analysis.normed.mul_action ⟷ Mathlib.Analysis.Normed.MulAction

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Topology.MetricSpace.Algebra
-import Mathbin.Analysis.Normed.Field.Basic
+import Topology.MetricSpace.Algebra
+import Analysis.Normed.Field.Basic
 
 #align_import analysis.normed.mul_action from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.normed.mul_action
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Algebra
 import Mathbin.Analysis.Normed.Field.Basic
 
+#align_import analysis.normed.mul_action from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 # Lemmas for `has_bounded_smul` over normed additive groups
 

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

@@ -33,39 +33,54 @@ variable [SeminormedAddGroup α] [SeminormedAddGroup β] [SMulZeroClass α β]
 
 variable [BoundedSMul α β]
 
+#print norm_smul_le /-
 theorem norm_smul_le (r : α) (x : β) : ‖r • x‖ ≤ ‖r‖ * ‖x‖ := by
   simpa [smul_zero] using dist_smul_pair r 0 x
 #align norm_smul_le norm_smul_le
+-/
 
+#print nnnorm_smul_le /-
 theorem nnnorm_smul_le (r : α) (x : β) : ‖r • x‖₊ ≤ ‖r‖₊ * ‖x‖₊ :=
   norm_smul_le _ _
 #align nnnorm_smul_le nnnorm_smul_le
+-/
 
+#print dist_smul_le /-
 theorem dist_smul_le (s : α) (x y : β) : dist (s • x) (s • y) ≤ ‖s‖ * dist x y := by
   simpa only [dist_eq_norm, sub_zero] using dist_smul_pair s x y
 #align dist_smul_le dist_smul_le
+-/
 
+#print nndist_smul_le /-
 theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s‖₊ * nndist x y :=
   dist_smul_le s x y
 #align nndist_smul_le nndist_smul_le
+-/
 
+#print edist_smul_le /-
 theorem edist_smul_le (s : α) (x y : β) : edist (s • x) (s • y) ≤ ‖s‖₊ • edist x y := by
   simpa only [edist_nndist, ENNReal.coe_mul] using ennreal.coe_le_coe.mpr (nndist_smul_le s x y)
 #align edist_smul_le edist_smul_le
+-/
 
+#print lipschitzWith_smul /-
 theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ ((· • ·) s : β → β) :=
   lipschitzWith_iff_dist_le_mul.2 <| dist_smul_le _
 #align lipschitz_with_smul lipschitzWith_smul
+-/
 
 end SeminormedAddGroup
 
+#print NonUnitalSeminormedRing.to_boundedSMul /-
 /-- Left multiplication is bounded. -/
 instance NonUnitalSeminormedRing.to_boundedSMul [NonUnitalSeminormedRing α] : BoundedSMul α α
     where
   dist_smul_pair' x y₁ y₂ := by simpa [mul_sub, dist_eq_norm] using norm_mul_le x (y₁ - y₂)
   dist_pair_smul' x₁ x₂ y := by simpa [sub_mul, dist_eq_norm] using norm_mul_le (x₁ - x₂) y
 #align non_unital_semi_normed_ring.to_has_bounded_smul NonUnitalSeminormedRing.to_boundedSMul
+-/
 
+#print NonUnitalSeminormedRing.to_has_bounded_op_smul /-
 /-- Right multiplication is bounded. -/
 instance NonUnitalSeminormedRing.to_has_bounded_op_smul [NonUnitalSeminormedRing α] :
     BoundedSMul αᵐᵒᵖ α
@@ -75,16 +90,19 @@ instance NonUnitalSeminormedRing.to_has_bounded_op_smul [NonUnitalSeminormedRing
   dist_pair_smul' x₁ x₂ y := by
     simpa [mul_sub, dist_eq_norm, mul_comm] using norm_mul_le y (x₁ - x₂).unop
 #align non_unital_semi_normed_ring.to_has_bounded_op_smul NonUnitalSeminormedRing.to_has_bounded_op_smul
+-/
 
 section SeminormedRing
 
 variable [SeminormedRing α] [SeminormedAddCommGroup β] [Module α β]
 
+#print BoundedSMul.of_norm_smul_le /-
 theorem BoundedSMul.of_norm_smul_le (h : ∀ (r : α) (x : β), ‖r • x‖ ≤ ‖r‖ * ‖x‖) :
     BoundedSMul α β :=
   { dist_smul_pair' := fun a b₁ b₂ => by simpa [smul_sub, dist_eq_norm] using h a (b₁ - b₂)
     dist_pair_smul' := fun a₁ a₂ b => by simpa [sub_smul, dist_eq_norm] using h (a₁ - a₂) b }
 #align has_bounded_smul.of_norm_smul_le BoundedSMul.of_norm_smul_le
+-/
 
 end SeminormedRing
 
@@ -94,6 +112,7 @@ variable [NormedDivisionRing α] [SeminormedAddGroup β]
 
 variable [MulActionWithZero α β] [BoundedSMul α β]
 
+#print norm_smul /-
 theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
   by
   by_cases h : r = 0
@@ -104,10 +123,13 @@ theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
       _ ≤ ‖r‖ * (‖r⁻¹‖ * ‖r • x‖) := (mul_le_mul_of_nonneg_left (norm_smul_le _ _) (norm_nonneg _))
       _ = ‖r • x‖ := by rw [norm_inv, ← mul_assoc, mul_inv_cancel (mt norm_eq_zero.1 h), one_mul]
 #align norm_smul norm_smul
+-/
 
+#print nnnorm_smul /-
 theorem nnnorm_smul (r : α) (x : β) : ‖r • x‖₊ = ‖r‖₊ * ‖x‖₊ :=
   NNReal.eq <| norm_smul r x
 #align nnnorm_smul nnnorm_smul
+-/
 
 end NormedDivisionRing
 
@@ -117,17 +139,23 @@ variable [NormedDivisionRing α] [SeminormedAddCommGroup β]
 
 variable [Module α β] [BoundedSMul α β]
 
+#print dist_smul₀ /-
 theorem dist_smul₀ (s : α) (x y : β) : dist (s • x) (s • y) = ‖s‖ * dist x y := by
   simp_rw [dist_eq_norm, (norm_smul _ _).symm, smul_sub]
 #align dist_smul₀ dist_smul₀
+-/
 
+#print nndist_smul₀ /-
 theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s‖₊ * nndist x y :=
   NNReal.eq <| dist_smul₀ s x y
 #align nndist_smul₀ nndist_smul₀
+-/
 
+#print edist_smul₀ /-
 theorem edist_smul₀ (s : α) (x y : β) : edist (s • x) (s • y) = ‖s‖₊ • edist x y := by
   simp only [edist_nndist, nndist_smul₀, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]
 #align edist_smul₀ edist_smul₀
+-/
 
 end NormedDivisionRingModule
 

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

@@ -103,7 +103,6 @@ theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
       ‖r‖ * ‖x‖ = ‖r‖ * ‖r⁻¹ • r • x‖ := by rw [inv_smul_smul₀ h]
       _ ≤ ‖r‖ * (‖r⁻¹‖ * ‖r • x‖) := (mul_le_mul_of_nonneg_left (norm_smul_le _ _) (norm_nonneg _))
       _ = ‖r • x‖ := by rw [norm_inv, ← mul_assoc, mul_inv_cancel (mt norm_eq_zero.1 h), one_mul]
-      
 #align norm_smul norm_smul
 
 theorem nnnorm_smul (r : α) (x : β) : ‖r • x‖₊ = ‖r‖₊ * ‖x‖₊ :=

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

@@ -33,74 +33,32 @@ variable [SeminormedAddGroup α] [SeminormedAddGroup β] [SMulZeroClass α β]
 
 variable [BoundedSMul α β]
 
-/- warning: norm_smul_le -> norm_smul_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (SeminormedAddGroup.toHasNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) x))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (SeminormedAddGroup.toNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) x))
-Case conversion may be inaccurate. Consider using '#align norm_smul_le norm_smul_leₓ'. -/
 theorem norm_smul_le (r : α) (x : β) : ‖r • x‖ ≤ ‖r‖ * ‖x‖ := by
   simpa [smul_zero] using dist_smul_pair r 0 x
 #align norm_smul_le norm_smul_le
 
-/- warning: nnnorm_smul_le -> nnnorm_smul_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
-Case conversion may be inaccurate. Consider using '#align nnnorm_smul_le nnnorm_smul_leₓ'. -/
 theorem nnnorm_smul_le (r : α) (x : β) : ‖r • x‖₊ ≤ ‖r‖₊ * ‖x‖₊ :=
   norm_smul_le _ _
 #align nnnorm_smul_le nnnorm_smul_le
 
-/- warning: dist_smul_le -> dist_smul_le is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (SeminormedAddGroup.toHasNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (SeminormedAddGroup.toNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-Case conversion may be inaccurate. Consider using '#align dist_smul_le dist_smul_leₓ'. -/
 theorem dist_smul_le (s : α) (x y : β) : dist (s • x) (s • y) ≤ ‖s‖ * dist x y := by
   simpa only [dist_eq_norm, sub_zero] using dist_smul_pair s x y
 #align dist_smul_le dist_smul_le
 
-/- warning: nndist_smul_le -> nndist_smul_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-Case conversion may be inaccurate. Consider using '#align nndist_smul_le nndist_smul_leₓ'. -/
 theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s‖₊ * nndist x y :=
   dist_smul_le s x y
 #align nndist_smul_le nndist_smul_le
 
-/- warning: edist_smul_le -> edist_smul_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s y)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2))) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s y)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2))) x y))
-Case conversion may be inaccurate. Consider using '#align edist_smul_le edist_smul_leₓ'. -/
 theorem edist_smul_le (s : α) (x y : β) : edist (s • x) (s • y) ≤ ‖s‖₊ • edist x y := by
   simpa only [edist_nndist, ENNReal.coe_mul] using ennreal.coe_le_coe.mpr (nndist_smul_le s x y)
 #align edist_smul_le edist_smul_le
 
-/- warning: lipschitz_with_smul -> lipschitzWith_smul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α), LipschitzWith.{u2, u2} β β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α), LipschitzWith.{u2, u2} β β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) ((fun (x._@.Mathlib.Analysis.Normed.MulAction._hyg.270 : α) (x._@.Mathlib.Analysis.Normed.MulAction._hyg.272 : β) => HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) x._@.Mathlib.Analysis.Normed.MulAction._hyg.270 x._@.Mathlib.Analysis.Normed.MulAction._hyg.272) s)
-Case conversion may be inaccurate. Consider using '#align lipschitz_with_smul lipschitzWith_smulₓ'. -/
 theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ ((· • ·) s : β → β) :=
   lipschitzWith_iff_dist_le_mul.2 <| dist_smul_le _
 #align lipschitz_with_smul lipschitzWith_smul
 
 end SeminormedAddGroup
 
-/- warning: non_unital_semi_normed_ring.to_has_bounded_smul -> NonUnitalSeminormedRing.to_boundedSMul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} α α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (Mul.toSMul.{u1} α (Distrib.toHasMul.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} α α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} α α (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align non_unital_semi_normed_ring.to_has_bounded_smul NonUnitalSeminormedRing.to_boundedSMulₓ'. -/
 /-- Left multiplication is bounded. -/
 instance NonUnitalSeminormedRing.to_boundedSMul [NonUnitalSeminormedRing α] : BoundedSMul α α
     where
@@ -108,12 +66,6 @@ instance NonUnitalSeminormedRing.to_boundedSMul [NonUnitalSeminormedRing α] : B
   dist_pair_smul' x₁ x₂ y := by simpa [sub_mul, dist_eq_norm] using norm_mul_le (x₁ - x₂) y
 #align non_unital_semi_normed_ring.to_has_bounded_smul NonUnitalSeminormedRing.to_boundedSMul
 
-/- warning: non_unital_semi_normed_ring.to_has_bounded_op_smul -> NonUnitalSeminormedRing.to_has_bounded_op_smul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} (MulOpposite.{u1} α) α (MulOpposite.pseudoMetricSpace.{u1} α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1)) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (MulOpposite.hasZero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))))) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (Mul.toHasOppositeSMul.{u1} α (Distrib.toHasMul.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} (MulOpposite.{u1} α) α (MulOpposite.instPseudoMetricSpaceMulOpposite.{u1} α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1)) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (MulOpposite.zero.{u1} α (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (Mul.toHasOppositeSMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align non_unital_semi_normed_ring.to_has_bounded_op_smul NonUnitalSeminormedRing.to_has_bounded_op_smulₓ'. -/
 /-- Right multiplication is bounded. -/
 instance NonUnitalSeminormedRing.to_has_bounded_op_smul [NonUnitalSeminormedRing α] :
     BoundedSMul αᵐᵒᵖ α
@@ -128,12 +80,6 @@ section SeminormedRing
 
 variable [SeminormedRing α] [SeminormedAddCommGroup β] [Module α β]
 
-/- warning: has_bounded_smul.of_norm_smul_le -> BoundedSMul.of_norm_smul_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))], (forall (r : α) (x : β), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (SeminormedRing.toHasNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) x))) -> (BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))], (forall (r : α) (x : β), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (SeminormedRing.toNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) x))) -> (BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))))
-Case conversion may be inaccurate. Consider using '#align has_bounded_smul.of_norm_smul_le BoundedSMul.of_norm_smul_leₓ'. -/
 theorem BoundedSMul.of_norm_smul_le (h : ∀ (r : α) (x : β), ‖r • x‖ ≤ ‖r‖ * ‖x‖) :
     BoundedSMul α β :=
   { dist_smul_pair' := fun a b₁ b₂ => by simpa [smul_sub, dist_eq_norm] using h a (b₁ - b₂)
@@ -148,12 +94,6 @@ variable [NormedDivisionRing α] [SeminormedAddGroup β]
 
 variable [MulActionWithZero α β] [BoundedSMul α β]
 
-/- warning: norm_smul -> norm_smul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} Real (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (NormedDivisionRing.toHasNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) x))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} Real (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (NormedDivisionRing.toNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) x))
-Case conversion may be inaccurate. Consider using '#align norm_smul norm_smulₓ'. -/
 theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
   by
   by_cases h : r = 0
@@ -166,12 +106,6 @@ theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
       
 #align norm_smul norm_smul
 
-/- warning: nnnorm_smul -> nnnorm_smul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} NNReal (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3))) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} NNReal (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
-Case conversion may be inaccurate. Consider using '#align nnnorm_smul nnnorm_smulₓ'. -/
 theorem nnnorm_smul (r : α) (x : β) : ‖r • x‖₊ = ‖r‖₊ * ‖x‖₊ :=
   NNReal.eq <| norm_smul r x
 #align nnnorm_smul nnnorm_smul
@@ -184,23 +118,14 @@ variable [NormedDivisionRing α] [SeminormedAddCommGroup β]
 
 variable [Module α β] [BoundedSMul α β]
 
-/- warning: dist_smul₀ -> dist_smul₀ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dist_smul₀ dist_smul₀ₓ'. -/
 theorem dist_smul₀ (s : α) (x y : β) : dist (s • x) (s • y) = ‖s‖ * dist x y := by
   simp_rw [dist_eq_norm, (norm_smul _ _).symm, smul_sub]
 #align dist_smul₀ dist_smul₀
 
-/- warning: nndist_smul₀ -> nndist_smul₀ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align nndist_smul₀ nndist_smul₀ₓ'. -/
 theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s‖₊ * nndist x y :=
   NNReal.eq <| dist_smul₀ s x y
 #align nndist_smul₀ nndist_smul₀
 
-/- warning: edist_smul₀ -> edist_smul₀ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align edist_smul₀ edist_smul₀ₓ'. -/
 theorem edist_smul₀ (s : α) (x y : β) : edist (s • x) (s • y) = ‖s‖₊ • edist x y := by
   simp only [edist_nndist, nndist_smul₀, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]
 #align edist_smul₀ edist_smul₀

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

@@ -185,30 +185,21 @@ variable [NormedDivisionRing α] [SeminormedAddCommGroup β]
 variable [Module α β] [BoundedSMul α β]
 
 /- warning: dist_smul₀ -> dist_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} Real (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (NormedDivisionRing.toHasNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} Real (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (NormedDivisionRing.toNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align dist_smul₀ dist_smul₀ₓ'. -/
 theorem dist_smul₀ (s : α) (x y : β) : dist (s • x) (s • y) = ‖s‖ * dist x y := by
   simp_rw [dist_eq_norm, (norm_smul _ _).symm, smul_sub]
 #align dist_smul₀ dist_smul₀
 
 /- warning: nndist_smul₀ -> nndist_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} NNReal (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} NNReal (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align nndist_smul₀ nndist_smul₀ₓ'. -/
 theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s‖₊ * nndist x y :=
   NNReal.eq <| dist_smul₀ s x y
 #align nndist_smul₀ nndist_smul₀
 
 /- warning: edist_smul₀ -> edist_smul₀ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} ENNReal (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s y)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} ENNReal (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s y)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) x y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align edist_smul₀ edist_smul₀ₓ'. -/
 theorem edist_smul₀ (s : α) (x y : β) : edist (s • x) (s • y) = ‖s‖₊ • edist x y := by
   simp only [edist_nndist, nndist_smul₀, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed.mul_action
-! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Normed.Field.Basic
 /-!
 # Lemmas for `has_bounded_smul` over normed additive groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Lemmas which hold only in `normed_space α β` are provided in another file.
 
 Notably we prove that `non_unital_semi_normed_ring`s have bounded actions by left- and right-

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -70,6 +70,12 @@ theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s
   dist_smul_le s x y
 #align nndist_smul_le nndist_smul_le
 
+/- warning: edist_smul_le -> edist_smul_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s y)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2))) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s y)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2))) x y))
+Case conversion may be inaccurate. Consider using '#align edist_smul_le edist_smul_leₓ'. -/
 theorem edist_smul_le (s : α) (x y : β) : edist (s • x) (s • y) ≤ ‖s‖₊ • edist x y := by
   simpa only [edist_nndist, ENNReal.coe_mul] using ennreal.coe_le_coe.mpr (nndist_smul_le s x y)
 #align edist_smul_le edist_smul_le
@@ -195,6 +201,12 @@ theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s
   NNReal.eq <| dist_smul₀ s x y
 #align nndist_smul₀ nndist_smul₀
 
+/- warning: edist_smul₀ -> edist_smul₀ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} ENNReal (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s y)) (SMul.smul.{0, 0} NNReal ENNReal (SMulZeroClass.toHasSmul.{0, 0} NNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} NNReal ENNReal (MulZeroClass.toHasZero.{0} NNReal (MulZeroOneClass.toMulZeroClass.{0} NNReal (MonoidWithZero.toMulZeroOneClass.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} NNReal ENNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} NNReal ENNReal NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (ENNReal.module.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Semiring.toModule.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (EDist.edist.{u2} β (PseudoMetricSpace.toEDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} ENNReal (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s y)) (HSMul.hSMul.{0, 0, 0} NNReal ENNReal ENNReal (instHSMul.{0, 0} NNReal ENNReal (Algebra.toSMul.{0, 0} NNReal ENNReal instNNRealCommSemiring (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.instAlgebraNNRealInstNNRealCommSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) x y))
+Case conversion may be inaccurate. Consider using '#align edist_smul₀ edist_smul₀ₓ'. -/
 theorem edist_smul₀ (s : α) (x y : β) : edist (s • x) (s • y) = ‖s‖₊ • edist x y := by
   simp only [edist_nndist, nndist_smul₀, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]
 #align edist_smul₀ edist_smul₀

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed.mul_action
-! leanprover-community/mathlib commit ba5ff5ad5d120fb0ef094ad2994967e9bfaf5112
+! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -70,6 +70,10 @@ theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s
   dist_smul_le s x y
 #align nndist_smul_le nndist_smul_le
 
+theorem edist_smul_le (s : α) (x y : β) : edist (s • x) (s • y) ≤ ‖s‖₊ • edist x y := by
+  simpa only [edist_nndist, ENNReal.coe_mul] using ennreal.coe_le_coe.mpr (nndist_smul_le s x y)
+#align edist_smul_le edist_smul_le
+
 /- warning: lipschitz_with_smul -> lipschitzWith_smul is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α), LipschitzWith.{u2, u2} β β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s)
@@ -191,5 +195,9 @@ theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s
   NNReal.eq <| dist_smul₀ s x y
 #align nndist_smul₀ nndist_smul₀
 
+theorem edist_smul₀ (s : α) (x y : β) : edist (s • x) (s • y) = ‖s‖₊ • edist x y := by
+  simp only [edist_nndist, nndist_smul₀, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]
+#align edist_smul₀ edist_smul₀
+
 end NormedDivisionRingModule
 

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

@@ -34,7 +34,7 @@ variable [BoundedSMul α β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (SeminormedAddGroup.toHasNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) x))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (r : β), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} β (SeminormedAddCommGroup.toNorm.{u1} β _inst_2) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} α (NormedField.toNorm.{u2} α _inst_1) _inst_4) (Norm.norm.{u1} β (SeminormedAddCommGroup.toNorm.{u1} β _inst_2) r))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (SeminormedAddGroup.toNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) x))
 Case conversion may be inaccurate. Consider using '#align norm_smul_le norm_smul_leₓ'. -/
 theorem norm_smul_le (r : α) (x : β) : ‖r • x‖ ≤ ‖r‖ * ‖x‖ := by
   simpa [smul_zero] using dist_smul_pair r 0 x
@@ -44,7 +44,7 @@ theorem norm_smul_le (r : α) (x : β) : ‖r • x‖ ≤ ‖r‖ * ‖x‖ :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (r : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} β (SeminormedAddGroup.toNNNorm.{u1} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} β _inst_2)) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 r)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u2} α (SeminormedAddGroup.toNNNorm.{u2} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} α (NormedRing.toNonUnitalNormedRing.{u2} α (NormedCommRing.toNormedRing.{u2} α (NormedField.toNormedCommRing.{u2} α _inst_1))))))) _inst_4) (NNNorm.nnnorm.{u1} β (SeminormedAddGroup.toNNNorm.{u1} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} β _inst_2)) r))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (r : α) (x : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
 Case conversion may be inaccurate. Consider using '#align nnnorm_smul_le nnnorm_smul_leₓ'. -/
 theorem nnnorm_smul_le (r : α) (x : β) : ‖r • x‖₊ ≤ ‖r‖₊ * ‖x‖₊ :=
   norm_smul_le _ _
@@ -54,7 +54,7 @@ theorem nnnorm_smul_le (r : α) (x : β) : ‖r • x‖₊ ≤ ‖r‖₊ * ‖
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (SeminormedAddGroup.toHasNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (s : β) (x : β), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} β (PseudoMetricSpace.toDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 s) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} α (NormedField.toNorm.{u2} α _inst_1) _inst_4) (Dist.dist.{u1} β (PseudoMetricSpace.toDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) s x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (SeminormedAddGroup.toNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align dist_smul_le dist_smul_leₓ'. -/
 theorem dist_smul_le (s : α) (x y : β) : dist (s • x) (s • y) ≤ ‖s‖ * dist x y := by
   simpa only [dist_eq_norm, sub_zero] using dist_smul_pair s x y
@@ -64,7 +64,7 @@ theorem dist_smul_le (s : α) (x y : β) : dist (s • x) (s • y) ≤ ‖s‖
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (s : β) (x : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNDist.nndist.{u1} β (PseudoMetricSpace.toNNDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 s) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u2} α (SeminormedAddGroup.toNNNorm.{u2} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} α (NormedRing.toNonUnitalNormedRing.{u2} α (NormedCommRing.toNormedRing.{u2} α (NormedField.toNormedCommRing.{u2} α _inst_1))))))) _inst_4) (NNDist.nndist.{u1} β (PseudoMetricSpace.toNNDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) s x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α) (x : β) (y : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align nndist_smul_le nndist_smul_leₓ'. -/
 theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s‖₊ * nndist x y :=
   dist_smul_le s x y
@@ -74,7 +74,7 @@ theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α), LipschitzWith.{u2, u2} β β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3) s)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α), LipschitzWith.{u1, u1} β β (PseudoMetricSpace.toPseudoEMetricSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) (NNNorm.nnnorm.{u2} α (SeminormedAddGroup.toNNNorm.{u2} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} α (NormedRing.toNonUnitalNormedRing.{u2} α (NormedCommRing.toNormedRing.{u2} α (NormedField.toNormedCommRing.{u2} α _inst_1))))))) _inst_4) ((fun (x._@.Mathlib.Analysis.NormedSpace.Basic._hyg.916 : α) (x._@.Mathlib.Analysis.NormedSpace.Basic._hyg.918 : β) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Analysis.NormedSpace.Basic._hyg.916 x._@.Mathlib.Analysis.NormedSpace.Basic._hyg.918) _inst_4)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedAddGroup.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : SMulZeroClass.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedAddGroup.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)] (s : α), LipschitzWith.{u2, u2} β β (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α _inst_1) s) ((fun (x._@.Mathlib.Analysis.Normed.MulAction._hyg.270 : α) (x._@.Mathlib.Analysis.Normed.MulAction._hyg.272 : β) => HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)) x._@.Mathlib.Analysis.Normed.MulAction._hyg.270 x._@.Mathlib.Analysis.Normed.MulAction._hyg.272) s)
 Case conversion may be inaccurate. Consider using '#align lipschitz_with_smul lipschitzWith_smulₓ'. -/
 theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ ((· • ·) s : β → β) :=
   lipschitzWith_iff_dist_le_mul.2 <| dist_smul_le _
@@ -82,6 +82,12 @@ theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ ((· • ·) s :
 
 end SeminormedAddGroup
 
+/- warning: non_unital_semi_normed_ring.to_has_bounded_smul -> NonUnitalSeminormedRing.to_boundedSMul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} α α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (Mul.toSMul.{u1} α (Distrib.toHasMul.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} α α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} α α (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align non_unital_semi_normed_ring.to_has_bounded_smul NonUnitalSeminormedRing.to_boundedSMulₓ'. -/
 /-- Left multiplication is bounded. -/
 instance NonUnitalSeminormedRing.to_boundedSMul [NonUnitalSeminormedRing α] : BoundedSMul α α
     where
@@ -89,6 +95,12 @@ instance NonUnitalSeminormedRing.to_boundedSMul [NonUnitalSeminormedRing α] : B
   dist_pair_smul' x₁ x₂ y := by simpa [sub_mul, dist_eq_norm] using norm_mul_le (x₁ - x₂) y
 #align non_unital_semi_normed_ring.to_has_bounded_smul NonUnitalSeminormedRing.to_boundedSMul
 
+/- warning: non_unital_semi_normed_ring.to_has_bounded_op_smul -> NonUnitalSeminormedRing.to_has_bounded_op_smul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} (MulOpposite.{u1} α) α (MulOpposite.pseudoMetricSpace.{u1} α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1)) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (MulOpposite.hasZero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))))) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (Mul.toHasOppositeSMul.{u1} α (Distrib.toHasMul.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : NonUnitalSeminormedRing.{u1} α], BoundedSMul.{u1, u1} (MulOpposite.{u1} α) α (MulOpposite.instPseudoMetricSpaceMulOpposite.{u1} α (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1)) (NonUnitalSeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (MulOpposite.zero.{u1} α (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))) (SemigroupWithZero.toZero.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1)))) (Mul.toHasOppositeSMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonUnitalRing.toNonUnitalNonAssocRing.{u1} α (NonUnitalSeminormedRing.toNonUnitalRing.{u1} α _inst_1))))
+Case conversion may be inaccurate. Consider using '#align non_unital_semi_normed_ring.to_has_bounded_op_smul NonUnitalSeminormedRing.to_has_bounded_op_smulₓ'. -/
 /-- Right multiplication is bounded. -/
 instance NonUnitalSeminormedRing.to_has_bounded_op_smul [NonUnitalSeminormedRing α] :
     BoundedSMul αᵐᵒᵖ α
@@ -103,6 +115,12 @@ section SeminormedRing
 
 variable [SeminormedRing α] [SeminormedAddCommGroup β] [Module α β]
 
+/- warning: has_bounded_smul.of_norm_smul_le -> BoundedSMul.of_norm_smul_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))], (forall (r : α) (x : β), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (SeminormedRing.toHasNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) x))) -> (BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SeminormedRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))], (forall (r : α) (x : β), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (SeminormedRing.toNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) x))) -> (BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α _inst_1) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (SeminormedRing.toRing.{u1} α _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))))
+Case conversion may be inaccurate. Consider using '#align has_bounded_smul.of_norm_smul_le BoundedSMul.of_norm_smul_leₓ'. -/
 theorem BoundedSMul.of_norm_smul_le (h : ∀ (r : α) (x : β), ‖r • x‖ ≤ ‖r‖ * ‖x‖) :
     BoundedSMul α β :=
   { dist_smul_pair' := fun a b₁ b₂ => by simpa [smul_sub, dist_eq_norm] using h a (b₁ - b₂)
@@ -121,7 +139,7 @@ variable [MulActionWithZero α β] [BoundedSMul α β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} Real (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (NormedDivisionRing.toHasNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toHasNorm.{u2} β _inst_2) x))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (r : β), Eq.{1} Real (Norm.norm.{u1} β (SeminormedAddCommGroup.toNorm.{u1} β _inst_2) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} α (NormedField.toNorm.{u2} α _inst_1) _inst_4) (Norm.norm.{u1} β (SeminormedAddCommGroup.toNorm.{u1} β _inst_2) r))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} Real (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))) r x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (NormedDivisionRing.toNorm.{u1} α _inst_1) r) (Norm.norm.{u2} β (SeminormedAddGroup.toNorm.{u2} β _inst_2) x))
 Case conversion may be inaccurate. Consider using '#align norm_smul norm_smulₓ'. -/
 theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
   by
@@ -139,7 +157,7 @@ theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} NNReal (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3))) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (r : β), Eq.{1} NNReal (NNNorm.nnnorm.{u1} β (SeminormedAddGroup.toNNNorm.{u1} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} β _inst_2)) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 r)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u2} α (SeminormedAddGroup.toNNNorm.{u2} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} α (NormedRing.toNonUnitalNormedRing.{u2} α (NormedCommRing.toNormedRing.{u2} α (NormedField.toNormedCommRing.{u2} α _inst_1))))))) _inst_4) (NNNorm.nnnorm.{u1} β (SeminormedAddGroup.toNNNorm.{u1} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} β _inst_2)) r))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddGroup.{u2} β] [_inst_3 : MulActionWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2)))))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))] (r : α) (x : β), Eq.{1} NNReal (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (AddGroup.toSubtractionMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β _inst_2))))) _inst_3)))) r x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) r) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β _inst_2) x))
 Case conversion may be inaccurate. Consider using '#align nnnorm_smul nnnorm_smulₓ'. -/
 theorem nnnorm_smul (r : α) (x : β) : ‖r • x‖₊ = ‖r‖₊ * ‖x‖₊ :=
   NNReal.eq <| norm_smul r x
@@ -157,7 +175,7 @@ variable [Module α β] [BoundedSMul α β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} Real (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} α (NormedDivisionRing.toHasNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (s : β) (x : β), Eq.{1} Real (Dist.dist.{u1} β (PseudoMetricSpace.toDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 s) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u2} α (NormedField.toNorm.{u2} α _inst_1) _inst_4) (Dist.dist.{u1} β (PseudoMetricSpace.toDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) s x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} Real (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} α (NormedDivisionRing.toNorm.{u1} α _inst_1) s) (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align dist_smul₀ dist_smul₀ₓ'. -/
 theorem dist_smul₀ (s : α) (x y : β) : dist (s • x) (s • y) = ‖s‖ * dist x y := by
   simp_rw [dist_eq_norm, (norm_smul _ _).symm, smul_sub]
@@ -167,7 +185,7 @@ theorem dist_smul₀ (s : α) (x y : β) : dist (s • x) (s • y) = ‖s‖ *
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} NNReal (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s x) (SMul.smul.{u1, u2} α β (SMulZeroClass.toHasSmul.{u1, u2} α β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} α β (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))))))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))) (Module.toMulActionWithZero.{u1, u2} α β (Ring.toSemiring.{u1} α (NormedRing.toRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3)))) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : NormedField.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u1} β] [_inst_3 : NormedSpace.{u2, u1} α β _inst_1 _inst_2] (_inst_4 : α) (s : β) (x : β), Eq.{1} NNReal (NNDist.nndist.{u1} β (PseudoMetricSpace.toNNDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 s) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (DivisionSemiring.toSemiring.{u2} α (Semifield.toDivisionSemiring.{u2} α (Field.toSemifield.{u2} α (NormedField.toField.{u2} α _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} β (SeminormedAddCommGroup.toAddCommGroup.{u1} β _inst_2)) (NormedSpace.toModule.{u2, u1} α β _inst_1 _inst_2 _inst_3)))))) _inst_4 x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u2} α (SeminormedAddGroup.toNNNorm.{u2} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} α (NormedRing.toNonUnitalNormedRing.{u2} α (NormedCommRing.toNormedRing.{u2} α (NormedField.toNormedCommRing.{u2} α _inst_1))))))) _inst_4) (NNDist.nndist.{u1} β (PseudoMetricSpace.toNNDist.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β _inst_2)) s x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : NormedDivisionRing.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Module.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))] [_inst_4 : BoundedSMul.{u1, u2} α β (SeminormedRing.toPseudoMetricSpace.{u1} α (NormedRing.toSeminormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))] (s : α) (x : β) (y : β), Eq.{1} NNReal (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s x) (HSMul.hSMul.{u1, u2, u2} α β β (instHSMul.{u1, u2} α β (SMulZeroClass.toSMul.{u1, u2} α β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} α β (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} α β (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1)))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} α β (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α (NormedDivisionRing.toDivisionRing.{u1} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) _inst_3))))) s y)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} α (SeminormedAddGroup.toNNNorm.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} α (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} α (NormedRing.toNonUnitalNormedRing.{u1} α (NormedDivisionRing.toNormedRing.{u1} α _inst_1)))))) s) (NNDist.nndist.{u2} β (PseudoMetricSpace.toNNDist.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align nndist_smul₀ nndist_smul₀ₓ'. -/
 theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s‖₊ * nndist x y :=
   NNReal.eq <| dist_smul₀ s x y

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -24,7 +24,6 @@ variable {α β : Type*}
 section SeminormedAddGroup
 
 variable [SeminormedAddGroup α] [SeminormedAddGroup β] [SMulZeroClass α β]
-
 variable [BoundedSMul α β]
 
 theorem norm_smul_le (r : α) (x : β) : ‖r • x‖ ≤ ‖r‖ * ‖x‖ := by
@@ -86,7 +85,6 @@ end SeminormedRing
 section NormedDivisionRing
 
 variable [NormedDivisionRing α] [SeminormedAddGroup β]
-
 variable [MulActionWithZero α β] [BoundedSMul α β]
 
 theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ := by
@@ -108,7 +106,6 @@ end NormedDivisionRing
 section NormedDivisionRingModule
 
 variable [NormedDivisionRing α] [SeminormedAddCommGroup β]
-
 variable [Module α β] [BoundedSMul α β]
 
 theorem dist_smul₀ (s : α) (x y : β) : dist (s • x) (s • y) = ‖s‖ * dist x y := by

Also adds:

• Lemmas linking the $L^\infty$ norm via WithLp to the standard one on products
• A new BoundedSMul.of_nnnorm_smul_le which eliminates all the positivity juggling.

In theory we could generalize even further to non-unital rings, but that would require more generalization of WithLp, and is trivial for someone to do later; the proofs here will still work.

@@ -78,6 +78,9 @@ theorem BoundedSMul.of_norm_smul_le (h : ∀ (r : α) (x : β), ‖r • x‖ 
     dist_pair_smul' := fun a₁ a₂ b => by simpa [sub_smul, dist_eq_norm] using h (a₁ - a₂) b }
 #align has_bounded_smul.of_norm_smul_le BoundedSMul.of_norm_smul_le
 
+theorem BoundedSMul.of_nnnorm_smul_le (h : ∀ (r : α) (x : β), ‖r • x‖₊ ≤ ‖r‖₊ * ‖x‖₊) :
+    BoundedSMul α β := .of_norm_smul_le h
+
 end SeminormedRing
 
 section NormedDivisionRing

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

@@ -43,7 +43,7 @@ theorem nndist_smul_le (s : α) (x y : β) : nndist (s • x) (s • y) ≤ ‖s
   dist_smul_le s x y
 #align nndist_smul_le nndist_smul_le
 
-theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ ((· • ·) s : β → β) :=
+theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ (s • · : β → β) :=
   lipschitzWith_iff_dist_le_mul.2 <| dist_smul_le _
 #align lipschitz_with_smul lipschitzWith_smul
 

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

This has nice performance benefits.

@@ -19,7 +19,7 @@ deduce `const_mul` and `mul_const` results as an immediate corollary.
 -/
 
 
-variable {α β : Type _}
+variable {α β : Type*}
 
 section SeminormedAddGroup
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.normed.mul_action
-! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.MetricSpace.Algebra
 import Mathlib.Analysis.Normed.Field.Basic
 
+#align_import analysis.normed.mul_action from "leanprover-community/mathlib"@"bc91ed7093bf098d253401e69df601fc33dde156"
+
 /-!
 # Lemmas for `BoundedSMul` over normed additive groups
 

100 sample uses of the new tactic gcongr, added in #3965.

@@ -95,7 +95,7 @@ theorem norm_smul (r : α) (x : β) : ‖r • x‖ = ‖r‖ * ‖x‖ := by
   · refine' le_antisymm (norm_smul_le r x) _
     calc
       ‖r‖ * ‖x‖ = ‖r‖ * ‖r⁻¹ • r • x‖ := by rw [inv_smul_smul₀ h]
-      _ ≤ ‖r‖ * (‖r⁻¹‖ * ‖r • x‖) := (mul_le_mul_of_nonneg_left (norm_smul_le _ _) (norm_nonneg _))
+      _ ≤ ‖r‖ * (‖r⁻¹‖ * ‖r • x‖) := by gcongr; apply norm_smul_le
       _ = ‖r • x‖ := by rw [norm_inv, ← mul_assoc, mul_inv_cancel (mt norm_eq_zero.1 h), one_mul]
 #align norm_smul norm_smul
 

The actual forward-porting was done in #4327 and #4328

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed.mul_action
-! leanprover-community/mathlib commit ba5ff5ad5d120fb0ef094ad2994967e9bfaf5112
+! leanprover-community/mathlib commit bc91ed7093bf098d253401e69df601fc33dde156
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

Forward-port of leanprover-community/mathlib#18990

Original title: feat(analysis/normed_space/basic): scaling a set scales its diameter, translating it leaves it unchanged

@@ -50,6 +50,10 @@ theorem lipschitzWith_smul (s : α) : LipschitzWith ‖s‖₊ ((· • ·) s :
   lipschitzWith_iff_dist_le_mul.2 <| dist_smul_le _
 #align lipschitz_with_smul lipschitzWith_smul
 
+theorem edist_smul_le (s : α) (x y : β) : edist (s • x) (s • y) ≤ ‖s‖₊ • edist x y :=
+  lipschitzWith_smul s x y
+#align edist_smul_le edist_smul_le
+
 end SeminormedAddGroup
 
 /-- Left multiplication is bounded. -/
@@ -115,4 +119,8 @@ theorem nndist_smul₀ (s : α) (x y : β) : nndist (s • x) (s • y) = ‖s
   NNReal.eq <| dist_smul₀ s x y
 #align nndist_smul₀ nndist_smul₀
 
+theorem edist_smul₀ (s : α) (x y : β) : edist (s • x) (s • y) = ‖s‖₊ • edist x y := by
+  simp only [edist_nndist, nndist_smul₀, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]
+#align edist_smul₀ edist_smul₀
+
 end NormedDivisionRingModule

Both the new file and the other fixes are done in the same PR, since according to the description of leanprover-community/mathlib#19053 "this should be very easy to forward-port".