algebra.order.chebyshev ⟷ Mathlib.Algebra.Order.Chebyshev

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

@@ -3,7 +3,7 @@ Copyright (c) 2023 Mantas Bakšys, Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
 -/
-import Algebra.BigOperators.Order
+import Algebra.Order.BigOperators.Group.Finset
 import Algebra.Order.Rearrangement
 import GroupTheory.Perm.Cycle.Basic
 

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

@@ -174,7 +174,7 @@ theorem sum_div_card_sq_le_sum_sq_div_card :
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
   · simp
-  rw [← card_pos, ← @Nat.cast_pos α] at hs 
+  rw [← card_pos, ← @Nat.cast_pos α] at hs
   rw [div_pow, div_le_div_iff (sq_pos_of_ne_zero _ hs.ne') hs, sq (s.card : α), mul_left_comm, ←
     mul_assoc]
   exact mul_le_mul_of_nonneg_right sq_sum_le_card_mul_sum_sq hs.le

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

@@ -59,7 +59,13 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
 theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
-    (∑ i in s, f i) • ∑ i in s, g i ≤ s.card • ∑ i in s, f i • g i := by classical
+    (∑ i in s, f i) • ∑ i in s, g i ≤ s.card • ∑ i in s, f i • g i := by
+  classical
+  obtain ⟨σ, hσ, hs⟩ := s.countable_to_set.exists_cycle_on
+  rw [← card_range s.card, sum_smul_sum_eq_sum_perm hσ]
+  exact
+    sum_le_card_nsmul _ _ _ fun n _ =>
+      hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
 -/
 

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

@@ -59,13 +59,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
 theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
-    (∑ i in s, f i) • ∑ i in s, g i ≤ s.card • ∑ i in s, f i • g i := by
-  classical
-  obtain ⟨σ, hσ, hs⟩ := s.countable_to_set.exists_cycle_on
-  rw [← card_range s.card, sum_smul_sum_eq_sum_perm hσ]
-  exact
-    sum_le_card_nsmul _ _ _ fun n _ =>
-      hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
+    (∑ i in s, f i) • ∑ i in s, g i ≤ s.card • ∑ i in s, f i • g i := by classical
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2023 Mantas Bakšys, Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
 -/
-import Mathbin.Algebra.BigOperators.Order
-import Mathbin.Algebra.Order.Rearrangement
-import Mathbin.GroupTheory.Perm.Cycle.Basic
+import Algebra.BigOperators.Order
+import Algebra.Order.Rearrangement
+import GroupTheory.Perm.Cycle.Basic
 
 #align_import algebra.order.chebyshev from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Mantas Bakšys, Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
-
-! This file was ported from Lean 3 source module algebra.order.chebyshev
-! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Order
 import Mathbin.Algebra.Order.Rearrangement
 import Mathbin.GroupTheory.Perm.Cycle.Basic
 
+#align_import algebra.order.chebyshev from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"
+
 /-!
 # Chebyshev's sum inequality
 

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

@@ -57,6 +57,7 @@ section Smul
 variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [OrderedSMul α β]
   {s : Finset ι} {σ : Perm ι} {f : ι → α} {g : ι → β}
 
+#print MonovaryOn.sum_smul_sum_le_card_smul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -69,7 +70,9 @@ theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
     sum_le_card_nsmul _ _ _ fun n _ =>
       hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
+-/
 
+#print AntivaryOn.card_smul_sum_le_sum_smul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -77,9 +80,11 @@ theorem AntivaryOn.card_smul_sum_le_sum_smul_sum (hfg : AntivaryOn f g s) :
     s.card • ∑ i in s, f i • g i ≤ (∑ i in s, f i) • ∑ i in s, g i := by
   convert hfg.dual_right.sum_smul_sum_le_card_smul_sum
 #align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sum
+-/
 
 variable [Fintype ι]
 
+#print Monovary.sum_smul_sum_le_card_smul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -87,7 +92,9 @@ theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
     (∑ i, f i) • ∑ i, g i ≤ Fintype.card ι • ∑ i, f i • g i :=
   (hfg.MonovaryOn _).sum_smul_sum_le_card_smul_sum
 #align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sum
+-/
 
+#print Antivary.card_smul_sum_le_sum_smul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -95,6 +102,7 @@ theorem Antivary.card_smul_sum_le_sum_smul_sum (hfg : Antivary f g) :
     Fintype.card ι • ∑ i, f i • g i ≤ (∑ i, f i) • ∑ i, g i := by
   convert (hfg.dual_right.monovary_on _).sum_smul_sum_le_card_smul_sum
 #align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sum
+-/
 
 end Smul
 
@@ -109,6 +117,7 @@ section Mul
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
+#print MonovaryOn.sum_mul_sum_le_card_mul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -116,7 +125,9 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
     (∑ i in s, f i) * ∑ i in s, g i ≤ s.card * ∑ i in s, f i * g i := by rw [← nsmul_eq_mul];
   exact hfg.sum_smul_sum_le_card_smul_sum
 #align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sum
+-/
 
+#print AntivaryOn.card_mul_sum_le_sum_mul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is greater than the size of the set times their scalar
 product. -/
@@ -124,15 +135,19 @@ theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
     (s.card : α) * ∑ i in s, f i * g i ≤ (∑ i in s, f i) * ∑ i in s, g i := by rw [← nsmul_eq_mul];
   exact hfg.card_smul_sum_le_sum_smul_sum
 #align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sum
+-/
 
+#print sq_sum_le_card_mul_sum_sq /-
 /-- Special case of **Chebyshev's Sum Inequality** or the **Cauchy-Schwarz Inequality**: The square
 of the sum is less than the size of the set times the sum of the squares. -/
 theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in s, f i ^ 2 := by
   simp_rw [sq]; exact (monovaryOn_self _ _).sum_mul_sum_le_card_mul_sum
 #align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sq
+-/
 
 variable [Fintype ι]
 
+#print Monovary.sum_mul_sum_le_card_mul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -140,7 +155,9 @@ theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
     (∑ i, f i) * ∑ i, g i ≤ Fintype.card ι * ∑ i, f i * g i :=
   (hfg.MonovaryOn _).sum_mul_sum_le_card_mul_sum
 #align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sum
+-/
 
+#print Antivary.card_mul_sum_le_sum_mul_sum /-
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -148,11 +165,13 @@ theorem Antivary.card_mul_sum_le_sum_mul_sum (hfg : Antivary f g) :
     (Fintype.card ι : α) * ∑ i, f i * g i ≤ (∑ i, f i) * ∑ i, g i :=
   (hfg.AntivaryOn _).card_mul_sum_le_sum_mul_sum
 #align antivary.card_mul_sum_le_sum_mul_sum Antivary.card_mul_sum_le_sum_mul_sum
+-/
 
 end Mul
 
 variable [LinearOrderedField α] {s : Finset ι} {f : ι → α}
 
+#print sum_div_card_sq_le_sum_sq_div_card /-
 theorem sum_div_card_sq_le_sum_sq_div_card :
     ((∑ i in s, f i) / s.card) ^ 2 ≤ (∑ i in s, f i ^ 2) / s.card :=
   by
@@ -163,4 +182,5 @@ theorem sum_div_card_sq_le_sum_sq_div_card :
     mul_assoc]
   exact mul_le_mul_of_nonneg_right sq_sum_le_card_mul_sum_sq hs.le
 #align sum_div_card_sq_le_sum_sq_div_card sum_div_card_sq_le_sum_sq_div_card
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -61,7 +61,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
 theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
-    ((∑ i in s, f i) • ∑ i in s, g i) ≤ s.card • ∑ i in s, f i • g i := by
+    (∑ i in s, f i) • ∑ i in s, g i ≤ s.card • ∑ i in s, f i • g i := by
   classical
   obtain ⟨σ, hσ, hs⟩ := s.countable_to_set.exists_cycle_on
   rw [← card_range s.card, sum_smul_sum_eq_sum_perm hσ]
@@ -74,7 +74,7 @@ theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
 theorem AntivaryOn.card_smul_sum_le_sum_smul_sum (hfg : AntivaryOn f g s) :
-    (s.card • ∑ i in s, f i • g i) ≤ (∑ i in s, f i) • ∑ i in s, g i := by
+    s.card • ∑ i in s, f i • g i ≤ (∑ i in s, f i) • ∑ i in s, g i := by
   convert hfg.dual_right.sum_smul_sum_le_card_smul_sum
 #align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sum
 
@@ -84,7 +84,7 @@ variable [Fintype ι]
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
 theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
-    ((∑ i, f i) • ∑ i, g i) ≤ Fintype.card ι • ∑ i, f i • g i :=
+    (∑ i, f i) • ∑ i, g i ≤ Fintype.card ι • ∑ i, f i • g i :=
   (hfg.MonovaryOn _).sum_smul_sum_le_card_smul_sum
 #align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sum
 
@@ -92,7 +92,7 @@ theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
 theorem Antivary.card_smul_sum_le_sum_smul_sum (hfg : Antivary f g) :
-    (Fintype.card ι • ∑ i, f i • g i) ≤ (∑ i, f i) • ∑ i, g i := by
+    Fintype.card ι • ∑ i, f i • g i ≤ (∑ i, f i) • ∑ i, g i := by
   convert (hfg.dual_right.monovary_on _).sum_smul_sum_le_card_smul_sum
 #align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sum
 
@@ -113,7 +113,7 @@ variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
 theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
-    ((∑ i in s, f i) * ∑ i in s, g i) ≤ s.card * ∑ i in s, f i * g i := by rw [← nsmul_eq_mul];
+    (∑ i in s, f i) * ∑ i in s, g i ≤ s.card * ∑ i in s, f i * g i := by rw [← nsmul_eq_mul];
   exact hfg.sum_smul_sum_le_card_smul_sum
 #align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sum
 
@@ -121,8 +121,8 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
 other is antitone), the product of their sum is greater than the size of the set times their scalar
 product. -/
 theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
-    ((s.card : α) * ∑ i in s, f i * g i) ≤ (∑ i in s, f i) * ∑ i in s, g i := by
-  rw [← nsmul_eq_mul]; exact hfg.card_smul_sum_le_sum_smul_sum
+    (s.card : α) * ∑ i in s, f i * g i ≤ (∑ i in s, f i) * ∑ i in s, g i := by rw [← nsmul_eq_mul];
+  exact hfg.card_smul_sum_le_sum_smul_sum
 #align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sum
 
 /-- Special case of **Chebyshev's Sum Inequality** or the **Cauchy-Schwarz Inequality**: The square
@@ -137,7 +137,7 @@ variable [Fintype ι]
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
 theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
-    ((∑ i, f i) * ∑ i, g i) ≤ Fintype.card ι * ∑ i, f i * g i :=
+    (∑ i, f i) * ∑ i, g i ≤ Fintype.card ι * ∑ i, f i * g i :=
   (hfg.MonovaryOn _).sum_mul_sum_le_card_mul_sum
 #align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sum
 
@@ -145,7 +145,7 @@ theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
 other is antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
 theorem Antivary.card_mul_sum_le_sum_mul_sum (hfg : Antivary f g) :
-    ((Fintype.card ι : α) * ∑ i, f i * g i) ≤ (∑ i, f i) * ∑ i, g i :=
+    (Fintype.card ι : α) * ∑ i, f i * g i ≤ (∑ i, f i) * ∑ i, g i :=
   (hfg.AntivaryOn _).card_mul_sum_le_sum_mul_sum
 #align antivary.card_mul_sum_le_sum_mul_sum Antivary.card_mul_sum_le_sum_mul_sum
 

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

@@ -63,11 +63,11 @@ scalar product. -/
 theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
     ((∑ i in s, f i) • ∑ i in s, g i) ≤ s.card • ∑ i in s, f i • g i := by
   classical
-    obtain ⟨σ, hσ, hs⟩ := s.countable_to_set.exists_cycle_on
-    rw [← card_range s.card, sum_smul_sum_eq_sum_perm hσ]
-    exact
-      sum_le_card_nsmul _ _ _ fun n _ =>
-        hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
+  obtain ⟨σ, hσ, hs⟩ := s.countable_to_set.exists_cycle_on
+  rw [← card_range s.card, sum_smul_sum_eq_sum_perm hσ]
+  exact
+    sum_le_card_nsmul _ _ _ fun n _ =>
+      hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
 
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
@@ -93,7 +93,7 @@ other is antitone), the scalar product of their sum is less than the size of the
 scalar product. -/
 theorem Antivary.card_smul_sum_le_sum_smul_sum (hfg : Antivary f g) :
     (Fintype.card ι • ∑ i, f i • g i) ≤ (∑ i, f i) • ∑ i, g i := by
-  convert(hfg.dual_right.monovary_on _).sum_smul_sum_le_card_smul_sum
+  convert (hfg.dual_right.monovary_on _).sum_smul_sum_le_card_smul_sum
 #align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sum
 
 end Smul

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

@@ -158,7 +158,7 @@ theorem sum_div_card_sq_le_sum_sq_div_card :
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
   · simp
-  rw [← card_pos, ← @Nat.cast_pos α] at hs
+  rw [← card_pos, ← @Nat.cast_pos α] at hs 
   rw [div_pow, div_le_div_iff (sq_pos_of_ne_zero _ hs.ne') hs, sq (s.card : α), mul_left_comm, ←
     mul_assoc]
   exact mul_le_mul_of_nonneg_right sq_sum_le_card_mul_sum_sq hs.le

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

@@ -45,7 +45,7 @@ file because it is easily deducible from the `monovary` API.
 
 open Equiv Equiv.Perm Finset Function OrderDual
 
-open BigOperators
+open scoped BigOperators
 
 variable {ι α β : Type _}
 

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

@@ -57,9 +57,6 @@ section Smul
 variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [OrderedSMul α β]
   {s : Finset ι} {σ : Perm ι} {f : ι → α} {g : ι → β}
 
-/- warning: monovary_on.sum_smul_sum_le_card_smul_sum -> MonovaryOn.sum_smul_sum_le_card_smul_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -73,9 +70,6 @@ theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
         hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
 
-/- warning: antivary_on.card_smul_sum_le_sum_smul_sum -> AntivaryOn.card_smul_sum_le_sum_smul_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -86,9 +80,6 @@ theorem AntivaryOn.card_smul_sum_le_sum_smul_sum (hfg : AntivaryOn f g s) :
 
 variable [Fintype ι]
 
-/- warning: monovary.sum_smul_sum_le_card_smul_sum -> Monovary.sum_smul_sum_le_card_smul_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -97,9 +88,6 @@ theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_smul_sum_le_card_smul_sum
 #align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sum
 
-/- warning: antivary.card_smul_sum_le_sum_smul_sum -> Antivary.card_smul_sum_le_sum_smul_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -121,12 +109,6 @@ section Mul
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
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-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -135,12 +117,6 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
   exact hfg.sum_smul_sum_le_card_smul_sum
 #align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sum
 
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-Case conversion may be inaccurate. Consider using '#align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is greater than the size of the set times their scalar
 product. -/
@@ -149,12 +125,6 @@ theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
   rw [← nsmul_eq_mul]; exact hfg.card_smul_sum_le_sum_smul_sum
 #align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sum
 
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-Case conversion may be inaccurate. Consider using '#align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sqₓ'. -/
 /-- Special case of **Chebyshev's Sum Inequality** or the **Cauchy-Schwarz Inequality**: The square
 of the sum is less than the size of the set times the sum of the squares. -/
 theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in s, f i ^ 2 := by
@@ -163,12 +133,6 @@ theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in
 
 variable [Fintype ι]
 
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-Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -177,12 +141,6 @@ theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_mul_sum_le_card_mul_sum
 #align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sum
 
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-Case conversion may be inaccurate. Consider using '#align antivary.card_mul_sum_le_sum_mul_sum Antivary.card_mul_sum_le_sum_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -195,12 +153,6 @@ end Mul
 
 variable [LinearOrderedField α] {s : Finset ι} {f : ι → α}
 
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-Case conversion may be inaccurate. Consider using '#align sum_div_card_sq_le_sum_sq_div_card sum_div_card_sq_le_sum_sq_div_cardₓ'. -/
 theorem sum_div_card_sq_le_sum_sq_div_card :
     ((∑ i in s, f i) / s.card) ^ 2 ≤ (∑ i in s, f i ^ 2) / s.card :=
   by

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

@@ -131,9 +131,7 @@ Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_su
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
 theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
-    ((∑ i in s, f i) * ∑ i in s, g i) ≤ s.card * ∑ i in s, f i * g i :=
-  by
-  rw [← nsmul_eq_mul]
+    ((∑ i in s, f i) * ∑ i in s, g i) ≤ s.card * ∑ i in s, f i * g i := by rw [← nsmul_eq_mul];
   exact hfg.sum_smul_sum_le_card_smul_sum
 #align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sum
 
@@ -147,10 +145,8 @@ Case conversion may be inaccurate. Consider using '#align antivary_on.card_mul_s
 other is antitone), the product of their sum is greater than the size of the set times their scalar
 product. -/
 theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
-    ((s.card : α) * ∑ i in s, f i * g i) ≤ (∑ i in s, f i) * ∑ i in s, g i :=
-  by
-  rw [← nsmul_eq_mul]
-  exact hfg.card_smul_sum_le_sum_smul_sum
+    ((s.card : α) * ∑ i in s, f i * g i) ≤ (∑ i in s, f i) * ∑ i in s, g i := by
+  rw [← nsmul_eq_mul]; exact hfg.card_smul_sum_le_sum_smul_sum
 #align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sum
 
 /- warning: sq_sum_le_card_mul_sum_sq -> sq_sum_le_card_mul_sum_sq is a dubious translation:
@@ -161,10 +157,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sqₓ'. -/
 /-- Special case of **Chebyshev's Sum Inequality** or the **Cauchy-Schwarz Inequality**: The square
 of the sum is less than the size of the set times the sum of the squares. -/
-theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in s, f i ^ 2 :=
-  by
-  simp_rw [sq]
-  exact (monovaryOn_self _ _).sum_mul_sum_le_card_mul_sum
+theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in s, f i ^ 2 := by
+  simp_rw [sq]; exact (monovaryOn_self _ _).sum_mul_sum_le_card_mul_sum
 #align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sq
 
 variable [Fintype ι]

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

@@ -58,10 +58,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
   {s : Finset ι} {σ : Perm ι} {f : ι → α} {g : ι → β}
 
 /- warning: monovary_on.sum_smul_sum_le_card_smul_sum -> MonovaryOn.sum_smul_sum_le_card_smul_sum is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
-but is expected to have type
-  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {s : Finset.{u3} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g (Finset.toSet.{u3} ι s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => g i))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Finset.card.{u3} ι s) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
@@ -77,10 +74,7 @@ theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
 
 /- warning: antivary_on.card_smul_sum_le_sum_smul_sum -> AntivaryOn.card_smul_sum_le_sum_smul_sum is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))))
-but is expected to have type
-  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {s : Finset.{u3} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g (Finset.toSet.{u3} ι s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Finset.card.{u3} ι s) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => g i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
@@ -93,10 +87,7 @@ theorem AntivaryOn.card_smul_sum_le_sum_smul_sum (hfg : AntivaryOn f g s) :
 variable [Fintype ι]
 
 /- warning: monovary.sum_smul_sum_le_card_smul_sum -> Monovary.sum_smul_sum_le_card_smul_sum is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Monovary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
-but is expected to have type
-  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], (Monovary.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => g i))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Fintype.card.{u3} ι _inst_5) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
@@ -107,10 +98,7 @@ theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
 #align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sum
 
 /- warning: antivary.card_smul_sum_le_sum_smul_sum -> Antivary.card_smul_sum_le_sum_smul_sum is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Antivary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))))
-but is expected to have type
-  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], (Antivary.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Fintype.card.{u3} ι _inst_5) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => g i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their

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

@@ -59,7 +59,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 
 /- warning: monovary_on.sum_smul_sum_le_card_smul_sum -> MonovaryOn.sum_smul_sum_le_card_smul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
 but is expected to have type
   forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {s : Finset.{u3} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g (Finset.toSet.{u3} ι s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => g i))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Finset.card.{u3} ι s) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sumₓ'. -/
@@ -78,7 +78,7 @@ theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
 
 /- warning: antivary_on.card_smul_sum_le_sum_smul_sum -> AntivaryOn.card_smul_sum_le_sum_smul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))))
 but is expected to have type
   forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {s : Finset.{u3} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g (Finset.toSet.{u3} ι s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Finset.card.{u3} ι s) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sumₓ'. -/
@@ -94,7 +94,7 @@ variable [Fintype ι]
 
 /- warning: monovary.sum_smul_sum_le_card_smul_sum -> Monovary.sum_smul_sum_le_card_smul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Monovary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Monovary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
 but is expected to have type
   forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], (Monovary.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => g i))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Fintype.card.{u3} ι _inst_5) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sumₓ'. -/
@@ -108,7 +108,7 @@ theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
 
 /- warning: antivary.card_smul_sum_le_sum_smul_sum -> Antivary.card_smul_sum_le_sum_smul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Antivary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Antivary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))))
 but is expected to have type
   forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], (Antivary.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Fintype.card.{u3} ι _inst_5) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sumₓ'. -/
@@ -135,7 +135,7 @@ variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
 /- warning: monovary_on.sum_mul_sum_le_card_mul_sum -> MonovaryOn.sum_mul_sum_le_card_mul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sumₓ'. -/
@@ -151,7 +151,7 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
 
 /- warning: antivary_on.card_mul_sum_le_sum_mul_sum -> AntivaryOn.card_mul_sum_le_sum_mul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sumₓ'. -/
@@ -167,7 +167,7 @@ theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
 
 /- warning: sq_sum_le_card_mul_sum_sq -> sq_sum_le_card_mul_sum_sq is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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 _inst_1))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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 _inst_1))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))))) (Nat.cast.{u2} α (Semiring.toNatCast.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
 Case conversion may be inaccurate. Consider using '#align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sqₓ'. -/
@@ -183,7 +183,7 @@ variable [Fintype ι]
 
 /- warning: monovary.sum_mul_sum_le_card_mul_sum -> Monovary.sum_mul_sum_le_card_mul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Monovary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Monovary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Monovary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sumₓ'. -/
@@ -197,7 +197,7 @@ theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
 
 /- warning: antivary.card_mul_sum_le_sum_mul_sum -> Antivary.card_mul_sum_le_sum_mul_sum is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Antivary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Antivary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Antivary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.card_mul_sum_le_sum_mul_sum Antivary.card_mul_sum_le_sum_mul_sumₓ'. -/
@@ -215,7 +215,7 @@ variable [LinearOrderedField α] {s : Finset ι} {f : ι → α}
 
 /- warning: sum_div_card_sq_le_sum_sq_div_card -> sum_div_card_sq_le_sum_sq_div_card is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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))))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s)))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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))))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s)))
 but is expected to have type
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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)))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) (Nat.cast.{u2} α (Semiring.toNatCast.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Nat.cast.{u2} α (Semiring.toNatCast.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (Finset.card.{u1} ι s)))
 Case conversion may be inaccurate. Consider using '#align sum_div_card_sq_le_sum_sq_div_card sum_div_card_sq_le_sum_sq_div_cardₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -137,7 +137,7 @@ variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
@@ -153,7 +153,7 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is greater than the size of the set times their scalar
@@ -169,7 +169,7 @@ theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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 _inst_1))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))))) (Nat.cast.{u2} α (NonAssocRing.toNatCast.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))))) (Nat.cast.{u2} α (Semiring.toNatCast.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
 Case conversion may be inaccurate. Consider using '#align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sqₓ'. -/
 /-- Special case of **Chebyshev's Sum Inequality** or the **Cauchy-Schwarz Inequality**: The square
 of the sum is less than the size of the set times the sum of the squares. -/
@@ -185,7 +185,7 @@ variable [Fintype ι]
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Monovary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Monovary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Monovary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
@@ -199,7 +199,7 @@ theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Antivary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Antivary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Antivary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.card_mul_sum_le_sum_mul_sum Antivary.card_mul_sum_le_sum_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is less than the size of the set times their scalar
@@ -217,7 +217,7 @@ variable [LinearOrderedField α] {s : Finset ι} {f : ι → α}
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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))))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s)))
 but is expected to have type
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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)))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) (Nat.cast.{u2} α (NonAssocRing.toNatCast.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Nat.cast.{u2} α (NonAssocRing.toNatCast.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (Finset.card.{u1} ι s)))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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)))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) (Nat.cast.{u2} α (Semiring.toNatCast.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Nat.cast.{u2} α (Semiring.toNatCast.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) (Finset.card.{u1} ι s)))
 Case conversion may be inaccurate. Consider using '#align sum_div_card_sq_le_sum_sq_div_card sum_div_card_sq_le_sum_sq_div_cardₓ'. -/
 theorem sum_div_card_sq_le_sum_sq_div_card :
     ((∑ i in s, f i) / s.card) ^ 2 ≤ (∑ i in s, f i ^ 2) / s.card :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
 
 ! This file was ported from Lean 3 source module algebra.order.chebyshev
-! leanprover-community/mathlib commit b7399344324326918d65d0c74e9571e3a8cb9199
+! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.GroupTheory.Perm.Cycle.Basic
 /-!
 # Chebyshev's sum inequality
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves the Chebyshev sum inequality.
 
 Chebyshev's inequality states `(∑ i in s, f i) * (∑ i in s, g i) ≤ s.card * ∑ i in s, f i * g i`

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

@@ -54,6 +54,12 @@ section Smul
 variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [OrderedSMul α β]
   {s : Finset ι} {σ : Perm ι} {f : ι → α} {g : ι → β}
 
+/- warning: monovary_on.sum_smul_sum_le_card_smul_sum -> MonovaryOn.sum_smul_sum_le_card_smul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
+but is expected to have type
+  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {s : Finset.{u3} ι} {f : ι -> α} {g : ι -> β}, (MonovaryOn.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g (Finset.toSet.{u3} ι s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => g i))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Finset.card.{u3} ι s) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))))
+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -67,6 +73,12 @@ theorem MonovaryOn.sum_smul_sum_le_card_smul_sum (hfg : MonovaryOn f g s) :
         hfg.sum_smul_comp_perm_le_sum_smul fun x hx => hs fun h => hx <| is_fixed_pt.perm_pow h _
 #align monovary_on.sum_smul_sum_le_card_smul_sum MonovaryOn.sum_smul_sum_le_card_smul_sum
 
+/- warning: antivary_on.card_smul_sum_le_sum_smul_sum -> AntivaryOn.card_smul_sum_le_sum_smul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Finset.card.{u1} ι s) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) s (fun (i : ι) => g i))))
+but is expected to have type
+  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {s : Finset.{u3} ι} {f : ι -> α} {g : ι -> β}, (AntivaryOn.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g (Finset.toSet.{u3} ι s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Finset.card.{u3} ι s) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => g i))))
+Case conversion may be inaccurate. Consider using '#align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -77,6 +89,12 @@ theorem AntivaryOn.card_smul_sum_le_sum_smul_sum (hfg : AntivaryOn f g s) :
 
 variable [Fintype ι]
 
+/- warning: monovary.sum_smul_sum_le_card_smul_sum -> Monovary.sum_smul_sum_le_card_smul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Monovary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))))
+but is expected to have type
+  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], (Monovary.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => g i))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Fintype.card.{u3} ι _inst_5) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -85,6 +103,12 @@ theorem Monovary.sum_smul_sum_le_card_smul_sum (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_smul_sum_le_card_smul_sum
 #align monovary.sum_smul_sum_le_card_smul_sum Monovary.sum_smul_sum_le_card_smul_sum
 
+/- warning: antivary.card_smul_sum_le_sum_smul_sum -> Antivary.card_smul_sum_le_sum_smul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u3} β] [_inst_3 : Module.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u3} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (StrictOrderedRing.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u1} ι], (Antivary.{u1, u2, u3} ι α β (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f g) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (SMul.smul.{0, u3} Nat β (AddMonoid.SMul.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (AddCommGroup.toAddGroup.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Fintype.card.{u1} ι _inst_5) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (SMul.smul.{u2, u3} α β (SMulZeroClass.toHasSmul.{u2, u3} α β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} α β (MulZeroClass.toHasZero.{u2} α (MulZeroOneClass.toMulZeroClass.{u2} α (MonoidWithZero.toMulZeroOneClass.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} α β (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} α β (Ring.toSemiring.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u3, u1} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => g i))))
+but is expected to have type
+  forall {ι : Type.{u3}} {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} β] [_inst_3 : Module.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))] [_inst_4 : OrderedSMul.{u2, u1} α β (StrictOrderedSemiring.toOrderedSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))] {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], (Antivary.{u3, u2, u1} ι α β (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))) (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (HSMul.hSMul.{0, u1, u1} Nat β β (instHSMul.{0, u1} Nat β (AddMonoid.SMul.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (AddCommGroup.toAddGroup.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Fintype.card.{u3} ι _inst_5) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (HSMul.hSMul.{u2, u1, u1} α β β (instHSMul.{u2, u1} α β (SMulZeroClass.toSMul.{u2, u1} α β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} α β (MonoidWithZero.toZero.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} α β (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} α β (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (Finset.sum.{u2, u3} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => f i)) (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => g i))))
+Case conversion may be inaccurate. Consider using '#align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the scalar product of their sum is less than the size of the set times their
 scalar product. -/
@@ -106,6 +130,12 @@ section Mul
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
+/- warning: monovary_on.sum_mul_sum_le_card_mul_sum -> MonovaryOn.sum_mul_sum_le_card_mul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (MonovaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -116,6 +146,12 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
   exact hfg.sum_smul_sum_le_card_smul_sum
 #align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sum
 
+/- warning: antivary_on.card_mul_sum_le_sum_mul_sum -> AntivaryOn.card_mul_sum_le_sum_mul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => g i))))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {f : ι -> α} {g : ι -> α}, (AntivaryOn.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g (Finset.toSet.{u2} ι s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Finset.card.{u2} ι s)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) s (fun (i : ι) => g i))))
+Case conversion may be inaccurate. Consider using '#align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is greater than the size of the set times their scalar
 product. -/
@@ -126,6 +162,12 @@ theorem AntivaryOn.card_mul_sum_le_sum_mul_sum (hfg : AntivaryOn f g s) :
   exact hfg.card_smul_sum_le_sum_smul_sum
 #align antivary_on.card_mul_sum_le_sum_mul_sum AntivaryOn.card_mul_sum_le_sum_mul_sum
 
+/- warning: sq_sum_le_card_mul_sum_sq -> sq_sum_le_card_mul_sum_sq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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 _inst_1))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {f : ι -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedRing.toPartialOrder.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => f i)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))))) (Nat.cast.{u2} α (NonAssocRing.toNatCast.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.card.{u1} ι s)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1)))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedRing.toLinearOrderedSemiring.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align sq_sum_le_card_mul_sum_sq sq_sum_le_card_mul_sum_sqₓ'. -/
 /-- Special case of **Chebyshev's Sum Inequality** or the **Cauchy-Schwarz Inequality**: The square
 of the sum is less than the size of the set times the sum of the squares. -/
 theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in s, f i ^ 2 :=
@@ -136,6 +178,12 @@ theorem sq_sum_le_card_mul_sum_sq : (∑ i in s, f i) ^ 2 ≤ s.card * ∑ i in
 
 variable [Fintype ι]
 
+/- warning: monovary.sum_mul_sum_le_card_mul_sum -> Monovary.sum_mul_sum_le_card_mul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Monovary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Monovary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -144,6 +192,12 @@ theorem Monovary.sum_mul_sum_le_card_mul_sum (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_mul_sum_le_card_mul_sum
 #align monovary.sum_mul_sum_le_card_mul_sum Monovary.sum_mul_sum_le_card_mul_sum
 
+/- warning: antivary.card_mul_sum_le_sum_mul_sum -> Antivary.card_mul_sum_le_sum_mul_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u1} ι], (Antivary.{u1, u2, u2} ι α α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) f g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))))))) (Fintype.card.{u1} ι _inst_2)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (Finset.univ.{u1} ι _inst_2) (fun (i : ι) => g i))))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {f : ι -> α} {g : ι -> α} [_inst_2 : Fintype.{u2} ι], (Antivary.{u2, u1, u1} ι α α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Nat.cast.{u1} α (NonAssocRing.toNatCast.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (Fintype.card.{u2} ι _inst_2)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (f i) (g i)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => f i)) (Finset.sum.{u1, u2} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))) (Finset.univ.{u2} ι _inst_2) (fun (i : ι) => g i))))
+Case conversion may be inaccurate. Consider using '#align antivary.card_mul_sum_le_sum_mul_sum Antivary.card_mul_sum_le_sum_mul_sumₓ'. -/
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -156,6 +210,12 @@ end Mul
 
 variable [LinearOrderedField α] {s : Finset ι} {f : ι → α}
 
+/- warning: sum_div_card_sq_le_sum_sq_div_card -> sum_div_card_sq_le_sum_sq_div_card is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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))))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (DivInvMonoid.toHasDiv.{u2} α (DivisionRing.toDivInvMonoid.{u2} α (Field.toDivisionRing.{u2} α (LinearOrderedField.toField.{u2} α _inst_1))))) (Finset.sum.{u2, u1} α ι (AddCommGroup.toAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (Ring.toMonoid.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))) (f i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u2} Nat α (CoeTCₓ.coe.{1, succ u2} Nat α (Nat.castCoe.{u2} α (AddMonoidWithOne.toNatCast.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1))))))))))) (Finset.card.{u1} ι s)))
+but is expected to have type
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {s : Finset.{u1} ι} {f : ι -> 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)))))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => f i)) (Nat.cast.{u2} α (NonAssocRing.toNatCast.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (Finset.card.{u1} ι s))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HDiv.hDiv.{u2, u2, u2} α α α (instHDiv.{u2} α (LinearOrderedField.toDiv.{u2} α _inst_1)) (Finset.sum.{u2, u1} α ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1)))))) s (fun (i : ι) => HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α (MonoidWithZero.toMonoid.{u2} α (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))))))))) (f i) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Nat.cast.{u2} α (NonAssocRing.toNatCast.{u2} α (Ring.toNonAssocRing.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α (LinearOrderedCommRing.toLinearOrderedRing.{u2} α (LinearOrderedField.toLinearOrderedCommRing.{u2} α _inst_1)))))) (Finset.card.{u1} ι s)))
+Case conversion may be inaccurate. Consider using '#align sum_div_card_sq_le_sum_sq_div_card sum_div_card_sq_le_sum_sq_div_cardₓ'. -/
 theorem sum_div_card_sq_le_sum_sq_div_card :
     ((∑ i in s, f i) / s.card) ^ 2 ≤ (∑ i in s, f i ^ 2) / s.card :=
   by

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

@@ -90,7 +90,7 @@ other is antitone), the scalar product of their sum is less than the size of the
 scalar product. -/
 theorem Antivary.card_smul_sum_le_sum_smul_sum (hfg : Antivary f g) :
     (Fintype.card ι • ∑ i, f i • g i) ≤ (∑ i, f i) • ∑ i, g i := by
-  convert (hfg.dual_right.monovary_on _).sum_smul_sum_le_card_smul_sum
+  convert(hfg.dual_right.monovary_on _).sum_smul_sum_le_card_smul_sum
 #align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sum
 
 end Smul

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

This matches our general policy and zpow_two_pos_of_ne_zero.

Also define sq_pos_of_ne_zero as an alias.

@@ -156,7 +156,7 @@ theorem sum_div_card_sq_le_sum_sq_div_card :
   obtain rfl | hs := s.eq_empty_or_nonempty
   · simp
   rw [← card_pos, ← @Nat.cast_pos α] at hs
-  rw [div_pow, div_le_div_iff (sq_pos_of_ne_zero _ hs.ne') hs, sq (s.card : α), mul_left_comm, ←
+  rw [div_pow, div_le_div_iff (sq_pos_of_ne_zero hs.ne') hs, sq (s.card : α), mul_left_comm, ←
     mul_assoc]
   exact mul_le_mul_of_nonneg_right sq_sum_le_card_mul_sum_sq hs.le
 #align sum_div_card_sq_le_sum_sq_div_card sum_div_card_sq_le_sum_sq_div_card

Take the content of

• some of Algebra.BigOperators.List.Basic
• some of Algebra.BigOperators.List.Lemmas
• some of Algebra.BigOperators.Multiset.Basic
• some of Algebra.BigOperators.Multiset.Lemmas
• Algebra.BigOperators.Multiset.Order
• Algebra.BigOperators.Order

and sort it into six files:

• Algebra.Order.BigOperators.Group.List. I credit Yakov for https://github.com/leanprover-community/mathlib/pull/8543.
• Algebra.Order.BigOperators.Group.Multiset. Copyright inherited from Algebra.BigOperators.Multiset.Order.
• Algebra.Order.BigOperators.Group.Finset. Copyright inherited from Algebra.BigOperators.Order.
• Algebra.Order.BigOperators.Ring.List. I credit Stuart for https://github.com/leanprover-community/mathlib/pull/10184.
• Algebra.Order.BigOperators.Ring.Multiset. I credit Ruben for https://github.com/leanprover-community/mathlib/pull/8787.
• Algebra.Order.BigOperators.Ring.Finset. I credit Floris for https://github.com/leanprover-community/mathlib/pull/1294.

Here are the design decisions at play:

• Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import Data.Nat.Order.Basic in a few List files.
• It's Algebra.Order.BigOperators instead of Algebra.BigOperators.Order because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators.
• There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under Algebra.Order.BigOperators.Group should be additivisable (except a few Nat- or Int-specific lemmas). In contrast, things under Algebra.Order.BigOperators.Ring are more prone to having heavy imports.
• Lemmas are separated according to List vs Multiset vs Finset. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the AbsoluteValue lemmas from Algebra.Order.BigOperators.Ring.Finset to a file Algebra.Order.BigOperators.Ring.AbsoluteValue and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset, Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset, etc...
• Finsupp big operator and finprod/finsum order lemmas also belong in Algebra.Order.BigOperators. I haven't done so in this PR because the diff is big enough like that.

@@ -3,8 +3,8 @@ Copyright (c) 2023 Mantas Bakšys, Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
 -/
-import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.GroupPower.Order
+import Mathlib.Algebra.Order.BigOperators.Group.Finset
 import Mathlib.Algebra.Order.Rearrangement
 import Mathlib.GroupTheory.Perm.Cycle.Basic
 

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -70,7 +70,7 @@ other is antitone), the scalar product of their sum is less than the size of the
 scalar product. -/
 theorem AntivaryOn.card_smul_sum_le_sum_smul_sum (hfg : AntivaryOn f g s) :
     (s.card • ∑ i in s, f i • g i) ≤ (∑ i in s, f i) • ∑ i in s, g i := by
-  refine hfg.dual_right.sum_smul_sum_le_card_smul_sum
+  exact hfg.dual_right.sum_smul_sum_le_card_smul_sum
 #align antivary_on.card_smul_sum_le_sum_smul_sum AntivaryOn.card_smul_sum_le_sum_smul_sum
 
 variable [Fintype ι]
@@ -88,7 +88,7 @@ other is antitone), the scalar product of their sum is less than the size of the
 scalar product. -/
 theorem Antivary.card_smul_sum_le_sum_smul_sum (hfg : Antivary f g) :
     (Fintype.card ι • ∑ i, f i • g i) ≤ (∑ i, f i) • ∑ i, g i := by
-  refine (hfg.dual_right.monovaryOn _).sum_smul_sum_le_card_smul_sum
+  exact (hfg.dual_right.monovaryOn _).sum_smul_sum_le_card_smul_sum
 #align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sum
 
 end SMul

The goal here is to have access to positivity earlier in the import hierarchy

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
 -/
 import Mathlib.Algebra.BigOperators.Order
+import Mathlib.Algebra.GroupPower.Order
 import Mathlib.Algebra.Order.Rearrangement
 import Mathlib.GroupTheory.Perm.Cycle.Basic
 

Normalising to naming convention rule number 6.

@@ -46,7 +46,7 @@ variable {ι α β : Type*}
 /-! ### Scalar multiplication versions -/
 
 
-section Smul
+section SMul
 
 variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [OrderedSMul α β]
   {s : Finset ι} {σ : Perm ι} {f : ι → α} {g : ι → β}
@@ -90,7 +90,7 @@ theorem Antivary.card_smul_sum_le_sum_smul_sum (hfg : Antivary f g) :
   refine (hfg.dual_right.monovaryOn _).sum_smul_sum_le_card_smul_sum
 #align antivary.card_smul_sum_le_sum_smul_sum Antivary.card_smul_sum_le_sum_smul_sum
 
-end Smul
+end SMul
 
 /-!
 ### Multiplication versions

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

This has nice performance benefits.

@@ -41,7 +41,7 @@ open Equiv Equiv.Perm Finset Function OrderDual
 
 open BigOperators
 
-variable {ι α β : Type _}
+variable {ι α β : Type*}
 
 /-! ### Scalar multiplication versions -/
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Mantas Bakšys, Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys, Yaël Dillies
-
-! This file was ported from Lean 3 source module algebra.order.chebyshev
-! leanprover-community/mathlib commit b7399344324326918d65d0c74e9571e3a8cb9199
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.Order.Rearrangement
 import Mathlib.GroupTheory.Perm.Cycle.Basic
 
+#align_import algebra.order.chebyshev from "leanprover-community/mathlib"@"b7399344324326918d65d0c74e9571e3a8cb9199"
+
 /-!
 # Chebyshev's sum inequality
 

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -106,7 +106,6 @@ section Mul
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` monovary together (eg they are both
 monotone/antitone), the product of their sum is less than the size of the set times their scalar
 product. -/
@@ -116,7 +115,6 @@ theorem MonovaryOn.sum_mul_sum_le_card_mul_sum (hfg : MonovaryOn f g s) :
   exact hfg.sum_smul_sum_le_card_smul_sum
 #align monovary_on.sum_mul_sum_le_card_mul_sum MonovaryOn.sum_mul_sum_le_card_mul_sum
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- **Chebyshev's Sum Inequality**: When `f` and `g` antivary together (eg one is monotone, the
 other is antitone), the product of their sum is greater than the size of the set times their scalar
 product. -/

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