data.real.pointwise ⟷ Mathlib.Data.Real.Pointwise

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

@@ -95,7 +95,7 @@ theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csInf_singleton 0
   by_cases BddAbove s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_csSup' hs h).symm
+  · exact ((OrderIso.smulRightDual ℝ ha').map_csSup' hs h).symm
   ·
     rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
       Real.sSup_of_not_bddAbove h, smul_zero]
@@ -117,7 +117,7 @@ theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csSup_singleton 0
   by_cases BddBelow s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_csInf' hs h).symm
+  · exact ((OrderIso.smulRightDual ℝ ha').map_csInf' hs h).symm
   ·
     rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
       Real.sInf_of_not_bddBelow h, smul_zero]

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

@@ -45,7 +45,7 @@ theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csInf_singleton 0
   by_cases BddBelow s
-  · exact ((OrderIso.smulLeft ℝ ha').map_csInf' hs h).symm
+  · exact ((OrderIso.smulRight ℝ ha').map_csInf' hs h).symm
   ·
     rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
       Real.sInf_of_not_bddBelow h, smul_zero]
@@ -67,7 +67,7 @@ theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csSup_singleton 0
   by_cases BddAbove s
-  · exact ((OrderIso.smulLeft ℝ ha').map_csSup' hs h).symm
+  · exact ((OrderIso.smulRight ℝ ha').map_csSup' hs h).symm
   ·
     rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
       Real.sSup_of_not_bddAbove h, smul_zero]

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Wieser
 -/
-import Mathbin.Algebra.Order.Module
-import Mathbin.Data.Real.Basic
+import Algebra.Order.Module
+import Data.Real.Basic
 
 #align_import data.real.pointwise from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Wieser
-
-! This file was ported from Lean 3 source module data.real.pointwise
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Module
 import Mathbin.Data.Real.Basic
 
+#align_import data.real.pointwise from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
 /-!
 # Pointwise operations on sets of reals
 

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

@@ -39,6 +39,7 @@ section MulActionWithZero
 
 variable [MulActionWithZero α ℝ] [OrderedSMul α ℝ] {a : α}
 
+#print Real.sInf_smul_of_nonneg /-
 theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) = a • sInf s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -52,11 +53,15 @@ theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) =
     rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
       Real.sInf_of_not_bddBelow h, smul_zero]
 #align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonneg
+-/
 
+#print Real.smul_iInf_of_nonneg /-
 theorem Real.smul_iInf_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨅ i, a • f i :=
   (Real.sInf_smul_of_nonneg ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
 #align real.smul_infi_of_nonneg Real.smul_iInf_of_nonneg
+-/
 
+#print Real.sSup_smul_of_nonneg /-
 theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) = a • sSup s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -70,10 +75,13 @@ theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) =
     rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
       Real.sSup_of_not_bddAbove h, smul_zero]
 #align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonneg
+-/
 
+#print Real.smul_iSup_of_nonneg /-
 theorem Real.smul_iSup_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨆ i, a • f i :=
   (Real.sSup_smul_of_nonneg ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
 #align real.smul_supr_of_nonneg Real.smul_iSup_of_nonneg
+-/
 
 end MulActionWithZero
 
@@ -81,6 +89,7 @@ section Module
 
 variable [Module α ℝ] [OrderedSMul α ℝ] {a : α}
 
+#print Real.sInf_smul_of_nonpos /-
 theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) = a • sSup s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -94,11 +103,15 @@ theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) =
     rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
       Real.sSup_of_not_bddAbove h, smul_zero]
 #align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonpos
+-/
 
+#print Real.smul_iSup_of_nonpos /-
 theorem Real.smul_iSup_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨅ i, a • f i :=
   (Real.sInf_smul_of_nonpos ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
 #align real.smul_supr_of_nonpos Real.smul_iSup_of_nonpos
+-/
 
+#print Real.sSup_smul_of_nonpos /-
 theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) = a • sInf s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -112,10 +125,13 @@ theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) =
     rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
       Real.sInf_of_not_bddBelow h, smul_zero]
 #align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonpos
+-/
 
+#print Real.smul_iInf_of_nonpos /-
 theorem Real.smul_iInf_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨆ i, a • f i :=
   (Real.sSup_smul_of_nonpos ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
 #align real.smul_infi_of_nonpos Real.smul_iInf_of_nonpos
+-/
 
 end Module
 
@@ -126,37 +142,53 @@ section Mul
 
 variable {r : ℝ}
 
+#print Real.mul_iInf_of_nonneg /-
 theorem Real.mul_iInf_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨅ i, r * f i :=
   Real.smul_iInf_of_nonneg ha f
 #align real.mul_infi_of_nonneg Real.mul_iInf_of_nonneg
+-/
 
+#print Real.mul_iSup_of_nonneg /-
 theorem Real.mul_iSup_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨆ i, r * f i :=
   Real.smul_iSup_of_nonneg ha f
 #align real.mul_supr_of_nonneg Real.mul_iSup_of_nonneg
+-/
 
+#print Real.mul_iInf_of_nonpos /-
 theorem Real.mul_iInf_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨆ i, r * f i :=
   Real.smul_iInf_of_nonpos ha f
 #align real.mul_infi_of_nonpos Real.mul_iInf_of_nonpos
+-/
 
+#print Real.mul_iSup_of_nonpos /-
 theorem Real.mul_iSup_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨅ i, r * f i :=
   Real.smul_iSup_of_nonpos ha f
 #align real.mul_supr_of_nonpos Real.mul_iSup_of_nonpos
+-/
 
+#print Real.iInf_mul_of_nonneg /-
 theorem Real.iInf_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨅ i, f i) * r = ⨅ i, f i * r := by
   simp only [Real.mul_iInf_of_nonneg ha, mul_comm]
 #align real.infi_mul_of_nonneg Real.iInf_mul_of_nonneg
+-/
 
+#print Real.iSup_mul_of_nonneg /-
 theorem Real.iSup_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨆ i, f i) * r = ⨆ i, f i * r := by
   simp only [Real.mul_iSup_of_nonneg ha, mul_comm]
 #align real.supr_mul_of_nonneg Real.iSup_mul_of_nonneg
+-/
 
+#print Real.iInf_mul_of_nonpos /-
 theorem Real.iInf_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨅ i, f i) * r = ⨆ i, f i * r := by
   simp only [Real.mul_iInf_of_nonpos ha, mul_comm]
 #align real.infi_mul_of_nonpos Real.iInf_mul_of_nonpos
+-/
 
+#print Real.iSup_mul_of_nonpos /-
 theorem Real.iSup_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i) * r = ⨅ i, f i * r := by
   simp only [Real.mul_iSup_of_nonpos ha, mul_comm]
 #align real.supr_mul_of_nonpos Real.iSup_mul_of_nonpos
+-/
 
 end Mul
 

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

@@ -31,7 +31,7 @@ don't have those yet.
 
 open Set
 
-open Pointwise
+open scoped Pointwise
 
 variable {ι : Sort _} {α : Type _} [LinearOrderedField α]
 

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

@@ -39,12 +39,6 @@ section MulActionWithZero
 
 variable [MulActionWithZero α ℝ] [OrderedSMul α ℝ] {a : α}
 
-/- warning: real.Inf_smul_of_nonneg -> Real.sInf_smul_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (InfSet.sInf.{0} Real Real.hasInf s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (InfSet.sInf.{0} Real Real.instInfSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonnegₓ'. -/
 theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) = a • sInf s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -59,22 +53,10 @@ theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) =
       Real.sInf_of_not_bddBelow h, smul_zero]
 #align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonneg
 
-/- warning: real.smul_infi_of_nonneg -> Real.smul_iInf_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
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-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonneg Real.smul_iInf_of_nonnegₓ'. -/
 theorem Real.smul_iInf_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨅ i, a • f i :=
   (Real.sInf_smul_of_nonneg ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
 #align real.smul_infi_of_nonneg Real.smul_iInf_of_nonneg
 
-/- warning: real.Sup_smul_of_nonneg -> Real.sSup_smul_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (SupSet.sSup.{0} Real Real.hasSup s)))
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-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (SupSet.sSup.{0} Real Real.instSupSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonnegₓ'. -/
 theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) = a • sSup s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -89,12 +71,6 @@ theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) =
       Real.sSup_of_not_bddAbove h, smul_zero]
 #align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonneg
 
-/- warning: real.smul_supr_of_nonneg -> Real.smul_iSup_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
-but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonneg Real.smul_iSup_of_nonnegₓ'. -/
 theorem Real.smul_iSup_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨆ i, a • f i :=
   (Real.sSup_smul_of_nonneg ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
 #align real.smul_supr_of_nonneg Real.smul_iSup_of_nonneg
@@ -105,12 +81,6 @@ section Module
 
 variable [Module α ℝ] [OrderedSMul α ℝ] {a : α}
 
-/- warning: real.Inf_smul_of_nonpos -> Real.sInf_smul_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (SupSet.sSup.{0} Real Real.hasSup s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (SupSet.sSup.{0} Real Real.instSupSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonposₓ'. -/
 theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) = a • sSup s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -125,22 +95,10 @@ theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) =
       Real.sSup_of_not_bddAbove h, smul_zero]
 #align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonpos
 
-/- warning: real.smul_supr_of_nonpos -> Real.smul_iSup_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
-but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonpos Real.smul_iSup_of_nonposₓ'. -/
 theorem Real.smul_iSup_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨅ i, a • f i :=
   (Real.sInf_smul_of_nonpos ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
 #align real.smul_supr_of_nonpos Real.smul_iSup_of_nonpos
 
-/- warning: real.Sup_smul_of_nonpos -> Real.sSup_smul_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (InfSet.sInf.{0} Real Real.hasInf s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (InfSet.sInf.{0} Real Real.instInfSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonposₓ'. -/
 theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) = a • sInf s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
@@ -155,12 +113,6 @@ theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) =
       Real.sInf_of_not_bddBelow h, smul_zero]
 #align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonpos
 
-/- warning: real.smul_infi_of_nonpos -> Real.smul_iInf_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
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-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonpos Real.smul_iInf_of_nonposₓ'. -/
 theorem Real.smul_iInf_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨆ i, a • f i :=
   (Real.sSup_smul_of_nonpos ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
 #align real.smul_infi_of_nonpos Real.smul_iInf_of_nonpos
@@ -174,82 +126,34 @@ section Mul
 
 variable {r : ℝ}
 
-/- warning: real.mul_infi_of_nonneg -> Real.mul_iInf_of_nonneg is a dubious translation:
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_infi_of_nonneg Real.mul_iInf_of_nonnegₓ'. -/
 theorem Real.mul_iInf_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨅ i, r * f i :=
   Real.smul_iInf_of_nonneg ha f
 #align real.mul_infi_of_nonneg Real.mul_iInf_of_nonneg
 
-/- warning: real.mul_supr_of_nonneg -> Real.mul_iSup_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_supr_of_nonneg Real.mul_iSup_of_nonnegₓ'. -/
 theorem Real.mul_iSup_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨆ i, r * f i :=
   Real.smul_iSup_of_nonneg ha f
 #align real.mul_supr_of_nonneg Real.mul_iSup_of_nonneg
 
-/- warning: real.mul_infi_of_nonpos -> Real.mul_iInf_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_infi_of_nonpos Real.mul_iInf_of_nonposₓ'. -/
 theorem Real.mul_iInf_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨆ i, r * f i :=
   Real.smul_iInf_of_nonpos ha f
 #align real.mul_infi_of_nonpos Real.mul_iInf_of_nonpos
 
-/- warning: real.mul_supr_of_nonpos -> Real.mul_iSup_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_supr_of_nonpos Real.mul_iSup_of_nonposₓ'. -/
 theorem Real.mul_iSup_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨅ i, r * f i :=
   Real.smul_iSup_of_nonpos ha f
 #align real.mul_supr_of_nonpos Real.mul_iSup_of_nonpos
 
-/- warning: real.infi_mul_of_nonneg -> Real.iInf_mul_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.infi_mul_of_nonneg Real.iInf_mul_of_nonnegₓ'. -/
 theorem Real.iInf_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨅ i, f i) * r = ⨅ i, f i * r := by
   simp only [Real.mul_iInf_of_nonneg ha, mul_comm]
 #align real.infi_mul_of_nonneg Real.iInf_mul_of_nonneg
 
-/- warning: real.supr_mul_of_nonneg -> Real.iSup_mul_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
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-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.supr_mul_of_nonneg Real.iSup_mul_of_nonnegₓ'. -/
 theorem Real.iSup_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨆ i, f i) * r = ⨆ i, f i * r := by
   simp only [Real.mul_iSup_of_nonneg ha, mul_comm]
 #align real.supr_mul_of_nonneg Real.iSup_mul_of_nonneg
 
-/- warning: real.infi_mul_of_nonpos -> Real.iInf_mul_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
-but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.infi_mul_of_nonpos Real.iInf_mul_of_nonposₓ'. -/
 theorem Real.iInf_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨅ i, f i) * r = ⨆ i, f i * r := by
   simp only [Real.mul_iInf_of_nonpos ha, mul_comm]
 #align real.infi_mul_of_nonpos Real.iInf_mul_of_nonpos
 
-/- warning: real.supr_mul_of_nonpos -> Real.iSup_mul_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
-but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.supr_mul_of_nonpos Real.iSup_mul_of_nonposₓ'. -/
 theorem Real.iSup_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i) * r = ⨅ i, f i * r := by
   simp only [Real.mul_iSup_of_nonpos ha, mul_comm]
 #align real.supr_mul_of_nonpos Real.iSup_mul_of_nonpos

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

@@ -41,7 +41,7 @@ variable [MulActionWithZero α ℝ] [OrderedSMul α ℝ] {a : α}
 
 /- warning: real.Inf_smul_of_nonneg -> Real.sInf_smul_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (InfSet.sInf.{0} Real Real.hasInf s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (InfSet.sInf.{0} Real Real.hasInf s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (InfSet.sInf.{0} Real Real.instInfSetReal s)))
 Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonnegₓ'. -/
@@ -61,7 +61,7 @@ theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) =
 
 /- warning: real.smul_infi_of_nonneg -> Real.smul_iInf_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
 but is expected to have type
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
 Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonneg Real.smul_iInf_of_nonnegₓ'. -/
@@ -71,7 +71,7 @@ theorem Real.smul_iInf_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i,
 
 /- warning: real.Sup_smul_of_nonneg -> Real.sSup_smul_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (SupSet.sSup.{0} Real Real.hasSup s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (SupSet.sSup.{0} Real Real.hasSup s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (SupSet.sSup.{0} Real Real.instSupSetReal s)))
 Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonnegₓ'. -/
@@ -91,7 +91,7 @@ theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) =
 
 /- warning: real.smul_supr_of_nonneg -> Real.smul_iSup_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
 but is expected to have type
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
 Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonneg Real.smul_iSup_of_nonnegₓ'. -/
@@ -107,7 +107,7 @@ variable [Module α ℝ] [OrderedSMul α ℝ] {a : α}
 
 /- warning: real.Inf_smul_of_nonpos -> Real.sInf_smul_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (SupSet.sSup.{0} Real Real.hasSup s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (SupSet.sSup.{0} Real Real.hasSup s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (SupSet.sSup.{0} Real Real.instSupSetReal s)))
 Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonposₓ'. -/
@@ -127,7 +127,7 @@ theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) =
 
 /- warning: real.smul_supr_of_nonpos -> Real.smul_iSup_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
 but is expected to have type
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
 Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonpos Real.smul_iSup_of_nonposₓ'. -/
@@ -137,7 +137,7 @@ theorem Real.smul_iSup_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i,
 
 /- warning: real.Sup_smul_of_nonpos -> Real.sSup_smul_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (InfSet.sInf.{0} Real Real.hasInf s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (InfSet.sInf.{0} Real Real.hasInf s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (InfSet.sInf.{0} Real Real.instInfSetReal s)))
 Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonposₓ'. -/
@@ -157,7 +157,7 @@ theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) =
 
 /- warning: real.smul_infi_of_nonpos -> Real.smul_iInf_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
 but is expected to have type
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
 Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonpos Real.smul_iInf_of_nonposₓ'. -/

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

@@ -39,65 +39,65 @@ section MulActionWithZero
 
 variable [MulActionWithZero α ℝ] [OrderedSMul α ℝ] {a : α}
 
-/- warning: real.Inf_smul_of_nonneg -> Real.infₛ_smul_of_nonneg is a dubious translation:
+/- warning: real.Inf_smul_of_nonneg -> Real.sInf_smul_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.infₛ.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (InfSet.infₛ.{0} Real Real.hasInf s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (InfSet.sInf.{0} Real Real.hasInf s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.infₛ.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (InfSet.infₛ.{0} Real Real.instInfSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonneg Real.infₛ_smul_of_nonnegₓ'. -/
-theorem Real.infₛ_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : infₛ (a • s) = a • infₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (InfSet.sInf.{0} Real Real.instInfSetReal s)))
+Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonnegₓ'. -/
+theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) = a • sInf s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.infₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sInf_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact cinfₛ_singleton 0
+    exact csInf_singleton 0
   by_cases BddBelow s
-  · exact ((OrderIso.smulLeft ℝ ha').map_cinfₛ' hs h).symm
+  · exact ((OrderIso.smulLeft ℝ ha').map_csInf' hs h).symm
   ·
-    rw [Real.infₛ_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
-      Real.infₛ_of_not_bddBelow h, smul_zero]
-#align real.Inf_smul_of_nonneg Real.infₛ_smul_of_nonneg
+    rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
+      Real.sInf_of_not_bddBelow h, smul_zero]
+#align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonneg
 
-/- warning: real.smul_infi_of_nonneg -> Real.smul_infᵢ_of_nonneg is a dubious translation:
+/- warning: real.smul_infi_of_nonneg -> Real.smul_iInf_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonneg Real.smul_infᵢ_of_nonnegₓ'. -/
-theorem Real.smul_infᵢ_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨅ i, a • f i :=
-  (Real.infₛ_smul_of_nonneg ha _).symm.trans <| congr_arg infₛ <| (range_comp _ _).symm
-#align real.smul_infi_of_nonneg Real.smul_infᵢ_of_nonneg
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
+Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonneg Real.smul_iInf_of_nonnegₓ'. -/
+theorem Real.smul_iInf_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨅ i, a • f i :=
+  (Real.sInf_smul_of_nonneg ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
+#align real.smul_infi_of_nonneg Real.smul_iInf_of_nonneg
 
-/- warning: real.Sup_smul_of_nonneg -> Real.supₛ_smul_of_nonneg is a dubious translation:
+/- warning: real.Sup_smul_of_nonneg -> Real.sSup_smul_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.supₛ.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (SupSet.supₛ.{0} Real Real.hasSup s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2)))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) Real.hasZero _inst_2))) a (SupSet.sSup.{0} Real Real.hasSup s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.supₛ.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (SupSet.supₛ.{0} Real Real.instSupSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonneg Real.supₛ_smul_of_nonnegₓ'. -/
-theorem Real.supₛ_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : supₛ (a • s) = a • supₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : MulActionWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (SupSet.sSup.{0} Real Real.instSupSetReal s)))
+Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonnegₓ'. -/
+theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) = a • sSup s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.supₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sSup_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact csupₛ_singleton 0
+    exact csSup_singleton 0
   by_cases BddAbove s
-  · exact ((OrderIso.smulLeft ℝ ha').map_csupₛ' hs h).symm
+  · exact ((OrderIso.smulLeft ℝ ha').map_csSup' hs h).symm
   ·
-    rw [Real.supₛ_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
-      Real.supₛ_of_not_bddAbove h, smul_zero]
-#align real.Sup_smul_of_nonneg Real.supₛ_smul_of_nonneg
+    rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
+      Real.sSup_of_not_bddAbove h, smul_zero]
+#align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonneg
 
-/- warning: real.smul_supr_of_nonneg -> Real.smul_supᵢ_of_nonneg is a dubious translation:
+/- warning: real.smul_supr_of_nonneg -> Real.smul_iSup_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real Real.hasZero (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) Real.hasZero (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) Real.hasZero _inst_2))) a (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonneg Real.smul_supᵢ_of_nonnegₓ'. -/
-theorem Real.smul_supᵢ_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨆ i, a • f i :=
-  (Real.supₛ_smul_of_nonneg ha _).symm.trans <| congr_arg supₛ <| (range_comp _ _).symm
-#align real.smul_supr_of_nonneg Real.smul_supᵢ_of_nonneg
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : MulActionWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) _inst_2)] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))))) a) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal _inst_2)))) a (f i))))
+Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonneg Real.smul_iSup_of_nonnegₓ'. -/
+theorem Real.smul_iSup_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨆ i, a • f i :=
+  (Real.sSup_smul_of_nonneg ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
+#align real.smul_supr_of_nonneg Real.smul_iSup_of_nonneg
 
 end MulActionWithZero
 
@@ -105,65 +105,65 @@ section Module
 
 variable [Module α ℝ] [OrderedSMul α ℝ] {a : α}
 
-/- warning: real.Inf_smul_of_nonpos -> Real.infₛ_smul_of_nonpos is a dubious translation:
+/- warning: real.Inf_smul_of_nonpos -> Real.sInf_smul_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.infₛ.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (SupSet.supₛ.{0} Real Real.hasSup s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.hasInf (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (SupSet.sSup.{0} Real Real.hasSup s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.infₛ.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (SupSet.supₛ.{0} Real Real.instSupSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonpos Real.infₛ_smul_of_nonposₓ'. -/
-theorem Real.infₛ_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : infₛ (a • s) = a • supₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (InfSet.sInf.{0} Real Real.instInfSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (SupSet.sSup.{0} Real Real.instSupSetReal s)))
+Case conversion may be inaccurate. Consider using '#align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonposₓ'. -/
+theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) = a • sSup s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.infₛ_empty, Real.supₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sInf_empty, Real.sSup_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact cinfₛ_singleton 0
+    exact csInf_singleton 0
   by_cases BddAbove s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_csupₛ' hs h).symm
+  · exact ((OrderIso.smulLeftDual ℝ ha').map_csSup' hs h).symm
   ·
-    rw [Real.infₛ_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
-      Real.supₛ_of_not_bddAbove h, smul_zero]
-#align real.Inf_smul_of_nonpos Real.infₛ_smul_of_nonpos
+    rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
+      Real.sSup_of_not_bddAbove h, smul_zero]
+#align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonpos
 
-/- warning: real.smul_supr_of_nonpos -> Real.smul_supᵢ_of_nonpos is a dubious translation:
+/- warning: real.smul_supr_of_nonpos -> Real.smul_iSup_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonpos Real.smul_supᵢ_of_nonposₓ'. -/
-theorem Real.smul_supᵢ_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨅ i, a • f i :=
-  (Real.infₛ_smul_of_nonpos ha _).symm.trans <| congr_arg infₛ <| (range_comp _ _).symm
-#align real.smul_supr_of_nonpos Real.smul_supᵢ_of_nonpos
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
+Case conversion may be inaccurate. Consider using '#align real.smul_supr_of_nonpos Real.smul_iSup_of_nonposₓ'. -/
+theorem Real.smul_iSup_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨅ i, a • f i :=
+  (Real.sInf_smul_of_nonpos ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
+#align real.smul_supr_of_nonpos Real.smul_iSup_of_nonpos
 
-/- warning: real.Sup_smul_of_nonpos -> Real.supₛ_smul_of_nonpos is a dubious translation:
+/- warning: real.Sup_smul_of_nonpos -> Real.sSup_smul_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.supₛ.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (InfSet.infₛ.{0} Real Real.hasInf s)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u1, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.hasSup (SMul.smul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2))))) a s)) (SMul.smul.{u1, 0} α Real (SMulZeroClass.toHasSmul.{u1, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u1, 0} α Real (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (Ring.toSemiring.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (InfSet.sInf.{0} Real Real.hasInf s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.supₛ.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (InfSet.infₛ.{0} Real Real.instInfSetReal s)))
-Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonpos Real.supₛ_smul_of_nonposₓ'. -/
-theorem Real.supₛ_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : supₛ (a • s) = a • infₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : Module.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u1, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (forall (s : Set.{0} Real), Eq.{1} Real (SupSet.sSup.{0} Real Real.instSupSetReal (HSMul.hSMul.{u1, 0, 0} α (Set.{0} Real) (Set.{0} Real) (instHSMul.{u1, 0} α (Set.{0} Real) (Set.smulSet.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2)))))) a s)) (HSMul.hSMul.{u1, 0, 0} α Real Real (instHSMul.{u1, 0} α Real (SMulZeroClass.toSMul.{u1, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u1, 0} α Real (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u1, 0} α Real (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u1, 0} α Real (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (InfSet.sInf.{0} Real Real.instInfSetReal s)))
+Case conversion may be inaccurate. Consider using '#align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonposₓ'. -/
+theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) = a • sInf s :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.supₛ_empty, Real.infₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sSup_empty, Real.sInf_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact csupₛ_singleton 0
+    exact csSup_singleton 0
   by_cases BddBelow s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_cinfₛ' hs h).symm
+  · exact ((OrderIso.smulLeftDual ℝ ha').map_csInf' hs h).symm
   ·
-    rw [Real.supₛ_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
-      Real.infₛ_of_not_bddBelow h, smul_zero]
-#align real.Sup_smul_of_nonpos Real.supₛ_smul_of_nonpos
+    rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
+      Real.sInf_of_not_bddBelow h, smul_zero]
+#align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonpos
 
-/- warning: real.smul_infi_of_nonpos -> Real.smul_infᵢ_of_nonpos is a dubious translation:
+/- warning: real.smul_infi_of_nonpos -> Real.smul_iInf_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid] [_inst_3 : OrderedSMul.{u2, 0} α Real (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid)))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) a (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))))))) -> (forall (f : ι -> Real), Eq.{1} Real (SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => SMul.smul.{u2, 0} α Real (SMulZeroClass.toHasSmul.{u2, 0} α Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (SMulWithZero.toSmulZeroClass.{u2, 0} α Real (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real Real.addCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (Ring.toSemiring.{u2} α (DivisionRing.toRing.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1)))) Real.addCommMonoid _inst_2)))) a (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonpos Real.smul_infᵢ_of_nonposₓ'. -/
-theorem Real.smul_infᵢ_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨆ i, a • f i :=
-  (Real.supₛ_smul_of_nonpos ha _).symm.trans <| congr_arg supₛ <| (range_comp _ _).symm
-#align real.smul_infi_of_nonpos Real.smul_infᵢ_of_nonpos
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] [_inst_2 : Module.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal] [_inst_3 : OrderedSMul.{u2, 0} α Real (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.orderedAddCommMonoid (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (AddMonoid.toZero.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (OrderedAddCommMonoid.toAddCommMonoid.{0} Real Real.orderedAddCommMonoid))) (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))] {a : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))))) -> (forall (f : ι -> Real), Eq.{1} Real (HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HSMul.hSMul.{u2, 0, 0} α Real Real (instHSMul.{u2, 0} α Real (SMulZeroClass.toSMul.{u2, 0} α Real Real.instZeroReal (SMulWithZero.toSMulZeroClass.{u2, 0} α Real (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instZeroReal (MulActionWithZero.toSMulWithZero.{u2, 0} α Real (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) Real.instZeroReal (Module.toMulActionWithZero.{u2, 0} α Real (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) Real.instAddCommMonoidReal _inst_2))))) a (f i))))
+Case conversion may be inaccurate. Consider using '#align real.smul_infi_of_nonpos Real.smul_iInf_of_nonposₓ'. -/
+theorem Real.smul_iInf_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨆ i, a • f i :=
+  (Real.sSup_smul_of_nonpos ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
+#align real.smul_infi_of_nonpos Real.smul_iInf_of_nonpos
 
 end Module
 
@@ -174,85 +174,85 @@ section Mul
 
 variable {r : ℝ}
 
-/- warning: real.mul_infi_of_nonneg -> Real.mul_infᵢ_of_nonneg is a dubious translation:
+/- warning: real.mul_infi_of_nonneg -> Real.mul_iInf_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_infi_of_nonneg Real.mul_infᵢ_of_nonnegₓ'. -/
-theorem Real.mul_infᵢ_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨅ i, r * f i :=
-  Real.smul_infᵢ_of_nonneg ha f
-#align real.mul_infi_of_nonneg Real.mul_infᵢ_of_nonneg
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
+Case conversion may be inaccurate. Consider using '#align real.mul_infi_of_nonneg Real.mul_iInf_of_nonnegₓ'. -/
+theorem Real.mul_iInf_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨅ i, r * f i :=
+  Real.smul_iInf_of_nonneg ha f
+#align real.mul_infi_of_nonneg Real.mul_iInf_of_nonneg
 
-/- warning: real.mul_supr_of_nonneg -> Real.mul_supᵢ_of_nonneg is a dubious translation:
+/- warning: real.mul_supr_of_nonneg -> Real.mul_iSup_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_supr_of_nonneg Real.mul_supᵢ_of_nonnegₓ'. -/
-theorem Real.mul_supᵢ_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨆ i, r * f i :=
-  Real.smul_supᵢ_of_nonneg ha f
-#align real.mul_supr_of_nonneg Real.mul_supᵢ_of_nonneg
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
+Case conversion may be inaccurate. Consider using '#align real.mul_supr_of_nonneg Real.mul_iSup_of_nonnegₓ'. -/
+theorem Real.mul_iSup_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨆ i, r * f i :=
+  Real.smul_iSup_of_nonneg ha f
+#align real.mul_supr_of_nonneg Real.mul_iSup_of_nonneg
 
-/- warning: real.mul_infi_of_nonpos -> Real.mul_infᵢ_of_nonpos is a dubious translation:
+/- warning: real.mul_infi_of_nonpos -> Real.mul_iInf_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_infi_of_nonpos Real.mul_infᵢ_of_nonposₓ'. -/
-theorem Real.mul_infᵢ_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨆ i, r * f i :=
-  Real.smul_infᵢ_of_nonpos ha f
-#align real.mul_infi_of_nonpos Real.mul_infᵢ_of_nonpos
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
+Case conversion may be inaccurate. Consider using '#align real.mul_infi_of_nonpos Real.mul_iInf_of_nonposₓ'. -/
+theorem Real.mul_iInf_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨆ i, r * f i :=
+  Real.smul_iInf_of_nonpos ha f
+#align real.mul_infi_of_nonpos Real.mul_iInf_of_nonpos
 
-/- warning: real.mul_supr_of_nonpos -> Real.mul_supᵢ_of_nonpos is a dubious translation:
+/- warning: real.mul_supr_of_nonpos -> Real.mul_iSup_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (f i))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
-Case conversion may be inaccurate. Consider using '#align real.mul_supr_of_nonpos Real.mul_supᵢ_of_nonposₓ'. -/
-theorem Real.mul_supᵢ_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨅ i, r * f i :=
-  Real.smul_supᵢ_of_nonpos ha f
-#align real.mul_supr_of_nonpos Real.mul_supᵢ_of_nonpos
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (f i))))
+Case conversion may be inaccurate. Consider using '#align real.mul_supr_of_nonpos Real.mul_iSup_of_nonposₓ'. -/
+theorem Real.mul_iSup_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨅ i, r * f i :=
+  Real.smul_iSup_of_nonpos ha f
+#align real.mul_supr_of_nonpos Real.mul_iSup_of_nonpos
 
-/- warning: real.infi_mul_of_nonneg -> Real.infᵢ_mul_of_nonneg is a dubious translation:
+/- warning: real.infi_mul_of_nonneg -> Real.iInf_mul_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i)) r) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i)) r) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.infi_mul_of_nonneg Real.infᵢ_mul_of_nonnegₓ'. -/
-theorem Real.infᵢ_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨅ i, f i) * r = ⨅ i, f i * r := by
-  simp only [Real.mul_infᵢ_of_nonneg ha, mul_comm]
-#align real.infi_mul_of_nonneg Real.infᵢ_mul_of_nonneg
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
+Case conversion may be inaccurate. Consider using '#align real.infi_mul_of_nonneg Real.iInf_mul_of_nonnegₓ'. -/
+theorem Real.iInf_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨅ i, f i) * r = ⨅ i, f i * r := by
+  simp only [Real.mul_iInf_of_nonneg ha, mul_comm]
+#align real.infi_mul_of_nonneg Real.iInf_mul_of_nonneg
 
-/- warning: real.supr_mul_of_nonneg -> Real.supᵢ_mul_of_nonneg is a dubious translation:
+/- warning: real.supr_mul_of_nonneg -> Real.iSup_mul_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i)) r) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i)) r) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.supr_mul_of_nonneg Real.supᵢ_mul_of_nonnegₓ'. -/
-theorem Real.supᵢ_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨆ i, f i) * r = ⨆ i, f i * r := by
-  simp only [Real.mul_supᵢ_of_nonneg ha, mul_comm]
-#align real.supr_mul_of_nonneg Real.supᵢ_mul_of_nonneg
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
+Case conversion may be inaccurate. Consider using '#align real.supr_mul_of_nonneg Real.iSup_mul_of_nonnegₓ'. -/
+theorem Real.iSup_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨆ i, f i) * r = ⨆ i, f i * r := by
+  simp only [Real.mul_iSup_of_nonneg ha, mul_comm]
+#align real.supr_mul_of_nonneg Real.iSup_mul_of_nonneg
 
-/- warning: real.infi_mul_of_nonpos -> Real.infᵢ_mul_of_nonpos is a dubious translation:
+/- warning: real.infi_mul_of_nonpos -> Real.iInf_mul_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i)) r) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i)) r) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.infi_mul_of_nonpos Real.infᵢ_mul_of_nonposₓ'. -/
-theorem Real.infᵢ_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨅ i, f i) * r = ⨆ i, f i * r := by
-  simp only [Real.mul_infᵢ_of_nonpos ha, mul_comm]
-#align real.infi_mul_of_nonpos Real.infᵢ_mul_of_nonpos
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => f i)) r) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
+Case conversion may be inaccurate. Consider using '#align real.infi_mul_of_nonpos Real.iInf_mul_of_nonposₓ'. -/
+theorem Real.iInf_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨅ i, f i) * r = ⨆ i, f i * r := by
+  simp only [Real.mul_iInf_of_nonpos ha, mul_comm]
+#align real.infi_mul_of_nonpos Real.iInf_mul_of_nonpos
 
-/- warning: real.supr_mul_of_nonpos -> Real.supᵢ_mul_of_nonpos is a dubious translation:
+/- warning: real.supr_mul_of_nonpos -> Real.iSup_mul_of_nonpos is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i)) r) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) r)))
 but is expected to have type
-  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i)) r) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
-Case conversion may be inaccurate. Consider using '#align real.supr_mul_of_nonpos Real.supᵢ_mul_of_nonposₓ'. -/
-theorem Real.supᵢ_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i) * r = ⨅ i, f i * r := by
-  simp only [Real.mul_supᵢ_of_nonpos ha, mul_comm]
-#align real.supr_mul_of_nonpos Real.supᵢ_mul_of_nonpos
+  forall {ι : Sort.{u1}} {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (f : ι -> Real), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => f i)) r) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) r)))
+Case conversion may be inaccurate. Consider using '#align real.supr_mul_of_nonpos Real.iSup_mul_of_nonposₓ'. -/
+theorem Real.iSup_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i) * r = ⨅ i, f i * r := by
+  simp only [Real.mul_iSup_of_nonpos ha, mul_comm]
+#align real.supr_mul_of_nonpos Real.iSup_mul_of_nonpos
 
 end Mul
 

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

Fix the names of the lemmas moved in #9241 to match the naming convention.

@@ -79,7 +79,7 @@ theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csInf_singleton 0
   by_cases h : BddAbove s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_csSup' hs h).symm
+  · exact ((OrderIso.smulRightDual ℝ ha').map_csSup' hs h).symm
   · rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
         Real.sSup_of_not_bddAbove h, smul_zero]
 #align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonpos
@@ -95,7 +95,7 @@ theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csSup_singleton 0
   by_cases h : BddBelow s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_csInf' hs h).symm
+  · exact ((OrderIso.smulRightDual ℝ ha').map_csInf' hs h).symm
   · rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
         Real.sInf_of_not_bddBelow h, smul_zero]
 #align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonpos

Sort the lemmas in Algebra.Order.Module into Algebra.Order.Module.Defs and Algebra.Order.Module.Pointwise. Generalise them.

A later PR will rename the lemmas to better match the naming convention.

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Wieser
 -/
-import Mathlib.Algebra.Order.Module
+import Mathlib.Algebra.Order.Module.OrderedSMul
 import Mathlib.Algebra.Order.Module.Pointwise
 import Mathlib.Data.Real.Archimedean
 

Remove the duplicates introduced in #8869 by sorting the lemmas in Algebra.Order.SMul into three files:

• Algebra.Order.Module.Defs for the order isomorphism induced by scalar multiplication by a positivity element
• Algebra.Order.Module.Pointwise for the order properties of scalar multiplication of sets. This file is new. I credit myself for https://github.com/leanprover-community/mathlib/pull/9078
• Algebra.Order.Module.OrderedSMul: The material about OrderedSMul per se. Inherits the copyright header from Algebra.Order.SMul. This file should eventually be deleted.

I move each #align to the correct file. On top of that, I delete unused redundant OrderedSMul instances (they were useful in Lean 3, but not anymore) and eq_of_smul_eq_smul_of_pos_of_le/eq_of_smul_eq_smul_of_neg_of_le since those lemmas are weird and unused.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Wieser
 -/
 import Mathlib.Algebra.Order.Module
+import Mathlib.Algebra.Order.Module.Pointwise
 import Mathlib.Data.Real.Archimedean
 
 #align_import data.real.pointwise from "leanprover-community/mathlib"@"dde670c9a3f503647fd5bfdf1037bad526d3397a"
@@ -40,7 +41,7 @@ theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csInf_singleton 0
   by_cases h : BddBelow s
-  · exact ((OrderIso.smulLeft ℝ ha').map_csInf' hs h).symm
+  · exact ((OrderIso.smulRight ha').map_csInf' hs h).symm
   · rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
         Real.sInf_of_not_bddBelow h, smul_zero]
 #align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonneg
@@ -56,7 +57,7 @@ theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) =
   · rw [zero_smul_set hs, zero_smul]
     exact csSup_singleton 0
   by_cases h : BddAbove s
-  · exact ((OrderIso.smulLeft ℝ ha').map_csSup' hs h).symm
+  · exact ((OrderIso.smulRight ha').map_csSup' hs h).symm
   · rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
         Real.sSup_of_not_bddAbove h, smul_zero]
 #align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonneg

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Wieser
 -/
 import Mathlib.Algebra.Order.Module
-import Mathlib.Data.Real.Basic
+import Mathlib.Data.Real.Archimedean
 
 #align_import data.real.pointwise from "leanprover-community/mathlib"@"dde670c9a3f503647fd5bfdf1037bad526d3397a"
 

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

This has nice performance benefits.

@@ -27,7 +27,7 @@ open Set
 
 open Pointwise
 
-variable {ι : Sort _} {α : Type _} [LinearOrderedField α]
+variable {ι : Sort*} {α : Type*} [LinearOrderedField α]
 
 section MulActionWithZero
 

• 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) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Wieser
-
-! This file was ported from Lean 3 source module data.real.pointwise
-! leanprover-community/mathlib commit dde670c9a3f503647fd5bfdf1037bad526d3397a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Order.Module
 import Mathlib.Data.Real.Basic
 
+#align_import data.real.pointwise from "leanprover-community/mathlib"@"dde670c9a3f503647fd5bfdf1037bad526d3397a"
+
 /-!
 # Pointwise operations on sets of reals
 

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -14,7 +14,7 @@ import Mathlib.Data.Real.Basic
 /-!
 # Pointwise operations on sets of reals
 
-This file relates `infₛ (a • s)`/`supₛ (a • s)` with `a • infₛ s`/`a • supₛ s` for `s : Set ℝ`.
+This file relates `sInf (a • s)`/`sSup (a • s)` with `a • sInf s`/`a • sSup s` for `s : Set ℝ`.
 
 From these, it relates `⨅ i, a • f i` / `⨆ i, a • f i` with `a • (⨅ i, f i)` / `a • (⨆ i, f i)`,
 and provides lemmas about distributing `*` over `⨅` and `⨆`.
@@ -36,37 +36,37 @@ section MulActionWithZero
 
 variable [MulActionWithZero α ℝ] [OrderedSMul α ℝ] {a : α}
 
-theorem Real.infₛ_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : infₛ (a • s) = a • infₛ s := by
+theorem Real.sInf_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sInf (a • s) = a • sInf s := by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.infₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sInf_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact cinfₛ_singleton 0
+    exact csInf_singleton 0
   by_cases h : BddBelow s
-  · exact ((OrderIso.smulLeft ℝ ha').map_cinfₛ' hs h).symm
-  · rw [Real.infₛ_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
-        Real.infₛ_of_not_bddBelow h, smul_zero]
-#align real.Inf_smul_of_nonneg Real.infₛ_smul_of_nonneg
+  · exact ((OrderIso.smulLeft ℝ ha').map_csInf' hs h).symm
+  · rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
+        Real.sInf_of_not_bddBelow h, smul_zero]
+#align real.Inf_smul_of_nonneg Real.sInf_smul_of_nonneg
 
-theorem Real.smul_infᵢ_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨅ i, a • f i :=
-  (Real.infₛ_smul_of_nonneg ha _).symm.trans <| congr_arg infₛ <| (range_comp _ _).symm
-#align real.smul_infi_of_nonneg Real.smul_infᵢ_of_nonneg
+theorem Real.smul_iInf_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨅ i, a • f i :=
+  (Real.sInf_smul_of_nonneg ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
+#align real.smul_infi_of_nonneg Real.smul_iInf_of_nonneg
 
-theorem Real.supₛ_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : supₛ (a • s) = a • supₛ s := by
+theorem Real.sSup_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : sSup (a • s) = a • sSup s := by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.supₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sSup_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact csupₛ_singleton 0
+    exact csSup_singleton 0
   by_cases h : BddAbove s
-  · exact ((OrderIso.smulLeft ℝ ha').map_csupₛ' hs h).symm
-  · rw [Real.supₛ_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
-        Real.supₛ_of_not_bddAbove h, smul_zero]
-#align real.Sup_smul_of_nonneg Real.supₛ_smul_of_nonneg
+  · exact ((OrderIso.smulLeft ℝ ha').map_csSup' hs h).symm
+  · rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
+        Real.sSup_of_not_bddAbove h, smul_zero]
+#align real.Sup_smul_of_nonneg Real.sSup_smul_of_nonneg
 
-theorem Real.smul_supᵢ_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨆ i, a • f i :=
-  (Real.supₛ_smul_of_nonneg ha _).symm.trans <| congr_arg supₛ <| (range_comp _ _).symm
-#align real.smul_supr_of_nonneg Real.smul_supᵢ_of_nonneg
+theorem Real.smul_iSup_of_nonneg (ha : 0 ≤ a) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨆ i, a • f i :=
+  (Real.sSup_smul_of_nonneg ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
+#align real.smul_supr_of_nonneg Real.smul_iSup_of_nonneg
 
 end MulActionWithZero
 
@@ -74,37 +74,37 @@ section Module
 
 variable [Module α ℝ] [OrderedSMul α ℝ] {a : α}
 
-theorem Real.infₛ_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : infₛ (a • s) = a • supₛ s := by
+theorem Real.sInf_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sInf (a • s) = a • sSup s := by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.infₛ_empty, Real.supₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sInf_empty, Real.sSup_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact cinfₛ_singleton 0
+    exact csInf_singleton 0
   by_cases h : BddAbove s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_csupₛ' hs h).symm
-  · rw [Real.infₛ_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
-        Real.supₛ_of_not_bddAbove h, smul_zero]
-#align real.Inf_smul_of_nonpos Real.infₛ_smul_of_nonpos
+  · exact ((OrderIso.smulLeftDual ℝ ha').map_csSup' hs h).symm
+  · rw [Real.sInf_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
+        Real.sSup_of_not_bddAbove h, smul_zero]
+#align real.Inf_smul_of_nonpos Real.sInf_smul_of_nonpos
 
-theorem Real.smul_supᵢ_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨅ i, a • f i :=
-  (Real.infₛ_smul_of_nonpos ha _).symm.trans <| congr_arg infₛ <| (range_comp _ _).symm
-#align real.smul_supr_of_nonpos Real.smul_supᵢ_of_nonpos
+theorem Real.smul_iSup_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨆ i, f i) = ⨅ i, a • f i :=
+  (Real.sInf_smul_of_nonpos ha _).symm.trans <| congr_arg sInf <| (range_comp _ _).symm
+#align real.smul_supr_of_nonpos Real.smul_iSup_of_nonpos
 
-theorem Real.supₛ_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : supₛ (a • s) = a • infₛ s := by
+theorem Real.sSup_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : sSup (a • s) = a • sInf s := by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  · rw [smul_set_empty, Real.supₛ_empty, Real.infₛ_empty, smul_zero]
+  · rw [smul_set_empty, Real.sSup_empty, Real.sInf_empty, smul_zero]
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
-    exact csupₛ_singleton 0
+    exact csSup_singleton 0
   by_cases h : BddBelow s
-  · exact ((OrderIso.smulLeftDual ℝ ha').map_cinfₛ' hs h).symm
-  · rw [Real.supₛ_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
-        Real.infₛ_of_not_bddBelow h, smul_zero]
-#align real.Sup_smul_of_nonpos Real.supₛ_smul_of_nonpos
+  · exact ((OrderIso.smulLeftDual ℝ ha').map_csInf' hs h).symm
+  · rw [Real.sSup_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
+        Real.sInf_of_not_bddBelow h, smul_zero]
+#align real.Sup_smul_of_nonpos Real.sSup_smul_of_nonpos
 
-theorem Real.smul_infᵢ_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨆ i, a • f i :=
-  (Real.supₛ_smul_of_nonpos ha _).symm.trans <| congr_arg supₛ <| (range_comp _ _).symm
-#align real.smul_infi_of_nonpos Real.smul_infᵢ_of_nonpos
+theorem Real.smul_iInf_of_nonpos (ha : a ≤ 0) (f : ι → ℝ) : (a • ⨅ i, f i) = ⨆ i, a • f i :=
+  (Real.sSup_smul_of_nonpos ha _).symm.trans <| congr_arg sSup <| (range_comp _ _).symm
+#align real.smul_infi_of_nonpos Real.smul_iInf_of_nonpos
 
 end Module
 
@@ -115,36 +115,36 @@ section Mul
 
 variable {r : ℝ}
 
-theorem Real.mul_infᵢ_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨅ i, r * f i :=
-  Real.smul_infᵢ_of_nonneg ha f
-#align real.mul_infi_of_nonneg Real.mul_infᵢ_of_nonneg
+theorem Real.mul_iInf_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨅ i, r * f i :=
+  Real.smul_iInf_of_nonneg ha f
+#align real.mul_infi_of_nonneg Real.mul_iInf_of_nonneg
 
-theorem Real.mul_supᵢ_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨆ i, r * f i :=
-  Real.smul_supᵢ_of_nonneg ha f
-#align real.mul_supr_of_nonneg Real.mul_supᵢ_of_nonneg
+theorem Real.mul_iSup_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨆ i, r * f i :=
+  Real.smul_iSup_of_nonneg ha f
+#align real.mul_supr_of_nonneg Real.mul_iSup_of_nonneg
 
-theorem Real.mul_infᵢ_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨆ i, r * f i :=
-  Real.smul_infᵢ_of_nonpos ha f
-#align real.mul_infi_of_nonpos Real.mul_infᵢ_of_nonpos
+theorem Real.mul_iInf_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨅ i, f i) = ⨆ i, r * f i :=
+  Real.smul_iInf_of_nonpos ha f
+#align real.mul_infi_of_nonpos Real.mul_iInf_of_nonpos
 
-theorem Real.mul_supᵢ_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨅ i, r * f i :=
-  Real.smul_supᵢ_of_nonpos ha f
-#align real.mul_supr_of_nonpos Real.mul_supᵢ_of_nonpos
+theorem Real.mul_iSup_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (r * ⨆ i, f i) = ⨅ i, r * f i :=
+  Real.smul_iSup_of_nonpos ha f
+#align real.mul_supr_of_nonpos Real.mul_iSup_of_nonpos
 
-theorem Real.infᵢ_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨅ i, f i) * r = ⨅ i, f i * r := by
-  simp only [Real.mul_infᵢ_of_nonneg ha, mul_comm]
-#align real.infi_mul_of_nonneg Real.infᵢ_mul_of_nonneg
+theorem Real.iInf_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨅ i, f i) * r = ⨅ i, f i * r := by
+  simp only [Real.mul_iInf_of_nonneg ha, mul_comm]
+#align real.infi_mul_of_nonneg Real.iInf_mul_of_nonneg
 
-theorem Real.supᵢ_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨆ i, f i) * r = ⨆ i, f i * r := by
-  simp only [Real.mul_supᵢ_of_nonneg ha, mul_comm]
-#align real.supr_mul_of_nonneg Real.supᵢ_mul_of_nonneg
+theorem Real.iSup_mul_of_nonneg (ha : 0 ≤ r) (f : ι → ℝ) : (⨆ i, f i) * r = ⨆ i, f i * r := by
+  simp only [Real.mul_iSup_of_nonneg ha, mul_comm]
+#align real.supr_mul_of_nonneg Real.iSup_mul_of_nonneg
 
-theorem Real.infᵢ_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨅ i, f i) * r = ⨆ i, f i * r := by
-  simp only [Real.mul_infᵢ_of_nonpos ha, mul_comm]
-#align real.infi_mul_of_nonpos Real.infᵢ_mul_of_nonpos
+theorem Real.iInf_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨅ i, f i) * r = ⨆ i, f i * r := by
+  simp only [Real.mul_iInf_of_nonpos ha, mul_comm]
+#align real.infi_mul_of_nonpos Real.iInf_mul_of_nonpos
 
-theorem Real.supᵢ_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i) * r = ⨅ i, f i * r := by
-  simp only [Real.mul_supᵢ_of_nonpos ha, mul_comm]
-#align real.supr_mul_of_nonpos Real.supᵢ_mul_of_nonpos
+theorem Real.iSup_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i) * r = ⨅ i, f i * r := by
+  simp only [Real.mul_iSup_of_nonpos ha, mul_comm]
+#align real.supr_mul_of_nonpos Real.iSup_mul_of_nonpos
 
 end Mul

@@ -14,7 +14,7 @@ import Mathlib.Data.Real.Basic
 /-!
 # Pointwise operations on sets of reals
 
-This file relates `Inf (a • s)`/`Sup (a • s)` with `a • Inf s`/`a • Sup s` for `s : Set ℝ`.
+This file relates `infₛ (a • s)`/`supₛ (a • s)` with `a • infₛ s`/`a • supₛ s` for `s : Set ℝ`.
 
 From these, it relates `⨅ i, a • f i` / `⨆ i, a • f i` with `a • (⨅ i, f i)` / `a • (⨆ i, f i)`,
 and provides lemmas about distributing `*` over `⨅` and `⨆`.

@@ -42,7 +42,7 @@ theorem Real.infₛ_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : infₛ (a •
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
     exact cinfₛ_singleton 0
-  by_cases BddBelow s
+  by_cases h : BddBelow s
   · exact ((OrderIso.smulLeft ℝ ha').map_cinfₛ' hs h).symm
   · rw [Real.infₛ_of_not_bddBelow (mt (bddBelow_smul_iff_of_pos ha').1 h),
         Real.infₛ_of_not_bddBelow h, smul_zero]
@@ -58,7 +58,7 @@ theorem Real.supₛ_smul_of_nonneg (ha : 0 ≤ a) (s : Set ℝ) : supₛ (a •
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
     exact csupₛ_singleton 0
-  by_cases BddAbove s
+  by_cases h : BddAbove s
   · exact ((OrderIso.smulLeft ℝ ha').map_csupₛ' hs h).symm
   · rw [Real.supₛ_of_not_bddAbove (mt (bddAbove_smul_iff_of_pos ha').1 h),
         Real.supₛ_of_not_bddAbove h, smul_zero]
@@ -80,7 +80,7 @@ theorem Real.infₛ_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : infₛ (a •
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
     exact cinfₛ_singleton 0
-  by_cases BddAbove s
+  by_cases h : BddAbove s
   · exact ((OrderIso.smulLeftDual ℝ ha').map_csupₛ' hs h).symm
   · rw [Real.infₛ_of_not_bddBelow (mt (bddBelow_smul_iff_of_neg ha').1 h),
         Real.supₛ_of_not_bddAbove h, smul_zero]
@@ -96,7 +96,7 @@ theorem Real.supₛ_smul_of_nonpos (ha : a ≤ 0) (s : Set ℝ) : supₛ (a •
   obtain rfl | ha' := ha.eq_or_lt
   · rw [zero_smul_set hs, zero_smul]
     exact csupₛ_singleton 0
-  by_cases BddBelow s
+  by_cases h : BddBelow s
   · exact ((OrderIso.smulLeftDual ℝ ha').map_cinfₛ' hs h).symm
   · rw [Real.supₛ_of_not_bddAbove (mt (bddAbove_smul_iff_of_neg ha').1 h),
         Real.infₛ_of_not_bddBelow h, smul_zero]
@@ -148,4 +148,3 @@ theorem Real.supᵢ_mul_of_nonpos (ha : r ≤ 0) (f : ι → ℝ) : (⨆ i, f i)
 #align real.supr_mul_of_nonpos Real.supᵢ_mul_of_nonpos
 
 end Mul
-

Comments and stylish changes only.