analysis.normed_space.banach_steinhaus ⟷ Mathlib.Analysis.NormedSpace.BanachSteinhaus

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Analysis.NormedSpace.OperatorNorm
-import Topology.MetricSpace.Baire
+import Analysis.NormedSpace.OperatorNorm.Basic
+import Topology.Baire.Lemmas
 import Topology.Algebra.Module.Basic
 
 #align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
@@ -66,7 +66,7 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
   · exact div_nonneg (Nat.cast_nonneg _) εk_pos.le
   intro y le_y y_lt
   calc
-    ‖g i y‖ = ‖g i (y + x) - g i x‖ := by rw [ContinuousLinearMap.map_add, add_sub_cancel]
+    ‖g i y‖ = ‖g i (y + x) - g i x‖ := by rw [ContinuousLinearMap.map_add, add_sub_cancel_right]
     _ ≤ ‖g i (y + x)‖ + ‖g i x‖ := (norm_sub_le _ _)
     _ ≤ m + m :=
       (add_le_add (real_norm_le (y + x) (by rwa [add_comm, add_mem_ball_iff_norm]) i)

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

@@ -127,7 +127,7 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
       intro x
       rcases cauchySeq_bdd (tendsto_pi_nhds.mp h x).CauchySeq with ⟨C, C_pos, hC⟩
       refine' ⟨C + ‖g 0 x‖, fun n => _⟩
-      simp_rw [dist_eq_norm] at hC 
+      simp_rw [dist_eq_norm] at hC
       calc
         ‖g n x‖ ≤ ‖g 0 x‖ + ‖g n x - g 0 x‖ := norm_le_insert' _ _
         _ ≤ C + ‖g 0 x‖ := by linarith [hC n 0]

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

@@ -62,7 +62,7 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
     replace hz := mem_Inter.mp (interior_iInter_subset _ (hε hz)) i
     apply interior_subset hz
   have εk_pos : 0 < ε / ‖k‖ := div_pos ε_pos (zero_lt_one.trans hk)
-  refine' ⟨(m + m : ℕ) / (ε / ‖k‖), fun i => ContinuousLinearMap.op_norm_le_of_shell ε_pos _ hk _⟩
+  refine' ⟨(m + m : ℕ) / (ε / ‖k‖), fun i => ContinuousLinearMap.opNorm_le_of_shell ε_pos _ hk _⟩
   · exact div_nonneg (Nat.cast_nonneg _) εk_pos.le
   intro y le_y y_lt
   calc
@@ -141,7 +141,7 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
     have lt_ε : ‖g n x - f x‖ < ε := by rw [← dist_eq_norm]; exact hn n (le_refl n)
     calc
       ‖f x‖ ≤ ‖g n x‖ + ‖g n x - f x‖ := norm_le_insert _ _
-      _ < ‖g n‖ * ‖x‖ + ε := by linarith [lt_ε, (g n).le_op_norm x]
+      _ < ‖g n‖ * ‖x‖ + ε := by linarith [lt_ε, (g n).le_opNorm x]
       _ ≤ C' * ‖x‖ + ε := by nlinarith [hC' n, norm_nonneg x]
 #align continuous_linear_map_of_tendsto continuousLinearMapOfTendsto
 -/

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Mathbin.Analysis.NormedSpace.OperatorNorm
-import Mathbin.Topology.MetricSpace.Baire
-import Mathbin.Topology.Algebra.Module.Basic
+import Analysis.NormedSpace.OperatorNorm
+import Topology.MetricSpace.Baire
+import Topology.Algebra.Module.Basic
 
 #align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module analysis.normed_space.banach_steinhaus
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.OperatorNorm
 import Mathbin.Topology.MetricSpace.Baire
 import Mathbin.Topology.Algebra.Module.Basic
 
+#align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # The Banach-Steinhaus theorem: Uniform Boundedness Principle
 

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

@@ -35,6 +35,7 @@ variable {E F 𝕜 𝕜₂ : Type _} [SeminormedAddCommGroup E] [SeminormedAddCo
   [NontriviallyNormedField 𝕜] [NontriviallyNormedField 𝕜₂] [NormedSpace 𝕜 E] [NormedSpace 𝕜₂ F]
   {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
+#print banach_steinhaus /-
 /-- This is the standard Banach-Steinhaus theorem, or Uniform Boundedness Principle.
 If a family of continuous linear maps from a Banach space into a normed space is pointwise
 bounded, then the norms of these linear maps are uniformly bounded. -/
@@ -79,11 +80,13 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
         ((one_le_div <| div_pos ε_pos (zero_lt_one.trans hk)).2 le_y))
     _ = (m + m : ℕ) / (ε / ‖k‖) * ‖y‖ := (mul_comm_div _ _ _).symm
 #align banach_steinhaus banach_steinhaus
+-/
 
 open scoped ENNReal
 
 open ENNReal
 
+#print banach_steinhaus_iSup_nnnorm /-
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
 theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
@@ -103,11 +106,13 @@ theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι →
   rw [← norm_toNNReal]
   exact coe_mono (Real.toNNReal_le_toNNReal <| hC' i)
 #align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnorm
+-/
 
 open scoped Topology
 
 open Filter
 
+#print continuousLinearMapOfTendsto /-
 /-- Given a *sequence* of continuous linear maps which converges pointwise and for which the
 domain is complete, the Banach-Steinhaus theorem is used to guarantee that the limit map
 is a *continuous* linear map as well. -/
@@ -142,4 +147,5 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
       _ < ‖g n‖ * ‖x‖ + ε := by linarith [lt_ε, (g n).le_op_norm x]
       _ ≤ C' * ‖x‖ + ε := by nlinarith [hC' n, norm_nonneg x]
 #align continuous_linear_map_of_tendsto continuousLinearMapOfTendsto
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -78,7 +78,6 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
       (le_mul_of_one_le_right (Nat.cast_nonneg _)
         ((one_le_div <| div_pos ε_pos (zero_lt_one.trans hk)).2 le_y))
     _ = (m + m : ℕ) / (ε / ‖k‖) * ‖y‖ := (mul_comm_div _ _ _).symm
-    
 #align banach_steinhaus banach_steinhaus
 
 open scoped ENNReal
@@ -99,7 +98,6 @@ theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι →
       calc
         (‖g i x‖₊ : ℝ≥0∞) ≤ ⨆ j, ‖g j x‖₊ := le_iSup _ i
         _ = p := hp₁
-        
   cases' banach_steinhaus h' with C' hC'
   refine' (iSup_le fun i => _).trans_lt (@coe_lt_top C'.to_nnreal)
   rw [← norm_toNNReal]
@@ -131,7 +129,6 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
       calc
         ‖g n x‖ ≤ ‖g 0 x‖ + ‖g n x - g 0 x‖ := norm_le_insert' _ _
         _ ≤ C + ‖g 0 x‖ := by linarith [hC n 0]
-        
     cases' banach_steinhaus h_point_bdd with C' hC'
     /- show the uniform bound from `banach_steinhaus` is a norm bound of the limit map
              by allowing "an `ε` of room." -/
@@ -144,6 +141,5 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
       ‖f x‖ ≤ ‖g n x‖ + ‖g n x - f x‖ := norm_le_insert _ _
       _ < ‖g n‖ * ‖x‖ + ε := by linarith [lt_ε, (g n).le_op_norm x]
       _ ≤ C' * ‖x‖ + ε := by nlinarith [hC' n, norm_nonneg x]
-      
 #align continuous_linear_map_of_tendsto continuousLinearMapOfTendsto
 

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

@@ -42,7 +42,7 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
     (h : ∀ x, ∃ C, ∀ i, ‖g i x‖ ≤ C) : ∃ C', ∀ i, ‖g i‖ ≤ C' :=
   by
   -- sequence of subsets consisting of those `x : E` with norms `‖g i x‖` bounded by `n`
-  let e : ℕ → Set E := fun n => ⋂ i : ι, { x : E | ‖g i x‖ ≤ n }
+  let e : ℕ → Set E := fun n => ⋂ i : ι, {x : E | ‖g i x‖ ≤ n}
   -- each of these sets is closed
   have hc : ∀ n : ℕ, IsClosed (e n) := fun i =>
     isClosed_iInter fun i => isClosed_le (Continuous.norm (g i).cont) continuous_const

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

@@ -127,7 +127,7 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
       intro x
       rcases cauchySeq_bdd (tendsto_pi_nhds.mp h x).CauchySeq with ⟨C, C_pos, hC⟩
       refine' ⟨C + ‖g 0 x‖, fun n => _⟩
-      simp_rw [dist_eq_norm] at hC
+      simp_rw [dist_eq_norm] at hC 
       calc
         ‖g n x‖ ≤ ‖g 0 x‖ + ‖g n x - g 0 x‖ := norm_le_insert' _ _
         _ ≤ C + ‖g 0 x‖ := by linarith [hC n 0]

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

@@ -81,7 +81,7 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
     
 #align banach_steinhaus banach_steinhaus
 
-open ENNReal
+open scoped ENNReal
 
 open ENNReal
 
@@ -106,7 +106,7 @@ theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι →
   exact coe_mono (Real.toNNReal_le_toNNReal <| hC' i)
 #align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnorm
 
-open Topology
+open scoped Topology
 
 open Filter
 

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

@@ -35,9 +35,6 @@ variable {E F 𝕜 𝕜₂ : Type _} [SeminormedAddCommGroup E] [SeminormedAddCo
   [NontriviallyNormedField 𝕜] [NontriviallyNormedField 𝕜₂] [NormedSpace 𝕜 E] [NormedSpace 𝕜₂ F]
   {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
-/- warning: banach_steinhaus -> banach_steinhaus is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align banach_steinhaus banach_steinhausₓ'. -/
 /-- This is the standard Banach-Steinhaus theorem, or Uniform Boundedness Principle.
 If a family of continuous linear maps from a Banach space into a normed space is pointwise
 bounded, then the norms of these linear maps are uniformly bounded. -/
@@ -88,9 +85,6 @@ open ENNReal
 
 open ENNReal
 
-/- warning: banach_steinhaus_supr_nnnorm -> banach_steinhaus_iSup_nnnorm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnormₓ'. -/
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
 theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
@@ -116,9 +110,6 @@ open Topology
 
 open Filter
 
-/- warning: continuous_linear_map_of_tendsto -> continuousLinearMapOfTendsto is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map_of_tendsto continuousLinearMapOfTendstoₓ'. -/
 /-- Given a *sequence* of continuous linear maps which converges pointwise and for which the
 domain is complete, the Banach-Steinhaus theorem is used to guarantee that the limit map
 is a *continuous* linear map as well. -/

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

@@ -148,9 +148,7 @@ def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E 
       AddMonoidHomClass.continuous_of_bound (linearMapOfTendsto _ _ h) C' fun x =>
         le_of_forall_pos_lt_add fun ε ε_pos => _
     cases' metric.tendsto_at_top.mp (tendsto_pi_nhds.mp h x) ε ε_pos with n hn
-    have lt_ε : ‖g n x - f x‖ < ε := by
-      rw [← dist_eq_norm]
-      exact hn n (le_refl n)
+    have lt_ε : ‖g n x - f x‖ < ε := by rw [← dist_eq_norm]; exact hn n (le_refl n)
     calc
       ‖f x‖ ≤ ‖g n x‖ + ‖g n x - f x‖ := norm_le_insert _ _
       _ < ‖g n‖ * ‖x‖ + ε := by linarith [lt_ε, (g n).le_op_norm x]

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

@@ -36,10 +36,7 @@ variable {E F 𝕜 𝕜₂ : Type _} [SeminormedAddCommGroup E] [SeminormedAddCo
   {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
 /- warning: banach_steinhaus -> banach_steinhaus is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toHasNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toHasNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), Exists.{1} Real (fun (C : Real) => forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} F (SeminormedAddCommGroup.toHasNorm.{u2} F _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (g i) x)) C)) -> (Exists.{1} Real (fun (C' : Real) => forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.hasOpNorm.{u3, u4, u1, u2} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂) (g i)) C'))
-but is expected to have type
-  forall {E : Type.{u4}} {F : Type.{u1}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u4} E] [_inst_2 : SeminormedAddCommGroup.{u1} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u2} 𝕜₂] [_inst_5 : NormedSpace.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u2} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (Semiring.toNonAssocSemiring.{u2} 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) (NormedField.toNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toNorm.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), Exists.{1} Real (fun (C : Real) => forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) _inst_2) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E F (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)))) (g i) x)) C)) -> (Exists.{1} Real (fun (C' : Real) => forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.hasOpNorm.{u3, u2, u4, u1} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂) (g i)) C'))
+<too large>
 Case conversion may be inaccurate. Consider using '#align banach_steinhaus banach_steinhausₓ'. -/
 /-- This is the standard Banach-Steinhaus theorem, or Uniform Boundedness Principle.
 If a family of continuous linear maps from a Banach space into a normed space is pointwise
@@ -92,10 +89,7 @@ open ENNReal
 open ENNReal
 
 /- warning: banach_steinhaus_supr_nnnorm -> banach_steinhaus_iSup_nnnorm is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toHasNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toHasNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (NNNorm.nnnorm.{u2} F (SeminormedAddGroup.toNNNorm.{u2} F (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} F _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (g i) x)))) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (NNNorm.nnnorm.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.toSeminormedAddCommGroup.{u3, u4, u1, u2} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7))) (g i)))) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
-but is expected to have type
-  forall {E : Type.{u4}} {F : Type.{u1}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u4} E] [_inst_2 : SeminormedAddCommGroup.{u1} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u2} 𝕜₂] [_inst_5 : NormedSpace.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u2} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (Semiring.toNonAssocSemiring.{u2} 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) (NormedField.toNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toNorm.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => ENNReal.some (NNNorm.nnnorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (SeminormedAddGroup.toNNNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E F (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)))) (g i) x)))) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => ENNReal.some (NNNorm.nnnorm.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddGroup.toNNNorm.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.toSeminormedAddCommGroup.{u3, u2, u4, u1} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7))) (g i)))) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnormₓ'. -/
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
@@ -123,10 +117,7 @@ open Topology
 open Filter
 
 /- warning: continuous_linear_map_of_tendsto -> continuousLinearMapOfTendsto is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toHasNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toHasNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] [_inst_9 : T2Space.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2)))] (g : Nat -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))) {f : E -> F}, (Filter.Tendsto.{0, max u1 u2} Nat (E -> F) (fun (n : Nat) (x : E) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F 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(ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) 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-  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] [_inst_9 : T2Space.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2)))] (g : Nat -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 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(NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)))) (g n) x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{max u1 u2} (forall (x : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (Pi.topologicalSpace.{u1, u2} E (fun (x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (fun (a : E) => UniformSpace.toTopologicalSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) a) (PseudoMetricSpace.toUniformSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) a) _inst_2)))) f)) -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))
+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_linear_map_of_tendsto continuousLinearMapOfTendstoₓ'. -/
 /-- Given a *sequence* of continuous linear maps which converges pointwise and for which the
 domain is complete, the Banach-Steinhaus theorem is used to guarantee that the limit map

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module analysis.normed_space.banach_steinhaus
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Algebra.Module.Basic
 /-!
 # The Banach-Steinhaus theorem: Uniform Boundedness Principle
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Herein we prove the Banach-Steinhaus theorem: any collection of bounded linear maps
 from a Banach space into a normed space which is pointwise bounded is uniformly bounded.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -32,6 +32,12 @@ variable {E F 𝕜 𝕜₂ : Type _} [SeminormedAddCommGroup E] [SeminormedAddCo
   [NontriviallyNormedField 𝕜] [NontriviallyNormedField 𝕜₂] [NormedSpace 𝕜 E] [NormedSpace 𝕜₂ F]
   {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
+/- warning: banach_steinhaus -> banach_steinhaus is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toHasNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toHasNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), Exists.{1} Real (fun (C : Real) => forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} F (SeminormedAddCommGroup.toHasNorm.{u2} F _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (g i) x)) C)) -> (Exists.{1} Real (fun (C' : Real) => forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.hasOpNorm.{u3, u4, u1, u2} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂) (g i)) C'))
+but is expected to have type
+  forall {E : Type.{u4}} {F : Type.{u1}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u4} E] [_inst_2 : SeminormedAddCommGroup.{u1} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u2} 𝕜₂] [_inst_5 : NormedSpace.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u2} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (Semiring.toNonAssocSemiring.{u2} 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) (NormedField.toNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toNorm.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), Exists.{1} Real (fun (C : Real) => forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) _inst_2) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E F (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)))) (g i) x)) C)) -> (Exists.{1} Real (fun (C' : Real) => forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.hasOpNorm.{u3, u2, u4, u1} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂) (g i)) C'))
+Case conversion may be inaccurate. Consider using '#align banach_steinhaus banach_steinhausₓ'. -/
 /-- This is the standard Banach-Steinhaus theorem, or Uniform Boundedness Principle.
 If a family of continuous linear maps from a Banach space into a normed space is pointwise
 bounded, then the norms of these linear maps are uniformly bounded. -/
@@ -82,6 +88,12 @@ open ENNReal
 
 open ENNReal
 
+/- warning: banach_steinhaus_supr_nnnorm -> banach_steinhaus_iSup_nnnorm is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toHasNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toHasNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (NNNorm.nnnorm.{u2} F (SeminormedAddGroup.toNNNorm.{u2} F (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} F _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (g i) x)))) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (NNNorm.nnnorm.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.toSeminormedAddCommGroup.{u3, u4, u1, u2} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7))) (g i)))) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
+but is expected to have type
+  forall {E : Type.{u4}} {F : Type.{u1}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u4} E] [_inst_2 : SeminormedAddCommGroup.{u1} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u2} 𝕜₂] [_inst_5 : NormedSpace.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u2} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (Semiring.toNonAssocSemiring.{u2} 𝕜₂ (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) (NormedField.toNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toNorm.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4)) σ₁₂] {ι : Type.{u5}} [_inst_8 : CompleteSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))] {g : ι -> (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6))}, (forall (x : E), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => ENNReal.some (NNNorm.nnnorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (SeminormedAddGroup.toNNNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) E F (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)))) (g i) x)))) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (iSup.{0, succ u5} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => ENNReal.some (NNNorm.nnnorm.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddGroup.toNNNorm.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u4 u1} (ContinuousLinearMap.{u3, u2, u4, u1} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜₂ (Semifield.toDivisionSemiring.{u2} 𝕜₂ (Field.toSemifield.{u2} 𝕜₂ (NormedField.toField.{u2} 𝕜₂ (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F (SeminormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{u3, u4} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u2, u1} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u2} 𝕜₂ _inst_4) _inst_2 _inst_6)) (ContinuousLinearMap.toSeminormedAddCommGroup.{u3, u2, u4, u1} 𝕜 𝕜₂ E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 σ₁₂ _inst_7))) (g i)))) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
+Case conversion may be inaccurate. Consider using '#align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnormₓ'. -/
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
 theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
@@ -107,6 +119,12 @@ open Topology
 
 open Filter
 
+/- warning: continuous_linear_map_of_tendsto -> continuousLinearMapOfTendsto is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toHasNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toHasNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] [_inst_9 : T2Space.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2)))] (g : Nat -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))) {f : E -> F}, (Filter.Tendsto.{0, max u1 u2} Nat (E -> F) (fun (n : Nat) (x : E) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) (g n) x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{max u1 u2} (E -> F) (Pi.topologicalSpace.{u1, u2} E (fun (x : E) => F) (fun (a : E) => UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2)))) f)) -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedCommRing.toNormedRing.{u4} 𝕜₂ (NormedField.toNormedCommRing.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))
+but is expected to have type
+  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜 : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_2 : SeminormedAddCommGroup.{u2} F] [_inst_3 : NontriviallyNormedField.{u3} 𝕜] [_inst_4 : NontriviallyNormedField.{u4} 𝕜₂] [_inst_5 : NormedSpace.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1] [_inst_6 : NormedSpace.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2] {σ₁₂ : RingHom.{u3, u4} 𝕜 𝕜₂ (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)))))) (Semiring.toNonAssocSemiring.{u4} 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))))} [_inst_7 : RingHomIsometric.{u3, u4} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) (NormedField.toNorm.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3)) (NormedField.toNorm.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4)) σ₁₂] [_inst_8 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] [_inst_9 : T2Space.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2)))] (g : Nat -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))) {f : E -> F}, (Filter.Tendsto.{0, max u1 u2} Nat (forall (x : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (fun (n : Nat) (x : E) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) E F (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u4, u1, u2} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)) 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6)))) (g n) x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{max u1 u2} (forall (x : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (Pi.topologicalSpace.{u1, u2} E (fun (x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) x) (fun (a : E) => UniformSpace.toTopologicalSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) a) (PseudoMetricSpace.toUniformSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) a) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) a) _inst_2)))) f)) -> (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜₂ (Semifield.toDivisionSemiring.{u4} 𝕜₂ (Field.toSemifield.{u4} 𝕜₂ (NormedField.toField.{u4} 𝕜₂ (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4))))) σ₁₂ E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F _inst_2)) (NormedSpace.toModule.{u3, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_3) _inst_1 _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜₂ F (NontriviallyNormedField.toNormedField.{u4} 𝕜₂ _inst_4) _inst_2 _inst_6))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map_of_tendsto continuousLinearMapOfTendstoₓ'. -/
 /-- Given a *sequence* of continuous linear maps which converges pointwise and for which the
 domain is complete, the Banach-Steinhaus theorem is used to guarantee that the limit map
 is a *continuous* linear map as well. -/

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

@@ -42,7 +42,7 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
   let e : ℕ → Set E := fun n => ⋂ i : ι, { x : E | ‖g i x‖ ≤ n }
   -- each of these sets is closed
   have hc : ∀ n : ℕ, IsClosed (e n) := fun i =>
-    isClosed_interᵢ fun i => isClosed_le (Continuous.norm (g i).cont) continuous_const
+    isClosed_iInter fun i => isClosed_le (Continuous.norm (g i).cont) continuous_const
   -- the union is the entire space; this is where we use `h`
   have hU : (⋃ n : ℕ, e n) = univ :=
     by
@@ -51,14 +51,14 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
     obtain ⟨m, hm⟩ := exists_nat_ge C
     exact ⟨e m, mem_range_self m, mem_Inter.mpr fun i => le_trans (hC i) hm⟩
   -- apply the Baire category theorem to conclude that for some `m : ℕ`, `e m` contains some `x`
-  rcases nonempty_interior_of_unionᵢ_of_closed hc hU with ⟨m, x, hx⟩
+  rcases nonempty_interior_of_iUnion_of_closed hc hU with ⟨m, x, hx⟩
   rcases metric.is_open_iff.mp isOpen_interior x hx with ⟨ε, ε_pos, hε⟩
   obtain ⟨k, hk⟩ := NormedField.exists_one_lt_norm 𝕜
   -- show all elements in the ball have norm bounded by `m` after applying any `g i`
   have real_norm_le : ∀ z : E, z ∈ Metric.ball x ε → ∀ i : ι, ‖g i z‖ ≤ m :=
     by
     intro z hz i
-    replace hz := mem_Inter.mp (interior_interᵢ_subset _ (hε hz)) i
+    replace hz := mem_Inter.mp (interior_iInter_subset _ (hε hz)) i
     apply interior_subset hz
   have εk_pos : 0 < ε / ‖k‖ := div_pos ε_pos (zero_lt_one.trans hk)
   refine' ⟨(m + m : ℕ) / (ε / ‖k‖), fun i => ContinuousLinearMap.op_norm_le_of_shell ε_pos _ hk _⟩
@@ -84,7 +84,7 @@ open ENNReal
 
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
-theorem banach_steinhaus_supᵢ_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
+theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
     (h : ∀ x, (⨆ i, ↑‖g i x‖₊) < ∞) : (⨆ i, ↑‖g i‖₊) < ∞ :=
   by
   have h' : ∀ x : E, ∃ C : ℝ, ∀ i : ι, ‖g i x‖ ≤ C :=
@@ -94,14 +94,14 @@ theorem banach_steinhaus_supᵢ_nnnorm {ι : Type _} [CompleteSpace E] {g : ι 
     refine' ⟨p, fun i => _⟩
     exact_mod_cast
       calc
-        (‖g i x‖₊ : ℝ≥0∞) ≤ ⨆ j, ‖g j x‖₊ := le_supᵢ _ i
+        (‖g i x‖₊ : ℝ≥0∞) ≤ ⨆ j, ‖g j x‖₊ := le_iSup _ i
         _ = p := hp₁
         
   cases' banach_steinhaus h' with C' hC'
-  refine' (supᵢ_le fun i => _).trans_lt (@coe_lt_top C'.to_nnreal)
+  refine' (iSup_le fun i => _).trans_lt (@coe_lt_top C'.to_nnreal)
   rw [← norm_toNNReal]
   exact coe_mono (Real.toNNReal_le_toNNReal <| hC' i)
-#align banach_steinhaus_supr_nnnorm banach_steinhaus_supᵢ_nnnorm
+#align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnorm
 
 open Topology
 

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

@@ -66,14 +66,14 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
   intro y le_y y_lt
   calc
     ‖g i y‖ = ‖g i (y + x) - g i x‖ := by rw [ContinuousLinearMap.map_add, add_sub_cancel]
-    _ ≤ ‖g i (y + x)‖ + ‖g i x‖ := norm_sub_le _ _
+    _ ≤ ‖g i (y + x)‖ + ‖g i x‖ := (norm_sub_le _ _)
     _ ≤ m + m :=
-      add_le_add (real_norm_le (y + x) (by rwa [add_comm, add_mem_ball_iff_norm]) i)
-        (real_norm_le x (Metric.mem_ball_self ε_pos) i)
+      (add_le_add (real_norm_le (y + x) (by rwa [add_comm, add_mem_ball_iff_norm]) i)
+        (real_norm_le x (Metric.mem_ball_self ε_pos) i))
     _ = (m + m : ℕ) := (m.cast_add m).symm
     _ ≤ (m + m : ℕ) * (‖y‖ / (ε / ‖k‖)) :=
-      le_mul_of_one_le_right (Nat.cast_nonneg _)
-        ((one_le_div <| div_pos ε_pos (zero_lt_one.trans hk)).2 le_y)
+      (le_mul_of_one_le_right (Nat.cast_nonneg _)
+        ((one_le_div <| div_pos ε_pos (zero_lt_one.trans hk)).2 le_y))
     _ = (m + m : ℕ) / (ε / ‖k‖) * ‖y‖ := (mul_comm_div _ _ _).symm
     
 #align banach_steinhaus banach_steinhaus

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

@@ -78,9 +78,9 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
     
 #align banach_steinhaus banach_steinhaus
 
-open Ennreal
+open ENNReal
 
-open Ennreal
+open ENNReal
 
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/

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

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.

@@ -35,7 +35,7 @@ theorem banach_steinhaus {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ
     (h : ∀ x, ∃ C, ∀ i, ‖g i x‖ ≤ C) : ∃ C', ∀ i, ‖g i‖ ≤ C' := by
   rw [show (∃ C, ∀ i, ‖g i‖ ≤ C) ↔ _ from (NormedSpace.equicontinuous_TFAE g).out 5 2]
   refine (norm_withSeminorms 𝕜₂ F).banach_steinhaus (fun _ x ↦ ?_)
-  simpa [bddAbove_def, forall_range_iff] using h x
+  simpa [bddAbove_def, forall_mem_range] using h x
 #align banach_steinhaus banach_steinhaus
 
 open ENNReal

• move definition to Topology/Defs/Basic;
• move lemmas to Topology/Baire/Lemmas;
• move instances to Topology/Baire/CompleteMetrizable and Topology/Baire/LocallyCompactRegular;
• assume [UniformSpace X] [IsCountablyGenerated (𝓤 X)] instead of [PseudoMetricSpace X] in the 1st theorem.

This way Lemmas file does not depend on analysis.

@@ -5,6 +5,7 @@ Authors: Jireh Loreaux
 -/
 import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
 import Mathlib.Analysis.LocallyConvex.Barrelled
+import Mathlib.Topology.Baire.CompleteMetrizable
 
 #align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

Split the 2300-line behemoth OperatorNorm.lean into 8 smaller files, of which the largest is 600 lines.

@@ -3,7 +3,7 @@ Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Mathlib.Analysis.NormedSpace.OperatorNorm
+import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
 import Mathlib.Analysis.LocallyConvex.Barrelled
 
 #align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

and corresponding lemmas for ℕ∞.

Also fix implicitness of iff lemmas.

@@ -47,8 +47,7 @@ theorem banach_steinhaus_iSup_nnnorm {ι : Type*} [CompleteSpace E] {g : ι →
     (h : ∀ x, (⨆ i, ↑‖g i x‖₊) < ∞) : (⨆ i, ↑‖g i‖₊) < ∞ := by
   rw [show ((⨆ i, ↑‖g i‖₊) < ∞) ↔ _ from (NormedSpace.equicontinuous_TFAE g).out 8 2]
   refine (norm_withSeminorms 𝕜₂ F).banach_steinhaus (fun _ x ↦ ?_)
-  simpa [← NNReal.bddAbove_coe, ← Set.range_comp] using
-    (WithTop.iSup_coe_lt_top (fun i ↦ ‖g i x‖₊)).mp (h x)
+  simpa [← NNReal.bddAbove_coe, ← Set.range_comp] using ENNReal.iSup_coe_lt_top.1 (h x)
 #align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnorm
 
 open Topology

@@ -4,25 +4,21 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
 import Mathlib.Analysis.NormedSpace.OperatorNorm
-import Mathlib.Topology.MetricSpace.Baire
-import Mathlib.Topology.Algebra.Module.Basic
+import Mathlib.Analysis.LocallyConvex.Barrelled
 
 #align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 
 /-!
 # The Banach-Steinhaus theorem: Uniform Boundedness Principle
 
-Herein we prove the Banach-Steinhaus theorem: any collection of bounded linear maps
-from a Banach space into a normed space which is pointwise bounded is uniformly bounded.
+Herein we prove the Banach-Steinhaus theorem for normed spaces: any collection of bounded linear
+maps from a Banach space into a normed space which is pointwise bounded is uniformly bounded.
 
-## TODO
-
-For now, we only prove the standard version by appeal to the Baire category theorem.
-Much more general versions exist (in particular, for maps from barrelled spaces to locally
-convex spaces), but these are not yet in `mathlib`.
+Note that we prove the more general version about barrelled spaces in
+`Analysis.LocallyConvex.Barrelled`, and the usual version below is indeed deduced from the
+more general setup.
 -/
 
-
 open Set
 
 variable {E F 𝕜 𝕜₂ : Type*} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
@@ -31,44 +27,14 @@ variable {E F 𝕜 𝕜₂ : Type*} [SeminormedAddCommGroup E] [SeminormedAddCom
 
 /-- This is the standard Banach-Steinhaus theorem, or Uniform Boundedness Principle.
 If a family of continuous linear maps from a Banach space into a normed space is pointwise
-bounded, then the norms of these linear maps are uniformly bounded. -/
+bounded, then the norms of these linear maps are uniformly bounded.
+
+See also `WithSeminorms.banach_steinhaus` for the general statement in barrelled spaces. -/
 theorem banach_steinhaus {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
     (h : ∀ x, ∃ C, ∀ i, ‖g i x‖ ≤ C) : ∃ C', ∀ i, ‖g i‖ ≤ C' := by
-  -- sequence of subsets consisting of those `x : E` with norms `‖g i x‖` bounded by `n`
-  let e : ℕ → Set E := fun n => ⋂ i : ι, { x : E | ‖g i x‖ ≤ n }
-  -- each of these sets is closed
-  have hc : ∀ n : ℕ, IsClosed (e n) := fun i =>
-    isClosed_iInter fun i => isClosed_le (Continuous.norm (g i).cont) continuous_const
-  -- the union is the entire space; this is where we use `h`
-  have hU : ⋃ n : ℕ, e n = univ := by
-    refine' eq_univ_of_forall fun x => _
-    cases' h x with C hC
-    obtain ⟨m, hm⟩ := exists_nat_ge C
-    exact ⟨e m, mem_range_self m, mem_iInter.mpr fun i => le_trans (hC i) hm⟩
-  -- apply the Baire category theorem to conclude that for some `m : ℕ`, `e m` contains some `x`
-  rcases nonempty_interior_of_iUnion_of_closed hc hU with ⟨m, x, hx⟩
-  rcases Metric.isOpen_iff.mp isOpen_interior x hx with ⟨ε, ε_pos, hε⟩
-  obtain ⟨k, hk⟩ := NormedField.exists_one_lt_norm 𝕜
-  -- show all elements in the ball have norm bounded by `m` after applying any `g i`
-  have real_norm_le : ∀ z : E, z ∈ Metric.ball x ε → ∀ i : ι, ‖g i z‖ ≤ m := by
-    intro z hz i
-    replace hz := mem_iInter.mp (interior_iInter_subset _ (hε hz)) i
-    apply interior_subset hz
-  have εk_pos : 0 < ε / ‖k‖ := div_pos ε_pos (zero_lt_one.trans hk)
-  refine' ⟨(m + m : ℕ) / (ε / ‖k‖), fun i => ContinuousLinearMap.op_norm_le_of_shell ε_pos _ hk _⟩
-  · exact div_nonneg (Nat.cast_nonneg _) εk_pos.le
-  intro y le_y y_lt
-  calc
-    ‖g i y‖ = ‖g i (y + x) - g i x‖ := by rw [ContinuousLinearMap.map_add, add_sub_cancel]
-    _ ≤ ‖g i (y + x)‖ + ‖g i x‖ := (norm_sub_le _ _)
-    _ ≤ m + m :=
-      (add_le_add (real_norm_le (y + x) (by rwa [add_comm, add_mem_ball_iff_norm]) i)
-        (real_norm_le x (Metric.mem_ball_self ε_pos) i))
-    _ = (m + m : ℕ) := (m.cast_add m).symm
-    _ ≤ (m + m : ℕ) * (‖y‖ / (ε / ‖k‖)) :=
-      (le_mul_of_one_le_right (Nat.cast_nonneg _)
-        ((one_le_div <| div_pos ε_pos (zero_lt_one.trans hk)).2 le_y))
-    _ = (m + m : ℕ) / (ε / ‖k‖) * ‖y‖ := (mul_comm_div _ _ _).symm
+  rw [show (∃ C, ∀ i, ‖g i‖ ≤ C) ↔ _ from (NormedSpace.equicontinuous_TFAE g).out 5 2]
+  refine (norm_withSeminorms 𝕜₂ F).banach_steinhaus (fun _ x ↦ ?_)
+  simpa [bddAbove_def, forall_range_iff] using h x
 #align banach_steinhaus banach_steinhaus
 
 open ENNReal
@@ -78,19 +44,11 @@ open ENNReal
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖·‖₊ : ℝ≥0∞`
 for convenience. -/
 theorem banach_steinhaus_iSup_nnnorm {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
-    (h : ∀ x, ⨆ i, ↑‖g i x‖₊ < ∞) : ⨆ i, ↑‖g i‖₊ < ∞ := by
-  have h' : ∀ x : E, ∃ C : ℝ, ∀ i : ι, ‖g i x‖ ≤ C := by
-    intro x
-    rcases lt_iff_exists_coe.mp (h x) with ⟨p, hp₁, _⟩
-    refine' ⟨p, fun i => _⟩
-    exact_mod_cast
-      calc
-        (‖g i x‖₊ : ℝ≥0∞) ≤ ⨆ j, ↑‖g j x‖₊ := le_iSup (fun j => (‖g j x‖₊ : ℝ≥0∞)) i
-        _ = p := hp₁
-  cases' banach_steinhaus h' with C' hC'
-  refine' (iSup_le fun i => _).trans_lt (@coe_lt_top C'.toNNReal)
-  rw [← norm_toNNReal]
-  exact coe_mono (Real.toNNReal_le_toNNReal <| hC' i)
+    (h : ∀ x, (⨆ i, ↑‖g i x‖₊) < ∞) : (⨆ i, ↑‖g i‖₊) < ∞ := by
+  rw [show ((⨆ i, ↑‖g i‖₊) < ∞) ↔ _ from (NormedSpace.equicontinuous_TFAE g).out 8 2]
+  refine (norm_withSeminorms 𝕜₂ F).banach_steinhaus (fun _ x ↦ ?_)
+  simpa [← NNReal.bddAbove_coe, ← Set.range_comp] using
+    (WithTop.iSup_coe_lt_top (fun i ↦ ‖g i x‖₊)).mp (h x)
 #align banach_steinhaus_supr_nnnorm banach_steinhaus_iSup_nnnorm
 
 open Topology
@@ -100,33 +58,9 @@ open Filter
 /-- Given a *sequence* of continuous linear maps which converges pointwise and for which the
 domain is complete, the Banach-Steinhaus theorem is used to guarantee that the limit map
 is a *continuous* linear map as well. -/
-def continuousLinearMapOfTendsto [CompleteSpace E] [T2Space F] (g : ℕ → E →SL[σ₁₂] F) {f : E → F}
-    (h : Tendsto (fun n x => g n x) atTop (𝓝 f)) : E →SL[σ₁₂] F where
-  toFun := f
-  map_add' := (linearMapOfTendsto _ _ h).map_add'
-  map_smul' := (linearMapOfTendsto _ _ h).map_smul'
-  cont := by
-    -- show that the maps are pointwise bounded and apply `banach_steinhaus`
-    have h_point_bdd : ∀ x : E, ∃ C : ℝ, ∀ n : ℕ, ‖g n x‖ ≤ C := by
-      intro x
-      rcases cauchySeq_bdd (tendsto_pi_nhds.mp h x).cauchySeq with ⟨C, -, hC⟩
-      refine' ⟨C + ‖g 0 x‖, fun n => _⟩
-      simp_rw [dist_eq_norm] at hC
-      calc
-        ‖g n x‖ ≤ ‖g 0 x‖ + ‖g n x - g 0 x‖ := norm_le_insert' _ _
-        _ ≤ C + ‖g 0 x‖ := by linarith [hC n 0]
-    cases' banach_steinhaus h_point_bdd with C' hC'
-    /- show the uniform bound from `banach_steinhaus` is a norm bound of the limit map
-             by allowing "an `ε` of room." -/
-    refine'
-      AddMonoidHomClass.continuous_of_bound (linearMapOfTendsto _ _ h) C' fun x =>
-        le_of_forall_pos_lt_add fun ε ε_pos => _
-    cases' Metric.tendsto_atTop.mp (tendsto_pi_nhds.mp h x) ε ε_pos with n hn
-    have lt_ε : ‖g n x - f x‖ < ε := by
-      rw [← dist_eq_norm]
-      exact hn n (le_refl n)
-    calc
-      ‖f x‖ ≤ ‖g n x‖ + ‖g n x - f x‖ := norm_le_insert _ _
-      _ < ‖g n‖ * ‖x‖ + ε := by linarith [lt_ε, (g n).le_op_norm x]
-      _ ≤ C' * ‖x‖ + ε := by nlinarith [hC' n, norm_nonneg x]
+abbrev continuousLinearMapOfTendsto {α : Type*} [CompleteSpace E] [T2Space F] {l : Filter α}
+    [l.IsCountablyGenerated] [l.NeBot] (g : α → E →SL[σ₁₂] F) {f : E → F}
+    (h : Tendsto (fun n x ↦ g n x) l (𝓝 f)) :
+    E →SL[σ₁₂] F :=
+  (norm_withSeminorms 𝕜₂ F).continuousLinearMapOfTendsto g h
 #align continuous_linear_map_of_tendsto continuousLinearMapOfTendsto

MIDDLE DOT is now valid Lean syntax for function arguments, which is what these docstrings are referring to.

@@ -75,7 +75,7 @@ open ENNReal
 
 open ENNReal
 
-/-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
+/-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖·‖₊ : ℝ≥0∞`
 for convenience. -/
 theorem banach_steinhaus_iSup_nnnorm {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
     (h : ∀ x, ⨆ i, ↑‖g i x‖₊ < ∞) : ⨆ i, ↑‖g i‖₊ < ∞ := by

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

This has nice performance benefits.

@@ -25,14 +25,14 @@ convex spaces), but these are not yet in `mathlib`.
 
 open Set
 
-variable {E F 𝕜 𝕜₂ : Type _} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
+variable {E F 𝕜 𝕜₂ : Type*} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
   [NontriviallyNormedField 𝕜] [NontriviallyNormedField 𝕜₂] [NormedSpace 𝕜 E] [NormedSpace 𝕜₂ F]
   {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂]
 
 /-- This is the standard Banach-Steinhaus theorem, or Uniform Boundedness Principle.
 If a family of continuous linear maps from a Banach space into a normed space is pointwise
 bounded, then the norms of these linear maps are uniformly bounded. -/
-theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
+theorem banach_steinhaus {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
     (h : ∀ x, ∃ C, ∀ i, ‖g i x‖ ≤ C) : ∃ C', ∀ i, ‖g i‖ ≤ C' := by
   -- sequence of subsets consisting of those `x : E` with norms `‖g i x‖` bounded by `n`
   let e : ℕ → Set E := fun n => ⋂ i : ι, { x : E | ‖g i x‖ ≤ n }
@@ -77,7 +77,7 @@ open ENNReal
 
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
-theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
+theorem banach_steinhaus_iSup_nnnorm {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
     (h : ∀ x, ⨆ i, ↑‖g i x‖₊ < ∞) : ⨆ i, ↑‖g i‖₊ < ∞ := by
   have h' : ∀ x : E, ∃ C : ℝ, ∀ i : ι, ‖g i x‖ ≤ C := by
     intro x

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module analysis.normed_space.banach_steinhaus
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.OperatorNorm
 import Mathlib.Topology.MetricSpace.Baire
 import Mathlib.Topology.Algebra.Module.Basic
 
+#align_import analysis.normed_space.banach_steinhaus from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # The Banach-Steinhaus theorem: Uniform Boundedness Principle
 

@@ -43,7 +43,7 @@ theorem banach_steinhaus {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ
   have hc : ∀ n : ℕ, IsClosed (e n) := fun i =>
     isClosed_iInter fun i => isClosed_le (Continuous.norm (g i).cont) continuous_const
   -- the union is the entire space; this is where we use `h`
-  have hU : (⋃ n : ℕ, e n) = univ := by
+  have hU : ⋃ n : ℕ, e n = univ := by
     refine' eq_univ_of_forall fun x => _
     cases' h x with C hC
     obtain ⟨m, hm⟩ := exists_nat_ge C
@@ -81,7 +81,7 @@ open ENNReal
 /-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖⬝‖₊ : ℝ≥0∞`
 for convenience. -/
 theorem banach_steinhaus_iSup_nnnorm {ι : Type _} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
-    (h : ∀ x, (⨆ i, ↑‖g i x‖₊) < ∞) : (⨆ i, ↑‖g i‖₊) < ∞ := by
+    (h : ∀ x, ⨆ i, ↑‖g i x‖₊ < ∞) : ⨆ i, ↑‖g i‖₊ < ∞ := by
   have h' : ∀ x : E, ∃ C : ℝ, ∀ i : ι, ‖g i x‖ ≤ C := by
     intro x
     rcases lt_iff_exists_coe.mp (h x) with ⟨p, hp₁, _⟩