm 𝕜 F)
+    (hq : Continuous q) : ∃ C, 0 < C ∧ (∀ x : F, q x ≤ C * ‖x‖) := by
+  have hq' : Tendsto q (𝓝 0) (𝓝 0) := map_zero q ▸ hq.tendsto 0
+  rcases NormedAddCommGroup.nhds_zero_basis_norm_lt.mem_iff.mp (hq' $ Iio_mem_nhds one_pos)
+    with ⟨ε, ε_pos, hε⟩
+  rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
+  have : 0 < ‖c‖ / ε := by positivity
+  refine ⟨‖c‖ / ε, this, fun x ↦ ?_⟩
+  by_cases hx : ‖x‖ = 0
+  . rw [hx, mul_zero]
+    exact le_of_eq (map_eq_zero_of_norm_zero q hq hx)
+  . refine (normSeminorm 𝕜 F).bound_of_shell q ε_pos hc (fun x hle hlt ↦ ?_) hx
+    refine (le_of_lt <| show q x < _ from hε hlt).trans ?_
+    rwa [← div_le_iff' this, one_div_div]
+
+/-- Let `E` be a topological vector space (over a `NontriviallyNormedField`) whose topology is
+generated by some family of seminorms `p`, and let `q` be a seminorm on `E`. If `q` is continuous,
+then it is uniformly controlled by *finitely many* seminorms of `p`, that is there
+is some finset `s` of the index set and some `C > 0` such that `q ≤ C • s.sup p`. -/
+lemma bound_of_continuous [Nonempty ι] [t : TopologicalSpace E] (hp : WithSeminorms p)
+    (q : Seminorm 𝕜 E) (hq : Continuous q) :
+    ∃ s : Finset ι, ∃ C : ℝ≥0, C ≠ 0 ∧ q ≤ C • s.sup p := by
+  -- The continuity of `q` gives us a finset `s` and a real `ε > 0`
+  -- such that `hε : (s.sup p).ball 0 ε ⊆ q.ball 0 1`.
+  rcases hp.hasBasis.mem_iff.mp (ball_mem_nhds hq one_pos) with ⟨V, hV, hε⟩
+  rcases p.basisSets_iff.mp hV with ⟨s, ε, ε_pos, rfl⟩
+  -- Now forget that `E` already had a topology and view it as the (semi)normed space
+  -- `(E, s.sup p)`.
+  clear hp hq t
+  letI : SeminormedAddCommGroup E :=
+    (s.sup p).toAddGroupSeminorm.toSeminormedAddCommGroup
+  letI : NormedSpace 𝕜 E := { norm_smul_le := fun a b ↦ le_of_eq (map_smul_eq_mul (s.sup p) a b) }
+  -- The inclusion `hε` tells us exactly that `q` is *still* continuous for this new topology
+  have : Continuous q :=
+    Seminorm.continuous one_pos (mem_of_superset (Metric.ball_mem_nhds _ ε_pos) hε)
+  -- Hence we can conclude by applying `bound_of_continuous_normed_space`.
+  rcases bound_of_continuous_normedSpace q this with ⟨C, C_pos, hC⟩
+  exact ⟨s, ⟨C, C_pos.le⟩, fun H ↦ C_pos.ne.symm (congr_arg NNReal.toReal H), hC⟩
+  -- Note that the key ingredient for this proof is that, by scaling arguments hidden in
+  -- `seminorm.continuous`, we only have to look at the `q`-ball of radius one, and the `s` we get
+  -- from that will automatically work for all other radii.
+
+end Seminorm
+
+end bounded_of_continuous
 
 section LocallyConvexSpace
 

@@ -353,9 +353,6 @@ theorem WithSeminorms.separating_of_T1 [T1Space E] (hp : WithSeminorms p) (x : E
     ∃ i, p i x ≠ 0 := by
   have := ((t1Space_TFAE E).out 0 9).mp (inferInstanceAs <| T1Space E)
   by_contra' h
-  -- In theory, `by_contra'` does `push_neg`, but it doesn't, and `push_neg` on his own
-  -- does nothing... So we have to do `simp` by hand.
-  simp only [not_exists, not_not] at h
   refine' hx (this _)
   rw [hp.hasBasis_zero_ball.specializes_iff]
   rintro ⟨s, r⟩ (hr : 0 < r)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -230,7 +230,7 @@ def IsBounded (p : ι → Seminorm 𝕜 E) (q : ι' → Seminorm 𝕜₂ F) (f :
 
 theorem isBounded_const (ι' : Type _) [Nonempty ι'] {p : ι → Seminorm 𝕜 E} {q : Seminorm 𝕜₂ F}
     (f : E →ₛₗ[σ₁₂] F) :
-    IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι)(C : ℝ≥0), q.comp f ≤ C • s.sup p := by
+    IsBounded p (fun _ : ι' => q) f ↔ ∃ (s : Finset ι) (C : ℝ≥0), q.comp f ≤ C • s.sup p := by
   simp only [IsBounded, forall_const]
 #align seminorm.is_bounded_const Seminorm.isBounded_const
 
@@ -245,7 +245,7 @@ theorem const_isBounded (ι : Type _) [Nonempty ι] {p : Seminorm 𝕜 E} {q : 
 
 theorem isBounded_sup {p : ι → Seminorm 𝕜 E} {q : ι' → Seminorm 𝕜₂ F} {f : E →ₛₗ[σ₁₂] F}
     (hf : IsBounded p q f) (s' : Finset ι') :
-    ∃ (C : ℝ≥0)(s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
+    ∃ (C : ℝ≥0) (s : Finset ι), (s'.sup q).comp f ≤ C • s.sup p := by
   classical
     obtain rfl | _ := s'.eq_empty_or_nonempty
     · exact ⟨1, ∅, by simp [Seminorm.bot_eq_zero]⟩
@@ -647,7 +647,7 @@ theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFami
 
 theorem cont_withSeminorms_normedSpace (F) [SeminormedAddCommGroup F] [NormedSpace 𝕝₂ F]
     [UniformSpace E] [UniformAddGroup E] {p : ι → Seminorm 𝕝 E} (hp : WithSeminorms p)
-    (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι)(C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
+    (f : E →ₛₗ[τ₁₂] F) (hf : ∃ (s : Finset ι) (C : ℝ≥0), (normSeminorm 𝕝₂ F).comp f ≤ C • s.sup p) :
     Continuous f := by
   rw [← Seminorm.isBounded_const (Fin 1)] at hf
   exact continuous_from_bounded hp (norm_withSeminorms 𝕝₂ F) f hf

@@ -74,7 +74,7 @@ namespace SeminormFamily
 
 /-- The sets of a filter basis for the neighborhood filter of 0. -/
 def basisSets (p : SeminormFamily 𝕜 E ι) : Set (Set E) :=
-  ⋃ (s : Finset ι) (r) (_hr : 0 < r), singleton <| ball (s.sup p) (0 : E) r
+  ⋃ (s : Finset ι) (r) (_ : 0 < r), singleton <| ball (s.sup p) (0 : E) r
 #align seminorm_family.basis_sets SeminormFamily.basisSets
 
 variable (p : SeminormFamily 𝕜 E ι)

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -380,7 +380,7 @@ variable {p : SeminormFamily 𝕜 E ι}
 
 /-- Convergence along filters for `WithSeminorms`.
 
-Variant with `finset.sup`. -/
+Variant with `Finset.sup`. -/
 theorem WithSeminorms.tendsto_nhds' (hp : WithSeminorms p) (u : F → E) {f : Filter F} (y₀ : E) :
     Filter.Tendsto u f (𝓝 y₀) ↔ ∀ (s : Finset ι) (ε), 0 < ε → ∀ᶠ x in f, s.sup p (u x - y₀) < ε :=
   by simp [hp.hasBasis_ball.tendsto_right_iff]

Positivity extensions for NonnegHomClass (this includes AbsoluteValue and Seminorm), IsAbsoluteValue, norm, the NNReal-to-Real coercion, factorials, square roots, distance (in a metric space), and diameter.

I tried to do these "properly" using Qq but I hit various errors I couldn't fix -- see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Qq.20doesn't.20know.20that.20two.20things.20have.20the.20same.20type for some examples.

cc @dwrensha

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -344,8 +344,6 @@ theorem WithSeminorms.T1_of_separating (hp : WithSeminorms p)
   rw [← isOpen_compl_iff, hp.isOpen_iff_mem_balls]
   rintro x (hx : x ≠ 0)
   cases' h x hx with i pi_nonzero
-  -- Porting note: the following line shouldn't be needed, but otherwise `positivity` fails later
-  have : p i x ≥ 0 := map_nonneg _ _
   refine' ⟨{i}, p i x, by positivity, subset_compl_singleton_iff.mpr _⟩
   rw [Finset.sup_singleton, mem_ball, zero_sub, map_neg_eq_map, not_lt]
 #align with_seminorms.t1_of_separating WithSeminorms.T1_of_separating

Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>