algebra.order.rearrangement ⟷ Mathlib.Algebra.Order.Rearrangement

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

@@ -73,8 +73,8 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
   set τ : perm ι := σ.trans (swap a (σ a)) with hτ
   have hτs : {x | τ x ≠ x} ⊆ s := by
     intro x hx
-    simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx 
-    split_ifs at hx  with h₁ h₂ h₃
+    simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx
+    split_ifs at hx with h₁ h₂ h₃
     · obtain rfl | hax := eq_or_ne x a
       · contradiction
       · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
@@ -86,24 +86,24 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
   obtain hσa | hσa := eq_or_ne a (σ a)
   · rw [hτ, ← hσa, swap_self, trans_refl]
   have h1s : σ⁻¹ a ∈ s := by
-    rw [Ne.def, ← inv_eq_iff_eq] at hσa 
+    rw [Ne.def, ← inv_eq_iff_eq] at hσa
     refine' mem_of_mem_insert_of_ne (hσ fun h => hσa _) hσa
-    rwa [apply_inv_self, eq_comm] at h 
+    rwa [apply_inv_self, eq_comm] at h
   simp only [← s.sum_erase_add _ h1s, add_comm]
   rw [← add_assoc, ← add_assoc]
   simp only [hτ, swap_apply_left, Function.comp_apply, Equiv.coe_trans, apply_inv_self]
   refine' add_le_add (smul_add_smul_le_smul_add_smul' _ _) (sum_congr rfl fun x hx => _).le
   · specialize hamax (σ⁻¹ a) h1s
-    rw [Prod.Lex.le_iff] at hamax 
+    rw [Prod.Lex.le_iff] at hamax
     cases hamax
     · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
     · exact hamax.2
   · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
-    rw [Prod.Lex.le_iff] at hamax 
+    rw [Prod.Lex.le_iff] at hamax
     cases hamax
     · exact hamax.le
     · exact hamax.1.le
-  · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx 
+  · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx
     rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
     rintro rfl
     exact has hx.2
@@ -119,8 +119,8 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ MonovaryOn f (g ∘ σ) s := by
   classical
   refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
-  · rw [MonovaryOn] at h 
-    push_neg at h 
+  · rw [MonovaryOn] at h
+    push_neg at h
     obtain ⟨x, hx, y, hy, hgxy, hfxy⟩ := h
     set τ : perm ι := (swap x y).trans σ
     have hτs : {x | τ x ≠ x} ⊆ s :=
@@ -135,7 +135,7 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     refine'
       add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz => _).le
         (smul_add_smul_lt_smul_add_smul hfxy hgxy)
-    simp_rw [mem_erase] at hz 
+    simp_rw [mem_erase] at hz
     rw [swap_apply_of_ne_of_ne hz.2.1 hz.1]
   · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
     simp_rw [Function.comp_apply, apply_inv_self]

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

@@ -64,7 +64,49 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
-    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g (σ i) ≤ ∑ i in s, f i • g i := by classical
+    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g (σ i) ≤ ∑ i in s, f i • g i := by
+  classical
+  revert hσ σ hfg
+  apply Finset.induction_on_max_value (fun i => toLex (g i, f i)) s
+  · simp only [le_rfl, Finset.sum_empty, imp_true_iff]
+  intro a s has hamax hind σ hfg hσ
+  set τ : perm ι := σ.trans (swap a (σ a)) with hτ
+  have hτs : {x | τ x ≠ x} ⊆ s := by
+    intro x hx
+    simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx 
+    split_ifs at hx  with h₁ h₂ h₃
+    · obtain rfl | hax := eq_or_ne x a
+      · contradiction
+      · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
+    · exact (hx <| σ.injective h₂.symm).elim
+    · exact mem_of_mem_insert_of_ne (hσ hx) (ne_of_apply_ne _ h₂)
+  specialize hind (hfg.subset <| subset_insert _ _) hτs
+  simp_rw [sum_insert has]
+  refine' le_trans _ (add_le_add_left hind _)
+  obtain hσa | hσa := eq_or_ne a (σ a)
+  · rw [hτ, ← hσa, swap_self, trans_refl]
+  have h1s : σ⁻¹ a ∈ s := by
+    rw [Ne.def, ← inv_eq_iff_eq] at hσa 
+    refine' mem_of_mem_insert_of_ne (hσ fun h => hσa _) hσa
+    rwa [apply_inv_self, eq_comm] at h 
+  simp only [← s.sum_erase_add _ h1s, add_comm]
+  rw [← add_assoc, ← add_assoc]
+  simp only [hτ, swap_apply_left, Function.comp_apply, Equiv.coe_trans, apply_inv_self]
+  refine' add_le_add (smul_add_smul_le_smul_add_smul' _ _) (sum_congr rfl fun x hx => _).le
+  · specialize hamax (σ⁻¹ a) h1s
+    rw [Prod.Lex.le_iff] at hamax 
+    cases hamax
+    · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
+    · exact hamax.2
+  · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
+    rw [Prod.Lex.le_iff] at hamax 
+    cases hamax
+    · exact hamax.le
+    · exact hamax.1.le
+  · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx 
+    rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
+    rintro rfl
+    exact has hx.2
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
 -/
 
@@ -74,7 +116,29 @@ which monovary together, is unchanged by a permutation if and only if `f` and `g
 together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ MonovaryOn f (g ∘ σ) s := by classical
+    ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ MonovaryOn f (g ∘ σ) s := by
+  classical
+  refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
+  · rw [MonovaryOn] at h 
+    push_neg at h 
+    obtain ⟨x, hx, y, hy, hgxy, hfxy⟩ := h
+    set τ : perm ι := (swap x y).trans σ
+    have hτs : {x | τ x ≠ x} ⊆ s :=
+      by
+      refine' (set_support_mul_subset σ <| swap x y).trans (Set.union_subset hσ fun z hz => _)
+      obtain ⟨_, rfl | rfl⟩ := swap_apply_ne_self_iff.1 hz <;> assumption
+    refine' ((hfg.sum_smul_comp_perm_le_sum_smul hτs).trans_lt' _).Ne
+    obtain rfl | hxy := eq_or_ne x y
+    · cases lt_irrefl _ hfxy
+    simp only [← s.sum_erase_add _ hx, ← (s.erase x).sum_erase_add _ (mem_erase.2 ⟨hxy.symm, hy⟩),
+      add_assoc, Equiv.coe_trans, Function.comp_apply, swap_apply_right, swap_apply_left]
+    refine'
+      add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz => _).le
+        (smul_add_smul_lt_smul_add_smul hfxy hgxy)
+    simp_rw [mem_erase] at hz 
+    rw [swap_apply_of_ne_of_ne hz.2.1 hz.1]
+  · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
+    simp_rw [Function.comp_apply, apply_inv_self]
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
 -/
 

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

@@ -64,49 +64,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
-    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g (σ i) ≤ ∑ i in s, f i • g i := by
-  classical
-  revert hσ σ hfg
-  apply Finset.induction_on_max_value (fun i => toLex (g i, f i)) s
-  · simp only [le_rfl, Finset.sum_empty, imp_true_iff]
-  intro a s has hamax hind σ hfg hσ
-  set τ : perm ι := σ.trans (swap a (σ a)) with hτ
-  have hτs : {x | τ x ≠ x} ⊆ s := by
-    intro x hx
-    simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx 
-    split_ifs at hx  with h₁ h₂ h₃
-    · obtain rfl | hax := eq_or_ne x a
-      · contradiction
-      · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
-    · exact (hx <| σ.injective h₂.symm).elim
-    · exact mem_of_mem_insert_of_ne (hσ hx) (ne_of_apply_ne _ h₂)
-  specialize hind (hfg.subset <| subset_insert _ _) hτs
-  simp_rw [sum_insert has]
-  refine' le_trans _ (add_le_add_left hind _)
-  obtain hσa | hσa := eq_or_ne a (σ a)
-  · rw [hτ, ← hσa, swap_self, trans_refl]
-  have h1s : σ⁻¹ a ∈ s := by
-    rw [Ne.def, ← inv_eq_iff_eq] at hσa 
-    refine' mem_of_mem_insert_of_ne (hσ fun h => hσa _) hσa
-    rwa [apply_inv_self, eq_comm] at h 
-  simp only [← s.sum_erase_add _ h1s, add_comm]
-  rw [← add_assoc, ← add_assoc]
-  simp only [hτ, swap_apply_left, Function.comp_apply, Equiv.coe_trans, apply_inv_self]
-  refine' add_le_add (smul_add_smul_le_smul_add_smul' _ _) (sum_congr rfl fun x hx => _).le
-  · specialize hamax (σ⁻¹ a) h1s
-    rw [Prod.Lex.le_iff] at hamax 
-    cases hamax
-    · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
-    · exact hamax.2
-  · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
-    rw [Prod.Lex.le_iff] at hamax 
-    cases hamax
-    · exact hamax.le
-    · exact hamax.1.le
-  · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx 
-    rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
-    rintro rfl
-    exact has hx.2
+    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g (σ i) ≤ ∑ i in s, f i • g i := by classical
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
 -/
 
@@ -116,29 +74,7 @@ which monovary together, is unchanged by a permutation if and only if `f` and `g
 together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ MonovaryOn f (g ∘ σ) s := by
-  classical
-  refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
-  · rw [MonovaryOn] at h 
-    push_neg at h 
-    obtain ⟨x, hx, y, hy, hgxy, hfxy⟩ := h
-    set τ : perm ι := (swap x y).trans σ
-    have hτs : {x | τ x ≠ x} ⊆ s :=
-      by
-      refine' (set_support_mul_subset σ <| swap x y).trans (Set.union_subset hσ fun z hz => _)
-      obtain ⟨_, rfl | rfl⟩ := swap_apply_ne_self_iff.1 hz <;> assumption
-    refine' ((hfg.sum_smul_comp_perm_le_sum_smul hτs).trans_lt' _).Ne
-    obtain rfl | hxy := eq_or_ne x y
-    · cases lt_irrefl _ hfxy
-    simp only [← s.sum_erase_add _ hx, ← (s.erase x).sum_erase_add _ (mem_erase.2 ⟨hxy.symm, hy⟩),
-      add_assoc, Equiv.coe_trans, Function.comp_apply, swap_apply_right, swap_apply_left]
-    refine'
-      add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz => _).le
-        (smul_add_smul_lt_smul_add_smul hfxy hgxy)
-    simp_rw [mem_erase] at hz 
-    rw [swap_apply_of_ne_of_ne hz.2.1 hz.1]
-  · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
-    simp_rw [Function.comp_apply, apply_inv_self]
+    ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ MonovaryOn f (g ∘ σ) s := by classical
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
 -/
 

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

@@ -3,12 +3,12 @@ Copyright (c) 2022 Mantas Bakšys. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
 -/
-import Mathbin.Algebra.BigOperators.Basic
-import Mathbin.Algebra.Order.Module
-import Mathbin.Data.Prod.Lex
-import Mathbin.GroupTheory.Perm.Support
-import Mathbin.Order.Monotone.Monovary
-import Mathbin.Tactic.Abel
+import Algebra.BigOperators.Basic
+import Algebra.Order.Module
+import Data.Prod.Lex
+import GroupTheory.Perm.Support
+import Order.Monotone.Monovary
+import Tactic.Abel
 
 #align_import algebra.order.rearrangement from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Mantas Bakšys. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
-
-! This file was ported from Lean 3 source module algebra.order.rearrangement
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Basic
 import Mathbin.Algebra.Order.Module
@@ -15,6 +10,8 @@ import Mathbin.GroupTheory.Perm.Support
 import Mathbin.Order.Monotone.Monovary
 import Mathbin.Tactic.Abel
 
+#align_import algebra.order.rearrangement from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
+
 /-!
 # Rearrangement inequality
 

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

@@ -63,6 +63,7 @@ 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_comp_perm_le_sum_smul /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
@@ -110,7 +111,9 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
     rintro rfl
     exact has hx.2
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
+-/
 
+#print MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -140,7 +143,9 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
   · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
     simp_rw [Function.comp_apply, apply_inv_self]
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
+-/
 
+#print MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -150,7 +155,9 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
   simp [← hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ, lt_iff_le_and_ne,
     hfg.sum_smul_comp_perm_le_sum_smul hσ]
 #align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff
+-/
 
+#print MonovaryOn.sum_comp_perm_smul_le_sum_smul /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
@@ -162,7 +169,9 @@ theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
     1
   exact σ.sum_comp' s (fun i j => f i • g j) hσ
 #align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smul
+-/
 
+#print MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
@@ -182,7 +191,9 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     · rw [σ.symm.eq_preimage_iff_image_eq]
       exact Set.image_perm hσinv
 #align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff
+-/
 
+#print MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
@@ -192,14 +203,18 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
   simp [← hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ, lt_iff_le_and_ne,
     hfg.sum_comp_perm_smul_le_sum_smul hσ]
 #align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff
+-/
 
+#print AntivaryOn.sum_smul_le_sum_smul_comp_perm /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g i ≤ ∑ i in s, f i • g (σ i) :=
   hfg.dual_right.sum_smul_comp_perm_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
+-/
 
+#print AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -208,7 +223,9 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
     ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ AntivaryOn f (g ∘ σ) s :=
   (hfg.dual_right.sum_smul_comp_perm_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff
+-/
 
+#print AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -218,14 +235,18 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
   simp [← hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ, lt_iff_le_and_ne, eq_comm,
     hfg.sum_smul_le_sum_smul_comp_perm hσ]
 #align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff
+-/
 
+#print AntivaryOn.sum_smul_le_sum_comp_perm_smul /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g i ≤ ∑ i in s, f (σ i) • g i :=
   hfg.dual_right.sum_comp_perm_smul_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
+-/
 
+#print AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -234,7 +255,9 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
     ∑ i in s, f (σ i) • g i = ∑ i in s, f i • g i ↔ AntivaryOn (f ∘ σ) g s :=
   (hfg.dual_right.sum_comp_perm_smul_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff
+-/
 
+#print AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -244,16 +267,20 @@ theorem AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
   simp [← hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ, eq_comm, lt_iff_le_and_ne,
     hfg.sum_smul_le_sum_comp_perm_smul hσ]
 #align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff
+-/
 
 variable [Fintype ι]
 
+#print Monovary.sum_smul_comp_perm_le_sum_smul /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
     ∑ i, f i • g (σ i) ≤ ∑ i, f i • g i :=
   (hfg.MonovaryOn _).sum_smul_comp_perm_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_smul_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smul
+-/
 
+#print Monovary.sum_smul_comp_perm_eq_sum_smul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -261,7 +288,9 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
     ∑ i, f i • g (σ i) = ∑ i, f i • g i ↔ Monovary f (g ∘ σ) := by
   simp [(hfg.monovary_on _).sum_smul_comp_perm_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iff
+-/
 
+#print Monovary.sum_smul_comp_perm_lt_sum_smul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -269,14 +298,18 @@ theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
     ∑ i, f i • g (σ i) < ∑ i, f i • g i ↔ ¬Monovary f (g ∘ σ) := by
   simp [(hfg.monovary_on _).sum_smul_comp_perm_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iff
+-/
 
+#print Monovary.sum_comp_perm_smul_le_sum_smul /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
     ∑ i, f (σ i) • g i ≤ ∑ i, f i • g i :=
   (hfg.MonovaryOn _).sum_comp_perm_smul_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smul
+-/
 
+#print Monovary.sum_comp_perm_smul_eq_sum_smul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -284,7 +317,9 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
     ∑ i, f (σ i) • g i = ∑ i, f i • g i ↔ Monovary (f ∘ σ) g := by
   simp [(hfg.monovary_on _).sum_comp_perm_smul_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iff
+-/
 
+#print Monovary.sum_comp_perm_smul_lt_sum_smul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -292,14 +327,18 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
     ∑ i, f (σ i) • g i < ∑ i, f i • g i ↔ ¬Monovary (f ∘ σ) g := by
   simp [(hfg.monovary_on _).sum_comp_perm_smul_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iff
+-/
 
+#print Antivary.sum_smul_le_sum_smul_comp_perm /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
     ∑ i, f i • g i ≤ ∑ i, f i • g (σ i) :=
   (hfg.AntivaryOn _).sum_smul_le_sum_smul_comp_perm fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_perm
+-/
 
+#print Antivary.sum_smul_eq_sum_smul_comp_perm_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -307,7 +346,9 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
     ∑ i, f i • g (σ i) = ∑ i, f i • g i ↔ Antivary f (g ∘ σ) := by
   simp [(hfg.antivary_on _).sum_smul_eq_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iff
+-/
 
+#print Antivary.sum_smul_lt_sum_smul_comp_perm_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -315,14 +356,18 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
     ∑ i, f i • g i < ∑ i, f i • g (σ i) ↔ ¬Antivary f (g ∘ σ) := by
   simp [(hfg.antivary_on _).sum_smul_lt_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iff
+-/
 
+#print Antivary.sum_smul_le_sum_comp_perm_smul /-
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
     ∑ i, f i • g i ≤ ∑ i, f (σ i) • g i :=
   (hfg.AntivaryOn _).sum_smul_le_sum_comp_perm_smul fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smul
+-/
 
+#print Antivary.sum_smul_eq_sum_comp_perm_smul_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -330,7 +375,9 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
     ∑ i, f (σ i) • g i = ∑ i, f i • g i ↔ Antivary (f ∘ σ) g := by
   simp [(hfg.antivary_on _).sum_smul_eq_sum_comp_perm_smul_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iff
+-/
 
+#print Antivary.sum_smul_lt_sum_comp_perm_smul_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -338,6 +385,7 @@ theorem Antivary.sum_smul_lt_sum_comp_perm_smul_iff (hfg : Antivary f g) :
     ∑ i, f i • g i < ∑ i, f (σ i) • g i ↔ ¬Antivary (f ∘ σ) g := by
   simp [(hfg.antivary_on _).sum_smul_lt_sum_comp_perm_smul_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iff
+-/
 
 end Smul
 
@@ -352,13 +400,16 @@ section Mul
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
+#print MonovaryOn.sum_mul_comp_perm_le_sum_mul /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
     ∑ i in s, f i * g (σ i) ≤ ∑ i in s, f i * g i :=
   hfg.sum_smul_comp_perm_le_sum_smul hσ
 #align monovary_on.sum_mul_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mul
+-/
 
+#print MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -367,7 +418,9 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
     ∑ i in s, f i * g (σ i) = ∑ i in s, f i * g i ↔ MonovaryOn f (g ∘ σ) s :=
   hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff
+-/
 
+#print MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -376,14 +429,18 @@ theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (hfg : MonovaryOn f g s)
     ∑ i in s, f i • g (σ i) < ∑ i in s, f i • g i ↔ ¬MonovaryOn f (g ∘ σ) s :=
   hfg.sum_smul_comp_perm_lt_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff
+-/
 
+#print MonovaryOn.sum_comp_perm_mul_le_sum_mul /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
     ∑ i in s, f (σ i) * g i ≤ ∑ i in s, f i * g i :=
   hfg.sum_comp_perm_smul_le_sum_smul hσ
 #align monovary_on.sum_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mul
+-/
 
+#print MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
@@ -392,7 +449,9 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
     ∑ i in s, f (σ i) * g i = ∑ i in s, f i * g i ↔ MonovaryOn (f ∘ σ) g s :=
   hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff
+-/
 
+#print MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
@@ -401,14 +460,18 @@ theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
     ∑ i in s, f (σ i) * g i < ∑ i in s, f i * g i ↔ ¬MonovaryOn (f ∘ σ) g s :=
   hfg.sum_comp_perm_smul_lt_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff
+-/
 
+#print AntivaryOn.sum_mul_le_sum_mul_comp_perm /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
     ∑ i in s, f i * g i ≤ ∑ i in s, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm hσ
 #align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_perm
+-/
 
+#print AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -417,7 +480,9 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
     ∑ i in s, f i * g (σ i) = ∑ i in s, f i * g i ↔ AntivaryOn f (g ∘ σ) s :=
   hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff
+-/
 
+#print AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -426,14 +491,18 @@ theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
     ∑ i in s, f i * g i < ∑ i in s, f i * g (σ i) ↔ ¬AntivaryOn f (g ∘ σ) s :=
   hfg.sum_smul_lt_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff
+-/
 
+#print AntivaryOn.sum_mul_le_sum_comp_perm_mul /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
     ∑ i in s, f i * g i ≤ ∑ i in s, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul hσ
 #align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mul
+-/
 
+#print AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -442,7 +511,9 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
     ∑ i in s, f (σ i) * g i = ∑ i in s, f i * g i ↔ AntivaryOn (f ∘ σ) g s :=
   hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff
+-/
 
+#print AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -451,16 +522,20 @@ theorem AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
     ∑ i in s, f i * g i < ∑ i in s, f (σ i) * g i ↔ ¬AntivaryOn (f ∘ σ) g s :=
   hfg.sum_smul_lt_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_lt_sum_comp_perm_mul_iff AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff
+-/
 
 variable [Fintype ι]
 
+#print Monovary.sum_mul_comp_perm_le_sum_mul /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
     ∑ i, f i * g (σ i) ≤ ∑ i, f i * g i :=
   hfg.sum_smul_comp_perm_le_sum_smul
 #align monovary.sum_mul_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mul
+-/
 
+#print Monovary.sum_mul_comp_perm_eq_sum_mul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -468,7 +543,9 @@ theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
     ∑ i, f i * g (σ i) = ∑ i, f i * g i ↔ Monovary f (g ∘ σ) :=
   hfg.sum_smul_comp_perm_eq_sum_smul_iff
 #align monovary.sum_mul_comp_perm_eq_sum_mul_iff Monovary.sum_mul_comp_perm_eq_sum_mul_iff
+-/
 
+#print Monovary.sum_mul_comp_perm_lt_sum_mul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -476,14 +553,18 @@ theorem Monovary.sum_mul_comp_perm_lt_sum_mul_iff (hfg : Monovary f g) :
     ∑ i, f i * g (σ i) < ∑ i, f i * g i ↔ ¬Monovary f (g ∘ σ) :=
   hfg.sum_smul_comp_perm_lt_sum_smul_iff
 #align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iff
+-/
 
+#print Monovary.sum_comp_perm_mul_le_sum_mul /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
     ∑ i, f (σ i) * g i ≤ ∑ i, f i * g i :=
   hfg.sum_comp_perm_smul_le_sum_smul
 #align monovary.sum_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mul
+-/
 
+#print Monovary.sum_comp_perm_mul_eq_sum_mul_iff /-
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -491,7 +572,9 @@ theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
     ∑ i, f (σ i) * g i = ∑ i, f i * g i ↔ Monovary (f ∘ σ) g :=
   hfg.sum_comp_perm_smul_eq_sum_smul_iff
 #align monovary.sum_comp_perm_mul_eq_sum_mul_iff Monovary.sum_comp_perm_mul_eq_sum_mul_iff
+-/
 
+#print Monovary.sum_comp_perm_mul_lt_sum_mul_iff /-
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -499,14 +582,18 @@ theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
     ∑ i, f (σ i) * g i < ∑ i, f i * g i ↔ ¬Monovary (f ∘ σ) g :=
   hfg.sum_comp_perm_smul_lt_sum_smul_iff
 #align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iff
+-/
 
+#print Antivary.sum_mul_le_sum_mul_comp_perm /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
     ∑ i, f i * g i ≤ ∑ i, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm
 #align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_perm
+-/
 
+#print Antivary.sum_mul_eq_sum_mul_comp_perm_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -514,7 +601,9 @@ theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
     ∑ i, f i * g (σ i) = ∑ i, f i * g i ↔ Antivary f (g ∘ σ) :=
   hfg.sum_smul_eq_sum_smul_comp_perm_iff
 #align antivary.sum_mul_eq_sum_mul_comp_perm_iff Antivary.sum_mul_eq_sum_mul_comp_perm_iff
+-/
 
+#print Antivary.sum_mul_lt_sum_mul_comp_perm_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -522,14 +611,18 @@ theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
     ∑ i, f i • g i < ∑ i, f i • g (σ i) ↔ ¬Antivary f (g ∘ σ) :=
   hfg.sum_smul_lt_sum_smul_comp_perm_iff
 #align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iff
+-/
 
+#print Antivary.sum_mul_le_sum_comp_perm_mul /-
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
     ∑ i, f i * g i ≤ ∑ i, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul
 #align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mul
+-/
 
+#print Antivary.sum_mul_eq_sum_comp_perm_mul_iff /-
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -537,7 +630,9 @@ theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
     ∑ i, f (σ i) * g i = ∑ i, f i * g i ↔ Antivary (f ∘ σ) g :=
   hfg.sum_smul_eq_sum_comp_perm_smul_iff
 #align antivary.sum_mul_eq_sum_comp_perm_mul_iff Antivary.sum_mul_eq_sum_comp_perm_mul_iff
+-/
 
+#print Antivary.sum_mul_lt_sum_comp_perm_mul_iff /-
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -545,6 +640,7 @@ theorem Antivary.sum_mul_lt_sum_comp_perm_mul_iff (hfg : Antivary f g) :
     ∑ i, f i * g i < ∑ i, f (σ i) * g i ↔ ¬Antivary (f ∘ σ) g :=
   hfg.sum_smul_lt_sum_comp_perm_smul_iff
 #align antivary.sum_mul_lt_sum_comp_perm_mul_iff Antivary.sum_mul_lt_sum_comp_perm_mul_iff
+-/
 
 end Mul
 

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

@@ -66,7 +66,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
-    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f i • g (σ i)) ≤ ∑ i in s, f i • g i := by
+    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g (σ i) ≤ ∑ i in s, f i • g i := by
   classical
   revert hσ σ hfg
   apply Finset.induction_on_max_value (fun i => toLex (g i, f i)) s
@@ -116,7 +116,7 @@ which monovary together, is unchanged by a permutation if and only if `f` and `g
 together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i • g (σ i)) = ∑ i in s, f i • g i) ↔ MonovaryOn f (g ∘ σ) s := by
+    ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ MonovaryOn f (g ∘ σ) s := by
   classical
   refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
   · rw [MonovaryOn] at h 
@@ -146,7 +146,7 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i • g (σ i)) < ∑ i in s, f i • g i) ↔ ¬MonovaryOn f (g ∘ σ) s := by
+    ∑ i in s, f i • g (σ i) < ∑ i in s, f i • g i ↔ ¬MonovaryOn f (g ∘ σ) s := by
   simp [← hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ, lt_iff_le_and_ne,
     hfg.sum_smul_comp_perm_le_sum_smul hσ]
 #align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff
@@ -154,7 +154,7 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
-    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f (σ i) • g i) ≤ ∑ i in s, f i • g i :=
+    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f (σ i) • g i ≤ ∑ i in s, f i • g i :=
   by
   convert
     hfg.sum_smul_comp_perm_le_sum_smul
@@ -168,7 +168,7 @@ which monovary together, is unchanged by a permutation if and only if `f ∘ σ`
 together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f (σ i) • g i) = ∑ i in s, f i • g i) ↔ MonovaryOn (f ∘ σ) g s :=
+    ∑ i in s, f (σ i) • g i = ∑ i in s, f i • g i ↔ MonovaryOn (f ∘ σ) g s :=
   by
   have hσinv : {x | σ⁻¹ x ≠ x} ⊆ s := (set_support_inv_eq _).Subset.trans hσ
   refine'
@@ -188,7 +188,7 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f (σ i) • g i) < ∑ i in s, f i • g i) ↔ ¬MonovaryOn (f ∘ σ) g s := by
+    ∑ i in s, f (σ i) • g i < ∑ i in s, f i • g i ↔ ¬MonovaryOn (f ∘ σ) g s := by
   simp [← hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ, lt_iff_le_and_ne,
     hfg.sum_comp_perm_smul_le_sum_smul hσ]
 #align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff
@@ -196,7 +196,7 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
-    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f i • g (σ i) :=
+    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g i ≤ ∑ i in s, f i • g (σ i) :=
   hfg.dual_right.sum_smul_comp_perm_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
 
@@ -205,7 +205,7 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
 together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i • g (σ i)) = ∑ i in s, f i • g i) ↔ AntivaryOn f (g ∘ σ) s :=
+    ∑ i in s, f i • g (σ i) = ∑ i in s, f i • g i ↔ AntivaryOn f (g ∘ σ) s :=
   (hfg.dual_right.sum_smul_comp_perm_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff
 
@@ -214,7 +214,7 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i • g i) < ∑ i in s, f i • g (σ i)) ↔ ¬AntivaryOn f (g ∘ σ) s := by
+    ∑ i in s, f i • g i < ∑ i in s, f i • g (σ i) ↔ ¬AntivaryOn f (g ∘ σ) s := by
   simp [← hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ, lt_iff_le_and_ne, eq_comm,
     hfg.sum_smul_le_sum_smul_comp_perm hσ]
 #align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff
@@ -222,7 +222,7 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
-    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f (σ i) • g i :=
+    (hσ : {x | σ x ≠ x} ⊆ s) : ∑ i in s, f i • g i ≤ ∑ i in s, f (σ i) • g i :=
   hfg.dual_right.sum_comp_perm_smul_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
 
@@ -231,7 +231,7 @@ theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
 together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f (σ i) • g i) = ∑ i in s, f i • g i) ↔ AntivaryOn (f ∘ σ) g s :=
+    ∑ i in s, f (σ i) • g i = ∑ i in s, f i • g i ↔ AntivaryOn (f ∘ σ) g s :=
   (hfg.dual_right.sum_comp_perm_smul_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff
 
@@ -240,7 +240,7 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i • g i) < ∑ i in s, f (σ i) • g i) ↔ ¬AntivaryOn (f ∘ σ) g s := by
+    ∑ i in s, f i • g i < ∑ i in s, f (σ i) • g i ↔ ¬AntivaryOn (f ∘ σ) g s := by
   simp [← hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ, eq_comm, lt_iff_le_and_ne,
     hfg.sum_smul_le_sum_comp_perm_smul hσ]
 #align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff
@@ -250,7 +250,7 @@ variable [Fintype ι]
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
-    (∑ i, f i • g (σ i)) ≤ ∑ i, f i • g i :=
+    ∑ i, f i • g (σ i) ≤ ∑ i, f i • g i :=
   (hfg.MonovaryOn _).sum_smul_comp_perm_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_smul_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smul
 
@@ -258,7 +258,7 @@ theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
-    ((∑ i, f i • g (σ i)) = ∑ i, f i • g i) ↔ Monovary f (g ∘ σ) := by
+    ∑ i, f i • g (σ i) = ∑ i, f i • g i ↔ Monovary f (g ∘ σ) := by
   simp [(hfg.monovary_on _).sum_smul_comp_perm_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iff
 
@@ -266,14 +266,14 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
-    ((∑ i, f i • g (σ i)) < ∑ i, f i • g i) ↔ ¬Monovary f (g ∘ σ) := by
+    ∑ i, f i • g (σ i) < ∑ i, f i • g i ↔ ¬Monovary f (g ∘ σ) := by
   simp [(hfg.monovary_on _).sum_smul_comp_perm_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iff
 
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
-    (∑ i, f (σ i) • g i) ≤ ∑ i, f i • g i :=
+    ∑ i, f (σ i) • g i ≤ ∑ i, f i • g i :=
   (hfg.MonovaryOn _).sum_comp_perm_smul_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smul
 
@@ -281,7 +281,7 @@ theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
-    ((∑ i, f (σ i) • g i) = ∑ i, f i • g i) ↔ Monovary (f ∘ σ) g := by
+    ∑ i, f (σ i) • g i = ∑ i, f i • g i ↔ Monovary (f ∘ σ) g := by
   simp [(hfg.monovary_on _).sum_comp_perm_smul_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iff
 
@@ -289,14 +289,14 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
-    ((∑ i, f (σ i) • g i) < ∑ i, f i • g i) ↔ ¬Monovary (f ∘ σ) g := by
+    ∑ i, f (σ i) • g i < ∑ i, f i • g i ↔ ¬Monovary (f ∘ σ) g := by
   simp [(hfg.monovary_on _).sum_comp_perm_smul_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iff
 
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
-    (∑ i, f i • g i) ≤ ∑ i, f i • g (σ i) :=
+    ∑ i, f i • g i ≤ ∑ i, f i • g (σ i) :=
   (hfg.AntivaryOn _).sum_smul_le_sum_smul_comp_perm fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_perm
 
@@ -304,7 +304,7 @@ theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
-    ((∑ i, f i • g (σ i)) = ∑ i, f i • g i) ↔ Antivary f (g ∘ σ) := by
+    ∑ i, f i • g (σ i) = ∑ i, f i • g i ↔ Antivary f (g ∘ σ) := by
   simp [(hfg.antivary_on _).sum_smul_eq_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iff
 
@@ -312,14 +312,14 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
-    ((∑ i, f i • g i) < ∑ i, f i • g (σ i)) ↔ ¬Antivary f (g ∘ σ) := by
+    ∑ i, f i • g i < ∑ i, f i • g (σ i) ↔ ¬Antivary f (g ∘ σ) := by
   simp [(hfg.antivary_on _).sum_smul_lt_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iff
 
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
-    (∑ i, f i • g i) ≤ ∑ i, f (σ i) • g i :=
+    ∑ i, f i • g i ≤ ∑ i, f (σ i) • g i :=
   (hfg.AntivaryOn _).sum_smul_le_sum_comp_perm_smul fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smul
 
@@ -327,7 +327,7 @@ theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
-    ((∑ i, f (σ i) • g i) = ∑ i, f i • g i) ↔ Antivary (f ∘ σ) g := by
+    ∑ i, f (σ i) • g i = ∑ i, f i • g i ↔ Antivary (f ∘ σ) g := by
   simp [(hfg.antivary_on _).sum_smul_eq_sum_comp_perm_smul_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iff
 
@@ -335,7 +335,7 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_lt_sum_comp_perm_smul_iff (hfg : Antivary f g) :
-    ((∑ i, f i • g i) < ∑ i, f (σ i) • g i) ↔ ¬Antivary (f ∘ σ) g := by
+    ∑ i, f i • g i < ∑ i, f (σ i) • g i ↔ ¬Antivary (f ∘ σ) g := by
   simp [(hfg.antivary_on _).sum_smul_lt_sum_comp_perm_smul_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iff
 
@@ -355,7 +355,7 @@ variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
-    (∑ i in s, f i * g (σ i)) ≤ ∑ i in s, f i * g i :=
+    ∑ i in s, f i * g (σ i) ≤ ∑ i in s, f i * g i :=
   hfg.sum_smul_comp_perm_le_sum_smul hσ
 #align monovary_on.sum_mul_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mul
 
@@ -364,7 +364,7 @@ which monovary together, is unchanged by a permutation if and only if `f` and `g
 together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i * g (σ i)) = ∑ i in s, f i * g i) ↔ MonovaryOn f (g ∘ σ) s :=
+    ∑ i in s, f i * g (σ i) = ∑ i in s, f i * g i ↔ MonovaryOn f (g ∘ σ) s :=
   hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff
 
@@ -373,14 +373,14 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i • g (σ i)) < ∑ i in s, f i • g i) ↔ ¬MonovaryOn f (g ∘ σ) s :=
+    ∑ i in s, f i • g (σ i) < ∑ i in s, f i • g i ↔ ¬MonovaryOn f (g ∘ σ) s :=
   hfg.sum_smul_comp_perm_lt_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
-    (∑ i in s, f (σ i) * g i) ≤ ∑ i in s, f i * g i :=
+    ∑ i in s, f (σ i) * g i ≤ ∑ i in s, f i * g i :=
   hfg.sum_comp_perm_smul_le_sum_smul hσ
 #align monovary_on.sum_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mul
 
@@ -389,7 +389,7 @@ which monovary together, is unchanged by a permutation if and only if `f ∘ σ`
 together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f (σ i) * g i) = ∑ i in s, f i * g i) ↔ MonovaryOn (f ∘ σ) g s :=
+    ∑ i in s, f (σ i) * g i = ∑ i in s, f i * g i ↔ MonovaryOn (f ∘ σ) g s :=
   hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff
 
@@ -398,14 +398,14 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f (σ i) * g i) < ∑ i in s, f i * g i) ↔ ¬MonovaryOn (f ∘ σ) g s :=
+    ∑ i in s, f (σ i) * g i < ∑ i in s, f i * g i ↔ ¬MonovaryOn (f ∘ σ) g s :=
   hfg.sum_comp_perm_smul_lt_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
-    (∑ i in s, f i * g i) ≤ ∑ i in s, f i * g (σ i) :=
+    ∑ i in s, f i * g i ≤ ∑ i in s, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm hσ
 #align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_perm
 
@@ -414,7 +414,7 @@ which antivary together, is unchanged by a permutation if and only if `f` and `g
 together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i * g (σ i)) = ∑ i in s, f i * g i) ↔ AntivaryOn f (g ∘ σ) s :=
+    ∑ i in s, f i * g (σ i) = ∑ i in s, f i * g i ↔ AntivaryOn f (g ∘ σ) s :=
   hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff
 
@@ -423,14 +423,14 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i * g i) < ∑ i in s, f i * g (σ i)) ↔ ¬AntivaryOn f (g ∘ σ) s :=
+    ∑ i in s, f i * g i < ∑ i in s, f i * g (σ i) ↔ ¬AntivaryOn f (g ∘ σ) s :=
   hfg.sum_smul_lt_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
-    (∑ i in s, f i * g i) ≤ ∑ i in s, f (σ i) * g i :=
+    ∑ i in s, f i * g i ≤ ∑ i in s, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul hσ
 #align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mul
 
@@ -439,7 +439,7 @@ which antivary together, is unchanged by a permutation if and only if `f ∘ σ`
 together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f (σ i) * g i) = ∑ i in s, f i * g i) ↔ AntivaryOn (f ∘ σ) g s :=
+    ∑ i in s, f (σ i) * g i = ∑ i in s, f i * g i ↔ AntivaryOn (f ∘ σ) g s :=
   hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff
 
@@ -448,7 +448,7 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
     (hσ : {x | σ x ≠ x} ⊆ s) :
-    ((∑ i in s, f i * g i) < ∑ i in s, f (σ i) * g i) ↔ ¬AntivaryOn (f ∘ σ) g s :=
+    ∑ i in s, f i * g i < ∑ i in s, f (σ i) * g i ↔ ¬AntivaryOn (f ∘ σ) g s :=
   hfg.sum_smul_lt_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_lt_sum_comp_perm_mul_iff AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff
 
@@ -457,7 +457,7 @@ variable [Fintype ι]
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
-    (∑ i, f i * g (σ i)) ≤ ∑ i, f i * g i :=
+    ∑ i, f i * g (σ i) ≤ ∑ i, f i * g i :=
   hfg.sum_smul_comp_perm_le_sum_smul
 #align monovary.sum_mul_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mul
 
@@ -465,7 +465,7 @@ theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
-    ((∑ i, f i * g (σ i)) = ∑ i, f i * g i) ↔ Monovary f (g ∘ σ) :=
+    ∑ i, f i * g (σ i) = ∑ i, f i * g i ↔ Monovary f (g ∘ σ) :=
   hfg.sum_smul_comp_perm_eq_sum_smul_iff
 #align monovary.sum_mul_comp_perm_eq_sum_mul_iff Monovary.sum_mul_comp_perm_eq_sum_mul_iff
 
@@ -473,14 +473,14 @@ theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_mul_comp_perm_lt_sum_mul_iff (hfg : Monovary f g) :
-    ((∑ i, f i * g (σ i)) < ∑ i, f i * g i) ↔ ¬Monovary f (g ∘ σ) :=
+    ∑ i, f i * g (σ i) < ∑ i, f i * g i ↔ ¬Monovary f (g ∘ σ) :=
   hfg.sum_smul_comp_perm_lt_sum_smul_iff
 #align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
-    (∑ i, f (σ i) * g i) ≤ ∑ i, f i * g i :=
+    ∑ i, f (σ i) * g i ≤ ∑ i, f i * g i :=
   hfg.sum_comp_perm_smul_le_sum_smul
 #align monovary.sum_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mul
 
@@ -488,7 +488,7 @@ theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
-    ((∑ i, f (σ i) * g i) = ∑ i, f i * g i) ↔ Monovary (f ∘ σ) g :=
+    ∑ i, f (σ i) * g i = ∑ i, f i * g i ↔ Monovary (f ∘ σ) g :=
   hfg.sum_comp_perm_smul_eq_sum_smul_iff
 #align monovary.sum_comp_perm_mul_eq_sum_mul_iff Monovary.sum_comp_perm_mul_eq_sum_mul_iff
 
@@ -496,14 +496,14 @@ theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
-    ((∑ i, f (σ i) * g i) < ∑ i, f i * g i) ↔ ¬Monovary (f ∘ σ) g :=
+    ∑ i, f (σ i) * g i < ∑ i, f i * g i ↔ ¬Monovary (f ∘ σ) g :=
   hfg.sum_comp_perm_smul_lt_sum_smul_iff
 #align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
-    (∑ i, f i * g i) ≤ ∑ i, f i * g (σ i) :=
+    ∑ i, f i * g i ≤ ∑ i, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm
 #align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_perm
 
@@ -511,7 +511,7 @@ theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
-    ((∑ i, f i * g (σ i)) = ∑ i, f i * g i) ↔ Antivary f (g ∘ σ) :=
+    ∑ i, f i * g (σ i) = ∑ i, f i * g i ↔ Antivary f (g ∘ σ) :=
   hfg.sum_smul_eq_sum_smul_comp_perm_iff
 #align antivary.sum_mul_eq_sum_mul_comp_perm_iff Antivary.sum_mul_eq_sum_mul_comp_perm_iff
 
@@ -519,14 +519,14 @@ theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
-    ((∑ i, f i • g i) < ∑ i, f i • g (σ i)) ↔ ¬Antivary f (g ∘ σ) :=
+    ∑ i, f i • g i < ∑ i, f i • g (σ i) ↔ ¬Antivary f (g ∘ σ) :=
   hfg.sum_smul_lt_sum_smul_comp_perm_iff
 #align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
-    (∑ i, f i * g i) ≤ ∑ i, f (σ i) * g i :=
+    ∑ i, f i * g i ≤ ∑ i, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul
 #align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mul
 
@@ -534,7 +534,7 @@ theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
-    ((∑ i, f (σ i) * g i) = ∑ i, f i * g i) ↔ Antivary (f ∘ σ) g :=
+    ∑ i, f (σ i) * g i = ∑ i, f i * g i ↔ Antivary (f ∘ σ) g :=
   hfg.sum_smul_eq_sum_comp_perm_smul_iff
 #align antivary.sum_mul_eq_sum_comp_perm_mul_iff Antivary.sum_mul_eq_sum_comp_perm_mul_iff
 
@@ -542,7 +542,7 @@ theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_lt_sum_comp_perm_mul_iff (hfg : Antivary f g) :
-    ((∑ i, f i * g i) < ∑ i, f (σ i) * g i) ↔ ¬Antivary (f ∘ σ) g :=
+    ∑ i, f i * g i < ∑ i, f (σ i) * g i ↔ ¬Antivary (f ∘ σ) g :=
   hfg.sum_smul_lt_sum_comp_perm_smul_iff
 #align antivary.sum_mul_lt_sum_comp_perm_mul_iff Antivary.sum_mul_lt_sum_comp_perm_mul_iff
 

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

@@ -66,86 +66,86 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i • g (σ i)) ≤ ∑ i in s, f i • g i := by
+    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f i • g (σ i)) ≤ ∑ i in s, f i • g i := by
   classical
-    revert hσ σ hfg
-    apply Finset.induction_on_max_value (fun i => toLex (g i, f i)) s
-    · simp only [le_rfl, Finset.sum_empty, imp_true_iff]
-    intro a s has hamax hind σ hfg hσ
-    set τ : perm ι := σ.trans (swap a (σ a)) with hτ
-    have hτs : { x | τ x ≠ x } ⊆ s := by
-      intro x hx
-      simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx 
-      split_ifs  at hx  with h₁ h₂ h₃
-      · obtain rfl | hax := eq_or_ne x a
-        · contradiction
-        · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
-      · exact (hx <| σ.injective h₂.symm).elim
-      · exact mem_of_mem_insert_of_ne (hσ hx) (ne_of_apply_ne _ h₂)
-    specialize hind (hfg.subset <| subset_insert _ _) hτs
-    simp_rw [sum_insert has]
-    refine' le_trans _ (add_le_add_left hind _)
-    obtain hσa | hσa := eq_or_ne a (σ a)
-    · rw [hτ, ← hσa, swap_self, trans_refl]
-    have h1s : σ⁻¹ a ∈ s := by
-      rw [Ne.def, ← inv_eq_iff_eq] at hσa 
-      refine' mem_of_mem_insert_of_ne (hσ fun h => hσa _) hσa
-      rwa [apply_inv_self, eq_comm] at h 
-    simp only [← s.sum_erase_add _ h1s, add_comm]
-    rw [← add_assoc, ← add_assoc]
-    simp only [hτ, swap_apply_left, Function.comp_apply, Equiv.coe_trans, apply_inv_self]
-    refine' add_le_add (smul_add_smul_le_smul_add_smul' _ _) (sum_congr rfl fun x hx => _).le
-    · specialize hamax (σ⁻¹ a) h1s
-      rw [Prod.Lex.le_iff] at hamax 
-      cases hamax
-      · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
-      · exact hamax.2
-    · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
-      rw [Prod.Lex.le_iff] at hamax 
-      cases hamax
-      · exact hamax.le
-      · exact hamax.1.le
-    · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx 
-      rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
-      rintro rfl
-      exact has hx.2
+  revert hσ σ hfg
+  apply Finset.induction_on_max_value (fun i => toLex (g i, f i)) s
+  · simp only [le_rfl, Finset.sum_empty, imp_true_iff]
+  intro a s has hamax hind σ hfg hσ
+  set τ : perm ι := σ.trans (swap a (σ a)) with hτ
+  have hτs : {x | τ x ≠ x} ⊆ s := by
+    intro x hx
+    simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx 
+    split_ifs at hx  with h₁ h₂ h₃
+    · obtain rfl | hax := eq_or_ne x a
+      · contradiction
+      · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
+    · exact (hx <| σ.injective h₂.symm).elim
+    · exact mem_of_mem_insert_of_ne (hσ hx) (ne_of_apply_ne _ h₂)
+  specialize hind (hfg.subset <| subset_insert _ _) hτs
+  simp_rw [sum_insert has]
+  refine' le_trans _ (add_le_add_left hind _)
+  obtain hσa | hσa := eq_or_ne a (σ a)
+  · rw [hτ, ← hσa, swap_self, trans_refl]
+  have h1s : σ⁻¹ a ∈ s := by
+    rw [Ne.def, ← inv_eq_iff_eq] at hσa 
+    refine' mem_of_mem_insert_of_ne (hσ fun h => hσa _) hσa
+    rwa [apply_inv_self, eq_comm] at h 
+  simp only [← s.sum_erase_add _ h1s, add_comm]
+  rw [← add_assoc, ← add_assoc]
+  simp only [hτ, swap_apply_left, Function.comp_apply, Equiv.coe_trans, apply_inv_self]
+  refine' add_le_add (smul_add_smul_le_smul_add_smul' _ _) (sum_congr rfl fun x hx => _).le
+  · specialize hamax (σ⁻¹ a) h1s
+    rw [Prod.Lex.le_iff] at hamax 
+    cases hamax
+    · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
+    · exact hamax.2
+  · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
+    rw [Prod.Lex.le_iff] at hamax 
+    cases hamax
+    · exact hamax.le
+    · exact hamax.1.le
+  · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx 
+    rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
+    rintro rfl
+    exact has hx.2
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
 
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i • g (σ i)) = ∑ i in s, f i • g i) ↔ MonovaryOn f (g ∘ σ) s := by
   classical
-    refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
-    · rw [MonovaryOn] at h 
-      push_neg  at h 
-      obtain ⟨x, hx, y, hy, hgxy, hfxy⟩ := h
-      set τ : perm ι := (swap x y).trans σ
-      have hτs : { x | τ x ≠ x } ⊆ s :=
-        by
-        refine' (set_support_mul_subset σ <| swap x y).trans (Set.union_subset hσ fun z hz => _)
-        obtain ⟨_, rfl | rfl⟩ := swap_apply_ne_self_iff.1 hz <;> assumption
-      refine' ((hfg.sum_smul_comp_perm_le_sum_smul hτs).trans_lt' _).Ne
-      obtain rfl | hxy := eq_or_ne x y
-      · cases lt_irrefl _ hfxy
-      simp only [← s.sum_erase_add _ hx, ← (s.erase x).sum_erase_add _ (mem_erase.2 ⟨hxy.symm, hy⟩),
-        add_assoc, Equiv.coe_trans, Function.comp_apply, swap_apply_right, swap_apply_left]
-      refine'
-        add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz => _).le
-          (smul_add_smul_lt_smul_add_smul hfxy hgxy)
-      simp_rw [mem_erase] at hz 
-      rw [swap_apply_of_ne_of_ne hz.2.1 hz.1]
-    · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
-      simp_rw [Function.comp_apply, apply_inv_self]
+  refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
+  · rw [MonovaryOn] at h 
+    push_neg at h 
+    obtain ⟨x, hx, y, hy, hgxy, hfxy⟩ := h
+    set τ : perm ι := (swap x y).trans σ
+    have hτs : {x | τ x ≠ x} ⊆ s :=
+      by
+      refine' (set_support_mul_subset σ <| swap x y).trans (Set.union_subset hσ fun z hz => _)
+      obtain ⟨_, rfl | rfl⟩ := swap_apply_ne_self_iff.1 hz <;> assumption
+    refine' ((hfg.sum_smul_comp_perm_le_sum_smul hτs).trans_lt' _).Ne
+    obtain rfl | hxy := eq_or_ne x y
+    · cases lt_irrefl _ hfxy
+    simp only [← s.sum_erase_add _ hx, ← (s.erase x).sum_erase_add _ (mem_erase.2 ⟨hxy.symm, hy⟩),
+      add_assoc, Equiv.coe_trans, Function.comp_apply, swap_apply_right, swap_apply_left]
+    refine'
+      add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz => _).le
+        (smul_add_smul_lt_smul_add_smul hfxy hgxy)
+    simp_rw [mem_erase] at hz 
+    rw [swap_apply_of_ne_of_ne hz.2.1 hz.1]
+  · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
+    simp_rw [Function.comp_apply, apply_inv_self]
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
 
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i • g (σ i)) < ∑ i in s, f i • g i) ↔ ¬MonovaryOn f (g ∘ σ) s := by
   simp [← hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ, lt_iff_le_and_ne,
     hfg.sum_smul_comp_perm_le_sum_smul hσ]
@@ -154,10 +154,11 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f (σ i) • g i) ≤ ∑ i in s, f i • g i :=
+    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f (σ i) • g i) ≤ ∑ i in s, f i • g i :=
   by
-  convert hfg.sum_smul_comp_perm_le_sum_smul
-      (show { x | σ⁻¹ x ≠ x } ⊆ s by simp only [set_support_inv_eq, hσ]) using
+  convert
+    hfg.sum_smul_comp_perm_le_sum_smul
+      (show {x | σ⁻¹ x ≠ x} ⊆ s by simp only [set_support_inv_eq, hσ]) using
     1
   exact σ.sum_comp' s (fun i j => f i • g j) hσ
 #align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smul
@@ -166,10 +167,10 @@ theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f (σ i) • g i) = ∑ i in s, f i • g i) ↔ MonovaryOn (f ∘ σ) g s :=
   by
-  have hσinv : { x | σ⁻¹ x ≠ x } ⊆ s := (set_support_inv_eq _).Subset.trans hσ
+  have hσinv : {x | σ⁻¹ x ≠ x} ⊆ s := (set_support_inv_eq _).Subset.trans hσ
   refine'
     (Iff.trans _ <| hfg.sum_smul_comp_perm_eq_sum_smul_iff hσinv).trans ⟨fun h => _, fun h => _⟩
   · simpa only [σ.sum_comp' s (fun i j => f i • g j) hσ]
@@ -186,7 +187,7 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f (σ i) • g i) < ∑ i in s, f i • g i) ↔ ¬MonovaryOn (f ∘ σ) g s := by
   simp [← hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ, lt_iff_le_and_ne,
     hfg.sum_comp_perm_smul_le_sum_smul hσ]
@@ -195,7 +196,7 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f i • g (σ i) :=
+    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f i • g (σ i) :=
   hfg.dual_right.sum_smul_comp_perm_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
 
@@ -203,7 +204,7 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i • g (σ i)) = ∑ i in s, f i • g i) ↔ AntivaryOn f (g ∘ σ) s :=
   (hfg.dual_right.sum_smul_comp_perm_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff
@@ -212,7 +213,7 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i • g i) < ∑ i in s, f i • g (σ i)) ↔ ¬AntivaryOn f (g ∘ σ) s := by
   simp [← hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ, lt_iff_le_and_ne, eq_comm,
     hfg.sum_smul_le_sum_smul_comp_perm hσ]
@@ -221,7 +222,7 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f (σ i) • g i :=
+    (hσ : {x | σ x ≠ x} ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f (σ i) • g i :=
   hfg.dual_right.sum_comp_perm_smul_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
 
@@ -229,7 +230,7 @@ theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f (σ i) • g i) = ∑ i in s, f i • g i) ↔ AntivaryOn (f ∘ σ) g s :=
   (hfg.dual_right.sum_comp_perm_smul_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff
@@ -238,7 +239,7 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i • g i) < ∑ i in s, f (σ i) • g i) ↔ ¬AntivaryOn (f ∘ σ) g s := by
   simp [← hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ, eq_comm, lt_iff_le_and_ne,
     hfg.sum_smul_le_sum_comp_perm_smul hσ]
@@ -353,8 +354,8 @@ variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
-theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i * g (σ i)) ≤ ∑ i in s, f i * g i :=
+theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
+    (∑ i in s, f i * g (σ i)) ≤ ∑ i in s, f i * g i :=
   hfg.sum_smul_comp_perm_le_sum_smul hσ
 #align monovary_on.sum_mul_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mul
 
@@ -362,7 +363,7 @@ theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s)
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i * g (σ i)) = ∑ i in s, f i * g i) ↔ MonovaryOn f (g ∘ σ) s :=
   hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff
@@ -371,15 +372,15 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i • g (σ i)) < ∑ i in s, f i • g i) ↔ ¬MonovaryOn f (g ∘ σ) s :=
   hfg.sum_smul_comp_perm_lt_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
-theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f (σ i) * g i) ≤ ∑ i in s, f i * g i :=
+theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
+    (∑ i in s, f (σ i) * g i) ≤ ∑ i in s, f i * g i :=
   hfg.sum_comp_perm_smul_le_sum_smul hσ
 #align monovary_on.sum_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mul
 
@@ -387,7 +388,7 @@ theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s)
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f (σ i) * g i) = ∑ i in s, f i * g i) ↔ MonovaryOn (f ∘ σ) g s :=
   hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff
@@ -396,15 +397,15 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f (σ i) * g i) < ∑ i in s, f i * g i) ↔ ¬MonovaryOn (f ∘ σ) g s :=
   hfg.sum_comp_perm_smul_lt_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
-theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i * g i) ≤ ∑ i in s, f i * g (σ i) :=
+theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
+    (∑ i in s, f i * g i) ≤ ∑ i in s, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm hσ
 #align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_perm
 
@@ -412,7 +413,7 @@ theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i * g (σ i)) = ∑ i in s, f i * g i) ↔ AntivaryOn f (g ∘ σ) s :=
   hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff
@@ -421,15 +422,15 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i * g i) < ∑ i in s, f i * g (σ i)) ↔ ¬AntivaryOn f (g ∘ σ) s :=
   hfg.sum_smul_lt_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff
 
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
-theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i * g i) ≤ ∑ i in s, f (σ i) * g i :=
+theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s) (hσ : {x | σ x ≠ x} ⊆ s) :
+    (∑ i in s, f i * g i) ≤ ∑ i in s, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul hσ
 #align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mul
 
@@ -437,7 +438,7 @@ theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f (σ i) * g i) = ∑ i in s, f i * g i) ↔ AntivaryOn (f ∘ σ) g s :=
   hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff
@@ -446,7 +447,7 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) :
+    (hσ : {x | σ x ≠ x} ⊆ s) :
     ((∑ i in s, f i * g i) < ∑ i in s, f (σ i) * g i) ↔ ¬AntivaryOn (f ∘ σ) g s :=
   hfg.sum_smul_lt_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_lt_sum_comp_perm_mul_iff AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff

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

@@ -75,8 +75,8 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
     set τ : perm ι := σ.trans (swap a (σ a)) with hτ
     have hτs : { x | τ x ≠ x } ⊆ s := by
       intro x hx
-      simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx
-      split_ifs  at hx with h₁ h₂ h₃
+      simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx 
+      split_ifs  at hx  with h₁ h₂ h₃
       · obtain rfl | hax := eq_or_ne x a
         · contradiction
         · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
@@ -88,24 +88,24 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
     obtain hσa | hσa := eq_or_ne a (σ a)
     · rw [hτ, ← hσa, swap_self, trans_refl]
     have h1s : σ⁻¹ a ∈ s := by
-      rw [Ne.def, ← inv_eq_iff_eq] at hσa
+      rw [Ne.def, ← inv_eq_iff_eq] at hσa 
       refine' mem_of_mem_insert_of_ne (hσ fun h => hσa _) hσa
-      rwa [apply_inv_self, eq_comm] at h
+      rwa [apply_inv_self, eq_comm] at h 
     simp only [← s.sum_erase_add _ h1s, add_comm]
     rw [← add_assoc, ← add_assoc]
     simp only [hτ, swap_apply_left, Function.comp_apply, Equiv.coe_trans, apply_inv_self]
     refine' add_le_add (smul_add_smul_le_smul_add_smul' _ _) (sum_congr rfl fun x hx => _).le
     · specialize hamax (σ⁻¹ a) h1s
-      rw [Prod.Lex.le_iff] at hamax
+      rw [Prod.Lex.le_iff] at hamax 
       cases hamax
       · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
       · exact hamax.2
     · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
-      rw [Prod.Lex.le_iff] at hamax
+      rw [Prod.Lex.le_iff] at hamax 
       cases hamax
       · exact hamax.le
       · exact hamax.1.le
-    · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx
+    · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx 
       rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
       rintro rfl
       exact has hx.2
@@ -119,8 +119,8 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     ((∑ i in s, f i • g (σ i)) = ∑ i in s, f i • g i) ↔ MonovaryOn f (g ∘ σ) s := by
   classical
     refine' ⟨not_imp_not.1 fun h => _, fun h => (hfg.sum_smul_comp_perm_le_sum_smul hσ).antisymm _⟩
-    · rw [MonovaryOn] at h
-      push_neg  at h
+    · rw [MonovaryOn] at h 
+      push_neg  at h 
       obtain ⟨x, hx, y, hy, hgxy, hfxy⟩ := h
       set τ : perm ι := (swap x y).trans σ
       have hτs : { x | τ x ≠ x } ⊆ s :=
@@ -135,7 +135,7 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
       refine'
         add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz => _).le
           (smul_add_smul_lt_smul_add_smul hfxy hgxy)
-      simp_rw [mem_erase] at hz
+      simp_rw [mem_erase] at hz 
       rw [swap_apply_of_ne_of_ne hz.2.1 hz.1]
     · convert h.sum_smul_comp_perm_le_sum_smul ((set_support_inv_eq _).Subset.trans hσ) using 1
       simp_rw [Function.comp_apply, apply_inv_self]

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

@@ -51,7 +51,7 @@ 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

@@ -63,9 +63,6 @@ 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_comp_perm_le_sum_smul -> MonovaryOn.sum_smul_comp_perm_le_sum_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
@@ -114,9 +111,6 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
       exact has hx.2
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
 
-/- warning: monovary_on.sum_smul_comp_perm_eq_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -147,9 +141,6 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
       simp_rw [Function.comp_apply, apply_inv_self]
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
 
-/- warning: monovary_on.sum_smul_comp_perm_lt_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -160,9 +151,6 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
     hfg.sum_smul_comp_perm_le_sum_smul hσ]
 #align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff
 
-/- warning: monovary_on.sum_comp_perm_smul_le_sum_smul -> MonovaryOn.sum_comp_perm_smul_le_sum_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
@@ -174,9 +162,6 @@ theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
   exact σ.sum_comp' s (fun i j => f i • g j) hσ
 #align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smul
 
-/- warning: monovary_on.sum_comp_perm_smul_eq_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
@@ -197,9 +182,6 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
       exact Set.image_perm hσinv
 #align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff
 
-/- warning: monovary_on.sum_comp_perm_smul_lt_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
@@ -210,9 +192,6 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
     hfg.sum_comp_perm_smul_le_sum_smul hσ]
 #align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff
 
-/- warning: antivary_on.sum_smul_le_sum_smul_comp_perm -> AntivaryOn.sum_smul_le_sum_smul_comp_perm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
@@ -220,9 +199,6 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
   hfg.dual_right.sum_smul_comp_perm_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
 
-/- warning: antivary_on.sum_smul_eq_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -232,9 +208,6 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
   (hfg.dual_right.sum_smul_comp_perm_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff
 
-/- warning: antivary_on.sum_smul_lt_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -245,9 +218,6 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
     hfg.sum_smul_le_sum_smul_comp_perm hσ]
 #align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff
 
-/- warning: antivary_on.sum_smul_le_sum_comp_perm_smul -> AntivaryOn.sum_smul_le_sum_comp_perm_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
@@ -255,9 +225,6 @@ theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
   hfg.dual_right.sum_comp_perm_smul_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
 
-/- warning: antivary_on.sum_smul_eq_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -267,9 +234,6 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
   (hfg.dual_right.sum_comp_perm_smul_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff
 
-/- warning: antivary_on.sum_smul_lt_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -282,9 +246,6 @@ theorem AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 
 variable [Fintype ι]
 
-/- warning: monovary.sum_smul_comp_perm_le_sum_smul -> Monovary.sum_smul_comp_perm_le_sum_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
@@ -292,9 +253,6 @@ theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_smul_comp_perm_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_smul_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smul
 
-/- warning: monovary.sum_smul_comp_perm_eq_sum_smul_iff -> Monovary.sum_smul_comp_perm_eq_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -303,9 +261,6 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_smul_comp_perm_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iff
 
-/- warning: monovary.sum_smul_comp_perm_lt_sum_smul_iff -> Monovary.sum_smul_comp_perm_lt_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -314,9 +269,6 @@ theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_smul_comp_perm_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iff
 
-/- warning: monovary.sum_comp_perm_smul_le_sum_smul -> Monovary.sum_comp_perm_smul_le_sum_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
@@ -324,9 +276,6 @@ theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_comp_perm_smul_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smul
 
-/- warning: monovary.sum_comp_perm_smul_eq_sum_smul_iff -> Monovary.sum_comp_perm_smul_eq_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -335,9 +284,6 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_comp_perm_smul_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iff
 
-/- warning: monovary.sum_comp_perm_smul_lt_sum_smul_iff -> Monovary.sum_comp_perm_smul_lt_sum_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -346,9 +292,6 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_comp_perm_smul_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iff
 
-/- warning: antivary.sum_smul_le_sum_smul_comp_perm -> Antivary.sum_smul_le_sum_smul_comp_perm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
@@ -356,9 +299,6 @@ theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
   (hfg.AntivaryOn _).sum_smul_le_sum_smul_comp_perm fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_perm
 
-/- warning: antivary.sum_smul_eq_sum_smul_comp_perm_iff -> Antivary.sum_smul_eq_sum_smul_comp_perm_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -367,9 +307,6 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
   simp [(hfg.antivary_on _).sum_smul_eq_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iff
 
-/- warning: antivary.sum_smul_lt_sum_smul_comp_perm_iff -> Antivary.sum_smul_lt_sum_smul_comp_perm_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -378,9 +315,6 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
   simp [(hfg.antivary_on _).sum_smul_lt_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iff
 
-/- warning: antivary.sum_smul_le_sum_comp_perm_smul -> Antivary.sum_smul_le_sum_comp_perm_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
@@ -388,9 +322,6 @@ theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
   (hfg.AntivaryOn _).sum_smul_le_sum_comp_perm_smul fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smul
 
-/- warning: antivary.sum_smul_eq_sum_comp_perm_smul_iff -> Antivary.sum_smul_eq_sum_comp_perm_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -399,9 +330,6 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
   simp [(hfg.antivary_on _).sum_smul_eq_sum_comp_perm_smul_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iff
 
-/- warning: antivary.sum_smul_lt_sum_comp_perm_smul_iff -> Antivary.sum_smul_lt_sum_comp_perm_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -423,12 +351,6 @@ 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_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s)
@@ -436,12 +358,6 @@ theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s)
   hfg.sum_smul_comp_perm_le_sum_smul hσ
 #align monovary_on.sum_mul_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mul
 
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 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -451,12 +367,6 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff
 
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 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -466,12 +376,6 @@ theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_smul_comp_perm_lt_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s)
@@ -479,12 +383,6 @@ theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s)
   hfg.sum_comp_perm_smul_le_sum_smul hσ
 #align monovary_on.sum_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mul
 
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 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
@@ -494,12 +392,6 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff
 
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 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
@@ -509,12 +401,6 @@ theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_comp_perm_smul_lt_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
@@ -522,12 +408,6 @@ theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
   hfg.sum_smul_le_sum_smul_comp_perm hσ
 #align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_perm
 
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 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -537,12 +417,6 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
   hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff
 
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 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -552,12 +426,6 @@ theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
   hfg.sum_smul_lt_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
@@ -565,12 +433,6 @@ theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
   hfg.sum_smul_le_sum_comp_perm_smul hσ
 #align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mul
 
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 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -580,12 +442,6 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
   hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff
 
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 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -597,12 +453,6 @@ theorem AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
 
 variable [Fintype ι]
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
@@ -610,12 +460,6 @@ theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
   hfg.sum_smul_comp_perm_le_sum_smul
 #align monovary.sum_mul_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mul
 
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 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -624,12 +468,6 @@ theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_smul_comp_perm_eq_sum_smul_iff
 #align monovary.sum_mul_comp_perm_eq_sum_mul_iff Monovary.sum_mul_comp_perm_eq_sum_mul_iff
 
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 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -638,12 +476,6 @@ theorem Monovary.sum_mul_comp_perm_lt_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_smul_comp_perm_lt_sum_smul_iff
 #align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iff
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
@@ -651,12 +483,6 @@ theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
   hfg.sum_comp_perm_smul_le_sum_smul
 #align monovary.sum_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mul
 
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 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -665,12 +491,6 @@ theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_comp_perm_smul_eq_sum_smul_iff
 #align monovary.sum_comp_perm_mul_eq_sum_mul_iff Monovary.sum_comp_perm_mul_eq_sum_mul_iff
 
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 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -679,12 +499,6 @@ theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_comp_perm_smul_lt_sum_smul_iff
 #align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iff
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
@@ -692,12 +506,6 @@ theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
   hfg.sum_smul_le_sum_smul_comp_perm
 #align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_perm
 
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 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -706,12 +514,6 @@ theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
   hfg.sum_smul_eq_sum_smul_comp_perm_iff
 #align antivary.sum_mul_eq_sum_mul_comp_perm_iff Antivary.sum_mul_eq_sum_mul_comp_perm_iff
 
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 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -720,12 +522,6 @@ theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
   hfg.sum_smul_lt_sum_smul_comp_perm_iff
 #align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iff
 
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 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
@@ -733,12 +529,6 @@ theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
   hfg.sum_smul_le_sum_comp_perm_smul
 #align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mul
 
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 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -747,12 +537,6 @@ theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
   hfg.sum_smul_eq_sum_comp_perm_smul_iff
 #align antivary.sum_mul_eq_sum_comp_perm_mul_iff Antivary.sum_mul_eq_sum_comp_perm_mul_iff
 
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-Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_comp_perm_mul_iff Antivary.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/

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

@@ -64,10 +64,7 @@ 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_comp_perm_le_sum_smul -> MonovaryOn.sum_smul_comp_perm_le_sum_smul is a dubious translation:
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(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} {σ : Equiv.Perm.{succ u3} ι} {f : ι -> α} {g : ι -> β}, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
@@ -118,10 +115,7 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
 
 /- warning: monovary_on.sum_smul_comp_perm_eq_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff is a dubious translation:
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s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
@@ -154,10 +148,7 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
 
 /- warning: monovary_on.sum_smul_comp_perm_lt_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff is a dubious translation:
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(OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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 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+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -170,10 +161,7 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 #align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff
 
 /- warning: monovary_on.sum_comp_perm_smul_le_sum_smul -> MonovaryOn.sum_comp_perm_smul_le_sum_smul is a dubious translation:
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-  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} {σ : Equiv.Perm.{succ 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 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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
@@ -187,10 +175,7 @@ theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
 #align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smul
 
 /- warning: monovary_on.sum_comp_perm_smul_eq_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff is a dubious translation:
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(LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
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s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
@@ -213,10 +198,7 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 #align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff
 
 /- warning: monovary_on.sum_comp_perm_smul_lt_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -229,10 +211,7 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 #align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff
 
 /- warning: antivary_on.sum_smul_le_sum_smul_comp_perm -> AntivaryOn.sum_smul_le_sum_smul_comp_perm is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
@@ -242,10 +221,7 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
 
 /- warning: antivary_on.sum_smul_eq_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff is a dubious translation:
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s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
@@ -257,10 +233,7 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 #align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff
 
 /- warning: antivary_on.sum_smul_lt_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff is a dubious translation:
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(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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -273,10 +246,7 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 #align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff
 
 /- warning: antivary_on.sum_smul_le_sum_comp_perm_smul -> AntivaryOn.sum_smul_le_sum_comp_perm_smul is a dubious translation:
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-  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} {σ : Equiv.Perm.{succ 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 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-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 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+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
@@ -286,10 +256,7 @@ theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
 
 /- warning: antivary_on.sum_smul_eq_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
-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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, 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(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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
@@ -301,10 +268,7 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 #align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff
 
 /- warning: antivary_on.sum_smul_lt_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff 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} {σ : Equiv.Perm.{succ 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 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(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} {σ : Equiv.Perm.{succ u3} ι} {f : ι -> α} {g : ι -> β}, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -319,10 +283,7 @@ theorem AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 variable [Fintype ι]
 
 /- warning: monovary.sum_smul_comp_perm_le_sum_smul -> Monovary.sum_smul_comp_perm_le_sum_smul is a dubious translation:
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-  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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
@@ -332,10 +293,7 @@ theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
 #align monovary.sum_smul_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smul
 
 /- warning: monovary.sum_smul_comp_perm_eq_sum_smul_iff -> Monovary.sum_smul_comp_perm_eq_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ 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(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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
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(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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 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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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
@@ -346,10 +304,7 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
 #align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iff
 
 /- warning: monovary.sum_smul_comp_perm_lt_sum_smul_iff -> Monovary.sum_smul_comp_perm_lt_sum_smul_iff is a dubious translation:
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-  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))] {σ : Equiv.Perm.{succ u1} ι} {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 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(AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
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(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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 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(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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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 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(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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -360,10 +315,7 @@ theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
 #align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iff
 
 /- warning: monovary.sum_comp_perm_smul_le_sum_smul -> Monovary.sum_comp_perm_smul_le_sum_smul is a dubious translation:
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-  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))] {σ : Equiv.Perm.{succ u1} ι} {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 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(AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i))))
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(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))] {σ : Equiv.Perm.{succ u3} ι} {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], 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(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_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
@@ -373,10 +325,7 @@ theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
 #align monovary.sum_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smul
 
 /- warning: monovary.sum_comp_perm_smul_eq_sum_smul_iff -> Monovary.sum_comp_perm_smul_eq_sum_smul_iff is a dubious translation:
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_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))] {σ : Equiv.Perm.{succ u1} ι} {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 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_inst_3)))) (f i) (g i)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
-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))] {σ : Equiv.Perm.{succ u3} ι} {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], 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(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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
@@ -387,10 +336,7 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
 #align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iff
 
 /- warning: monovary.sum_comp_perm_smul_lt_sum_smul_iff -> Monovary.sum_comp_perm_smul_lt_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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 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-  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 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+<too large>
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -401,10 +347,7 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
 #align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iff
 
 /- warning: antivary.sum_smul_le_sum_smul_comp_perm -> Antivary.sum_smul_le_sum_smul_comp_perm is a dubious translation:
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-  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))] {σ : Equiv.Perm.{succ u1} ι} {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 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_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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 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(LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
@@ -414,10 +357,7 @@ theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
 #align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_perm
 
 /- warning: antivary.sum_smul_eq_sum_smul_comp_perm_iff -> Antivary.sum_smul_eq_sum_smul_comp_perm_iff is a dubious translation:
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(LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g i)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
@@ -428,10 +368,7 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 #align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iff
 
 /- warning: antivary.sum_smul_lt_sum_smul_comp_perm_iff -> Antivary.sum_smul_lt_sum_smul_comp_perm_iff is a dubious translation:
-lean 3 declaration is
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_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))] {σ : Equiv.Perm.{succ u1} ι} {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 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_inst_2))) _inst_3)))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
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(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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 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(LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -442,10 +379,7 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 #align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iff
 
 /- warning: antivary.sum_smul_le_sum_comp_perm_smul -> Antivary.sum_smul_le_sum_comp_perm_smul is a dubious translation:
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_inst_2))) _inst_3)))) (f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i))))
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(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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
@@ -455,10 +389,7 @@ theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
 #align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smul
 
 /- warning: antivary.sum_smul_eq_sum_comp_perm_smul_iff -> Antivary.sum_smul_eq_sum_comp_perm_smul_iff is a dubious translation:
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-  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))] {σ : Equiv.Perm.{succ u1} ι} {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 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_inst_3)))) (f i) (g i)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
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(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))] {σ : Equiv.Perm.{succ u3} ι} {f : ι -> α} {g : ι -> β} [_inst_5 : Fintype.{u3} ι], 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(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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
@@ -469,10 +400,7 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
 #align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iff
 
 /- warning: antivary.sum_smul_lt_sum_comp_perm_smul_iff -> Antivary.sum_smul_lt_sum_comp_perm_smul_iff is a dubious translation:
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-  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))] {σ : Equiv.Perm.{succ u1} ι} {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 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_inst_2))) _inst_3)))) (f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
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-  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 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(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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if

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

@@ -67,7 +67,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
@@ -121,7 +121,7 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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)))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s)))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s)))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
@@ -157,7 +157,7 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -173,7 +173,7 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
@@ -190,7 +190,7 @@ theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
@@ -216,7 +216,7 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -232,7 +232,7 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
@@ -245,7 +245,7 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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)))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s)))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s)))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
@@ -260,7 +260,7 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -276,7 +276,7 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
@@ -289,7 +289,7 @@ theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
@@ -304,7 +304,7 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -322,7 +322,7 @@ variable [Fintype ι]
 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
@@ -335,7 +335,7 @@ theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
@@ -349,7 +349,7 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -363,7 +363,7 @@ theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
@@ -376,7 +376,7 @@ theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
@@ -390,7 +390,7 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -404,7 +404,7 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
@@ -417,7 +417,7 @@ theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
@@ -431,7 +431,7 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -445,7 +445,7 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
@@ -458,7 +458,7 @@ theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
@@ -472,7 +472,7 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
+  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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -499,7 +499,7 @@ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
@@ -512,7 +512,7 @@ theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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)))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s)))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
@@ -527,7 +527,7 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g i)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g i)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -542,7 +542,7 @@ theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
@@ -555,7 +555,7 @@ theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s)))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
@@ -570,7 +570,7 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -585,7 +585,7 @@ theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
@@ -598,7 +598,7 @@ theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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)))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s)))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
@@ -613,7 +613,7 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -628,7 +628,7 @@ theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
@@ -641,7 +641,7 @@ theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s)))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s)))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
@@ -656,7 +656,7 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_lt_sum_comp_perm_mul_iff AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -673,7 +673,7 @@ variable [Fintype ι]
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
@@ -686,7 +686,7 @@ theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_comp_perm_eq_sum_mul_iff Monovary.sum_mul_comp_perm_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
@@ -700,7 +700,7 @@ theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -714,7 +714,7 @@ theorem Monovary.sum_mul_comp_perm_lt_sum_mul_iff (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
@@ -727,7 +727,7 @@ theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_mul_eq_sum_mul_iff Monovary.sum_comp_perm_mul_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
@@ -741,7 +741,7 @@ theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
@@ -755,7 +755,7 @@ theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
@@ -768,7 +768,7 @@ theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_eq_sum_mul_comp_perm_iff Antivary.sum_mul_eq_sum_mul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
@@ -782,7 +782,7 @@ theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
@@ -796,7 +796,7 @@ theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i))))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
@@ -809,7 +809,7 @@ theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_eq_sum_comp_perm_mul_iff Antivary.sum_mul_eq_sum_comp_perm_mul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
@@ -823,7 +823,7 @@ theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 but is expected to have type
-  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_comp_perm_mul_iff Antivary.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if

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

@@ -65,7 +65,7 @@ variable [LinearOrderedRing α] [LinearOrderedAddCommGroup β] [Module α β] [O
 
 /- warning: monovary_on.sum_smul_comp_perm_le_sum_smul -> MonovaryOn.sum_smul_comp_perm_le_sum_smul 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smulₓ'. -/
@@ -155,7 +155,7 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 
 /- warning: monovary_on.sum_smul_comp_perm_lt_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
@@ -171,7 +171,7 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 
 /- warning: monovary_on.sum_comp_perm_smul_le_sum_smul -> MonovaryOn.sum_comp_perm_smul_le_sum_smul 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smulₓ'. -/
@@ -214,7 +214,7 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
 
 /- warning: monovary_on.sum_comp_perm_smul_lt_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
@@ -230,7 +230,7 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 
 /- warning: antivary_on.sum_smul_le_sum_smul_comp_perm -> AntivaryOn.sum_smul_le_sum_smul_comp_perm 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_permₓ'. -/
@@ -258,7 +258,7 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 
 /- warning: antivary_on.sum_smul_lt_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
@@ -274,7 +274,7 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 
 /- warning: antivary_on.sum_smul_le_sum_comp_perm_smul -> AntivaryOn.sum_smul_le_sum_comp_perm_smul 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smulₓ'. -/
@@ -302,7 +302,7 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 
 /- warning: antivary_on.sum_smul_lt_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
+  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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
@@ -320,7 +320,7 @@ variable [Fintype ι]
 
 /- warning: monovary.sum_smul_comp_perm_le_sum_smul -> Monovary.sum_smul_comp_perm_le_sum_smul 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smulₓ'. -/
@@ -347,7 +347,7 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
 
 /- warning: monovary.sum_smul_comp_perm_lt_sum_smul_iff -> Monovary.sum_smul_comp_perm_lt_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+  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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
@@ -361,7 +361,7 @@ theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
 
 /- warning: monovary.sum_comp_perm_smul_le_sum_smul -> Monovary.sum_comp_perm_smul_le_sum_smul 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smulₓ'. -/
@@ -388,7 +388,7 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
 
 /- warning: monovary.sum_comp_perm_smul_lt_sum_smul_iff -> Monovary.sum_comp_perm_smul_lt_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+  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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
@@ -402,7 +402,7 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
 
 /- warning: antivary.sum_smul_le_sum_smul_comp_perm -> Antivary.sum_smul_le_sum_smul_comp_perm 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_permₓ'. -/
@@ -429,7 +429,7 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 
 /- warning: antivary.sum_smul_lt_sum_smul_comp_perm_iff -> Antivary.sum_smul_lt_sum_smul_comp_perm_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+  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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
@@ -443,7 +443,7 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 
 /- warning: antivary.sum_smul_le_sum_comp_perm_smul -> Antivary.sum_smul_le_sum_comp_perm_smul 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smulₓ'. -/
@@ -470,7 +470,7 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
 
 /- warning: antivary.sum_smul_lt_sum_comp_perm_smul_iff -> Antivary.sum_smul_lt_sum_comp_perm_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+  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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toHasLt.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
@@ -497,7 +497,7 @@ variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
 /- warning: monovary_on.sum_mul_comp_perm_le_sum_mul -> MonovaryOn.sum_mul_comp_perm_le_sum_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mulₓ'. -/
@@ -525,7 +525,7 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
 
 /- warning: monovary_on.sum_mul_comp_perm_lt_sum_mul_iff -> MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g i)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g i)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iffₓ'. -/
@@ -540,7 +540,7 @@ theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (hfg : MonovaryOn f g s)
 
 /- warning: monovary_on.sum_comp_perm_mul_le_sum_mul -> MonovaryOn.sum_comp_perm_mul_le_sum_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mulₓ'. -/
@@ -568,7 +568,7 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
 
 /- warning: monovary_on.sum_comp_perm_mul_lt_sum_mul_iff -> MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iffₓ'. -/
@@ -583,7 +583,7 @@ theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
 
 /- warning: antivary_on.sum_mul_le_sum_mul_comp_perm -> AntivaryOn.sum_mul_le_sum_mul_comp_perm is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_permₓ'. -/
@@ -611,7 +611,7 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
 
 /- warning: antivary_on.sum_mul_lt_sum_mul_comp_perm_iff -> AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iffₓ'. -/
@@ -626,7 +626,7 @@ theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
 
 /- warning: antivary_on.sum_mul_le_sum_comp_perm_mul -> AntivaryOn.sum_mul_le_sum_comp_perm_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mulₓ'. -/
@@ -654,7 +654,7 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
 
 /- warning: antivary_on.sum_mul_lt_sum_comp_perm_mul_iff -> AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {s : Finset.{u2} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (Finset.toSet.{u2} ι s)) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g (Finset.toSet.{u2} ι s))))
 Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_lt_sum_comp_perm_mul_iff AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/
@@ -671,7 +671,7 @@ variable [Fintype ι]
 
 /- warning: monovary.sum_mul_comp_perm_le_sum_mul -> Monovary.sum_mul_comp_perm_le_sum_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mulₓ'. -/
@@ -698,7 +698,7 @@ theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
 
 /- warning: monovary.sum_mul_comp_perm_lt_sum_mul_iff -> Monovary.sum_mul_comp_perm_lt_sum_mul_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iffₓ'. -/
@@ -712,7 +712,7 @@ theorem Monovary.sum_mul_comp_perm_lt_sum_mul_iff (hfg : Monovary f g) :
 
 /- warning: monovary.sum_comp_perm_mul_le_sum_mul -> Monovary.sum_comp_perm_mul_le_sum_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mulₓ'. -/
@@ -739,7 +739,7 @@ theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
 
 /- warning: monovary.sum_comp_perm_mul_lt_sum_mul_iff -> Monovary.sum_comp_perm_mul_lt_sum_mul_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iffₓ'. -/
@@ -753,7 +753,7 @@ theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
 
 /- warning: antivary.sum_mul_le_sum_mul_comp_perm -> Antivary.sum_mul_le_sum_mul_comp_perm is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_permₓ'. -/
@@ -780,7 +780,7 @@ theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
 
 /- warning: antivary.sum_mul_lt_sum_mul_comp_perm_iff -> Antivary.sum_mul_lt_sum_mul_comp_perm_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iffₓ'. -/
@@ -794,7 +794,7 @@ theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
 
 /- warning: antivary.sum_mul_le_sum_comp_perm_mul -> Antivary.sum_mul_le_sum_comp_perm_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i))))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i))))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mulₓ'. -/
@@ -821,7 +821,7 @@ theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
 
 /- warning: antivary.sum_mul_lt_sum_comp_perm_mul_iff -> Antivary.sum_mul_lt_sum_comp_perm_mul_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toHasLt.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
 but is expected to have type
   forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
 Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_comp_perm_mul_iff Antivary.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
 
 ! This file was ported from Lean 3 source module algebra.order.rearrangement
-! leanprover-community/mathlib commit b3f25363ae62cb169e72cd6b8b1ac97bacf21ca7
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.Abel
 /-!
 # Rearrangement inequality
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves the rearrangement inequality and deduces the conditions for equality and strict
 inequality.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -60,6 +60,12 @@ 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_comp_perm_le_sum_smul -> MonovaryOn.sum_smul_comp_perm_le_sum_smul 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
@@ -108,6 +114,12 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
       exact has hx.2
 #align monovary_on.sum_smul_comp_perm_le_sum_smul MonovaryOn.sum_smul_comp_perm_le_sum_smul
 
+/- warning: monovary_on.sum_smul_comp_perm_eq_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (Eq.{succ u3} β (Finset.sum.{u3, u1} β ι 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(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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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)))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s)))
+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -138,6 +150,12 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
       simp_rw [Function.comp_apply, apply_inv_self]
 #align monovary_on.sum_smul_comp_perm_eq_sum_smul_iff MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff
 
+/- warning: monovary_on.sum_smul_comp_perm_lt_sum_smul_iff -> MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -148,6 +166,12 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
     hfg.sum_smul_comp_perm_le_sum_smul hσ]
 #align monovary_on.sum_smul_comp_perm_lt_sum_smul_iff MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff
 
+/- warning: monovary_on.sum_comp_perm_smul_le_sum_smul -> MonovaryOn.sum_comp_perm_smul_le_sum_smul 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 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(OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
@@ -159,6 +183,12 @@ theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
   exact σ.sum_comp' s (fun i j => f i • g j) hσ
 #align monovary_on.sum_comp_perm_smul_le_sum_smul MonovaryOn.sum_comp_perm_smul_le_sum_smul
 
+/- warning: monovary_on.sum_comp_perm_smul_eq_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff 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} {σ : Equiv.Perm.{succ 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 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(LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (Finset.sum.{u1, u3} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) s (fun (i : ι) => 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(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 (FunLike.coe.{succ u3, 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(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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
@@ -179,6 +209,12 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
       exact Set.image_perm hσinv
 #align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff
 
+/- warning: monovary_on.sum_comp_perm_smul_lt_sum_smul_iff -> MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff 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} {σ : Equiv.Perm.{succ 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 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(_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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 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(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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
@@ -189,6 +225,12 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
     hfg.sum_comp_perm_smul_le_sum_smul hσ]
 #align monovary_on.sum_comp_perm_smul_lt_sum_smul_iff MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff
 
+/- warning: antivary_on.sum_smul_le_sum_smul_comp_perm -> AntivaryOn.sum_smul_le_sum_smul_comp_perm 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 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(OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g 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) => 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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
@@ -196,6 +238,12 @@ theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
   hfg.dual_right.sum_smul_comp_perm_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
 
+/- warning: antivary_on.sum_smul_eq_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff 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} {σ : Equiv.Perm.{succ 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 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(LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) f (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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)))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s)))
+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -205,6 +253,12 @@ theorem AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
   (hfg.dual_right.sum_smul_comp_perm_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_smul_comp_perm_iff AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff
 
+/- warning: antivary_on.sum_smul_lt_sum_smul_comp_perm_iff -> AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff 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} {σ : Equiv.Perm.{succ 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 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(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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) ((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))))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) (Finset.toSet.{u3} ι s))))
+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -215,6 +269,12 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
     hfg.sum_smul_le_sum_smul_comp_perm hσ]
 #align antivary_on.sum_smul_lt_sum_smul_comp_perm_iff AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff
 
+/- warning: antivary_on.sum_smul_le_sum_comp_perm_smul -> AntivaryOn.sum_smul_le_sum_comp_perm_smul 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (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)))) (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 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(OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_2))) _inst_3))))) (f i) (g 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) => 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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
@@ -222,6 +282,12 @@ theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
   hfg.dual_right.sum_comp_perm_smul_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
 
+/- warning: antivary_on.sum_smul_eq_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff 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} {σ : Equiv.Perm.{succ 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 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(LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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)))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s)))
+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -231,6 +297,12 @@ theorem AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
   (hfg.dual_right.sum_comp_perm_smul_eq_sum_smul_iff hσ).trans monovaryOn_toDual_right
 #align antivary_on.sum_smul_eq_sum_comp_perm_smul_iff AntivaryOn.sum_smul_eq_sum_comp_perm_smul_iff
 
+/- warning: antivary_on.sum_smul_lt_sum_comp_perm_smul_iff -> AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff 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} {σ : Equiv.Perm.{succ 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 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(OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) 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))))
+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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (setOf.{u3} ι (fun (x : ι) => Ne.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ x) x)) (Finset.toSet.{u3} ι s)) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g (Finset.toSet.{u3} ι s))))
+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_smul_lt_sum_comp_perm_smul_iff AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -243,6 +315,12 @@ theorem AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff (hfg : AntivaryOn f g s)
 
 variable [Fintype ι]
 
+/- warning: monovary.sum_smul_comp_perm_le_sum_smul -> Monovary.sum_smul_comp_perm_le_sum_smul 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
@@ -250,6 +328,12 @@ theorem Monovary.sum_smul_comp_perm_le_sum_smul (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_smul_comp_perm_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_smul_comp_perm_le_sum_smul Monovary.sum_smul_comp_perm_le_sum_smul
 
+/- warning: monovary.sum_smul_comp_perm_eq_sum_smul_iff -> Monovary.sum_smul_comp_perm_eq_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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} 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_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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -258,6 +342,12 @@ theorem Monovary.sum_smul_comp_perm_eq_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_smul_comp_perm_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_eq_sum_smul_iff Monovary.sum_smul_comp_perm_eq_sum_smul_iff
 
+/- warning: monovary.sum_smul_comp_perm_lt_sum_smul_iff -> Monovary.sum_smul_comp_perm_lt_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -266,6 +356,12 @@ theorem Monovary.sum_smul_comp_perm_lt_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_smul_comp_perm_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_smul_comp_perm_lt_sum_smul_iff Monovary.sum_smul_comp_perm_lt_sum_smul_iff
 
+/- warning: monovary.sum_comp_perm_smul_le_sum_smul -> Monovary.sum_comp_perm_smul_le_sum_smul 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is maximized when
 `f` and `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
@@ -273,6 +369,12 @@ theorem Monovary.sum_comp_perm_smul_le_sum_smul (hfg : Monovary f g) :
   (hfg.MonovaryOn _).sum_comp_perm_smul_le_sum_smul fun i _ => mem_univ _
 #align monovary.sum_comp_perm_smul_le_sum_smul Monovary.sum_comp_perm_smul_le_sum_smul
 
+/- warning: monovary.sum_comp_perm_smul_eq_sum_smul_iff -> Monovary.sum_comp_perm_smul_eq_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -281,6 +383,12 @@ theorem Monovary.sum_comp_perm_smul_eq_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_comp_perm_smul_eq_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_eq_sum_smul_iff Monovary.sum_comp_perm_smul_eq_sum_smul_iff
 
+/- warning: monovary.sum_comp_perm_smul_lt_sum_smul_iff -> Monovary.sum_comp_perm_smul_lt_sum_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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} 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(AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2))) _inst_3)))) (f i) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -289,6 +397,12 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
   simp [(hfg.monovary_on _).sum_comp_perm_smul_lt_sum_smul_iff fun i _ => mem_univ _]
 #align monovary.sum_comp_perm_smul_lt_sum_smul_iff Monovary.sum_comp_perm_smul_lt_sum_smul_iff
 
+/- warning: antivary.sum_smul_le_sum_smul_comp_perm -> Antivary.sum_smul_le_sum_smul_comp_perm 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
@@ -296,6 +410,12 @@ theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
   (hfg.AntivaryOn _).sum_smul_le_sum_smul_comp_perm fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_perm
 
+/- warning: antivary.sum_smul_eq_sum_smul_comp_perm_iff -> Antivary.sum_smul_eq_sum_smul_comp_perm_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ))))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ 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) => 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)))) (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -304,6 +424,12 @@ theorem Antivary.sum_smul_eq_sum_smul_comp_perm_iff (hfg : Antivary f g) :
   simp [(hfg.antivary_on _).sum_smul_eq_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_smul_comp_perm_iff Antivary.sum_smul_eq_sum_smul_comp_perm_iff
 
+/- warning: antivary.sum_smul_lt_sum_smul_comp_perm_iff -> Antivary.sum_smul_lt_sum_smul_comp_perm_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u3} ι ι β g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i))))) (Not (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 (Function.comp.{succ u3, succ u3, succ u1} ι ι β g (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -312,6 +438,12 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
   simp [(hfg.antivary_on _).sum_smul_lt_sum_smul_comp_perm_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_lt_sum_smul_comp_perm_iff Antivary.sum_smul_lt_sum_smul_comp_perm_iff
 
+/- warning: antivary.sum_smul_le_sum_comp_perm_smul -> Antivary.sum_smul_le_sum_comp_perm_smul 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))] {σ : Equiv.Perm.{succ u1} ι} {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)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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))] {σ : Equiv.Perm.{succ u3} ι} {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)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
@@ -319,6 +451,12 @@ theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
   (hfg.AntivaryOn _).sum_smul_le_sum_comp_perm_smul fun i _ => mem_univ _
 #align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smul
 
+/- warning: antivary.sum_smul_eq_sum_comp_perm_smul_iff -> Antivary.sum_smul_eq_sum_comp_perm_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u3} β (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (Eq.{succ u1} β (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise scalar multiplication of `f` and
 `g`, which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -327,6 +465,12 @@ theorem Antivary.sum_smul_eq_sum_comp_perm_smul_iff (hfg : Antivary f g) :
   simp [(hfg.antivary_on _).sum_smul_eq_sum_comp_perm_smul_iff fun i _ => mem_univ _]
 #align antivary.sum_smul_eq_sum_comp_perm_smul_iff Antivary.sum_smul_eq_sum_comp_perm_smul_iff
 
+/- warning: antivary.sum_smul_lt_sum_comp_perm_smul_iff -> Antivary.sum_smul_lt_sum_comp_perm_smul_iff 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))] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u3} β (Preorder.toLT.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_2)))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+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))] {σ : Equiv.Perm.{succ u3} ι} {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) -> (Iff (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_2)))) (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))) (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 (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u3, succ u3, succ u2} ι ι α f (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.Perm.{succ u3} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} ι ι) σ)) g)))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -348,6 +492,12 @@ section Mul
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 
+/- warning: monovary_on.sum_mul_comp_perm_le_sum_mul -> MonovaryOn.sum_mul_comp_perm_le_sum_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {s : Finset.{u1} ι} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) (setOf.{u1} ι (fun (x : ι) => Ne.{succ u1} ι (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ x) x)) ((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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ 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) => 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} {σ : Equiv.Perm.{succ 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)) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (setOf.{u2} ι (fun (x : ι) => Ne.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) x) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ x) x)) (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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s)
@@ -355,6 +505,12 @@ theorem MonovaryOn.sum_mul_comp_perm_le_sum_mul (hfg : MonovaryOn f g s)
   hfg.sum_smul_comp_perm_le_sum_smul hσ
 #align monovary_on.sum_mul_comp_perm_le_sum_mul MonovaryOn.sum_mul_comp_perm_le_sum_mul
 
+/- warning: monovary_on.sum_mul_comp_perm_eq_sum_mul_iff -> MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -364,6 +520,12 @@ theorem MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_smul_comp_perm_eq_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_eq_sum_mul_iff MonovaryOn.sum_mul_comp_perm_eq_sum_mul_iff
 
+/- warning: monovary_on.sum_mul_comp_perm_lt_sum_mul_iff -> MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise scalar multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -373,6 +535,12 @@ theorem MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_smul_comp_perm_lt_sum_smul_iff hσ
 #align monovary_on.sum_mul_comp_perm_lt_sum_mul_iff MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff
 
+/- warning: monovary_on.sum_comp_perm_mul_le_sum_mul -> MonovaryOn.sum_comp_perm_mul_le_sum_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s)
@@ -380,6 +548,12 @@ theorem MonovaryOn.sum_comp_perm_mul_le_sum_mul (hfg : MonovaryOn f g s)
   hfg.sum_comp_perm_smul_le_sum_smul hσ
 #align monovary_on.sum_comp_perm_mul_le_sum_mul MonovaryOn.sum_comp_perm_mul_le_sum_mul
 
+/- warning: monovary_on.sum_comp_perm_mul_eq_sum_mul_iff -> MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `f`. -/
@@ -389,6 +563,12 @@ theorem MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_comp_perm_smul_eq_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_eq_sum_mul_iff MonovaryOn.sum_comp_perm_mul_eq_sum_mul_iff
 
+/- warning: monovary_on.sum_comp_perm_mul_lt_sum_mul_iff -> MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not monovary together. Stated by permuting the entries of `f`. -/
@@ -398,6 +578,12 @@ theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
   hfg.sum_comp_perm_smul_lt_sum_smul_iff hσ
 #align monovary_on.sum_comp_perm_mul_lt_sum_mul_iff MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff
 
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+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
@@ -405,6 +591,12 @@ theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
   hfg.sum_smul_le_sum_smul_comp_perm hσ
 #align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_perm
 
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+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -414,6 +606,12 @@ theorem AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
   hfg.sum_smul_eq_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_eq_sum_mul_comp_perm_iff AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff
 
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+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -423,6 +621,12 @@ theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
   hfg.sum_smul_lt_sum_smul_comp_perm_iff hσ
 #align antivary_on.sum_mul_lt_sum_mul_comp_perm_iff AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff
 
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+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
@@ -430,6 +634,12 @@ theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
   hfg.sum_smul_le_sum_comp_perm_smul hσ
 #align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mul
 
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+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -439,6 +649,12 @@ theorem AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
   hfg.sum_smul_eq_sum_comp_perm_smul_iff hσ
 #align antivary_on.sum_mul_eq_sum_comp_perm_mul_iff AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff
 
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+Case conversion may be inaccurate. Consider using '#align antivary_on.sum_mul_lt_sum_comp_perm_mul_iff AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/
@@ -450,6 +666,12 @@ theorem AntivaryOn.sum_mul_lt_sum_comp_perm_mul_iff (hfg : AntivaryOn f g s)
 
 variable [Fintype ι]
 
+/- warning: monovary.sum_mul_comp_perm_le_sum_mul -> Monovary.sum_mul_comp_perm_le_sum_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `g`. -/
 theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
@@ -457,6 +679,12 @@ theorem Monovary.sum_mul_comp_perm_le_sum_mul (hfg : Monovary f g) :
   hfg.sum_smul_comp_perm_le_sum_smul
 #align monovary.sum_mul_comp_perm_le_sum_mul Monovary.sum_mul_comp_perm_le_sum_mul
 
+/- warning: monovary.sum_mul_comp_perm_eq_sum_mul_iff -> Monovary.sum_mul_comp_perm_eq_sum_mul_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_comp_perm_eq_sum_mul_iff Monovary.sum_mul_comp_perm_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -465,6 +693,12 @@ theorem Monovary.sum_mul_comp_perm_eq_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_smul_comp_perm_eq_sum_smul_iff
 #align monovary.sum_mul_comp_perm_eq_sum_mul_iff Monovary.sum_mul_comp_perm_eq_sum_mul_iff
 
+/- warning: monovary.sum_mul_comp_perm_lt_sum_mul_iff -> Monovary.sum_mul_comp_perm_lt_sum_mul_iff is a dubious translation:
+lean 3 declaration is
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+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ 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) => 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)))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -473,6 +707,12 @@ theorem Monovary.sum_mul_comp_perm_lt_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_smul_comp_perm_lt_sum_smul_iff
 #align monovary.sum_mul_comp_perm_lt_sum_mul_iff Monovary.sum_mul_comp_perm_lt_sum_mul_iff
 
+/- warning: monovary.sum_comp_perm_mul_le_sum_mul -> Monovary.sum_comp_perm_mul_le_sum_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is maximized when `f` and
 `g` monovary together. Stated by permuting the entries of `f`. -/
 theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
@@ -480,6 +720,12 @@ theorem Monovary.sum_comp_perm_mul_le_sum_mul (hfg : Monovary f g) :
   hfg.sum_comp_perm_smul_le_sum_smul
 #align monovary.sum_comp_perm_mul_le_sum_mul Monovary.sum_comp_perm_mul_le_sum_mul
 
+/- warning: monovary.sum_comp_perm_mul_eq_sum_mul_iff -> Monovary.sum_comp_perm_mul_eq_sum_mul_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_mul_eq_sum_mul_iff Monovary.sum_comp_perm_mul_eq_sum_mul_iffₓ'. -/
 /-- **Equality case of Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which monovary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` monovary
 together. Stated by permuting the entries of `g`. -/
@@ -488,6 +734,12 @@ theorem Monovary.sum_comp_perm_mul_eq_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_comp_perm_smul_eq_sum_smul_iff
 #align monovary.sum_comp_perm_mul_eq_sum_mul_iff Monovary.sum_comp_perm_mul_eq_sum_mul_iff
 
+/- warning: monovary.sum_comp_perm_mul_lt_sum_mul_iff -> Monovary.sum_comp_perm_mul_lt_sum_mul_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
+Case conversion may be inaccurate. Consider using '#align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iffₓ'. -/
 /-- **Strict inequality case of Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which monovary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not monovary together. Stated by permuting the entries of `g`. -/
@@ -496,6 +748,12 @@ theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
   hfg.sum_comp_perm_smul_lt_sum_smul_iff
 #align monovary.sum_comp_perm_mul_lt_sum_mul_iff Monovary.sum_comp_perm_mul_lt_sum_mul_iff
 
+/- warning: antivary.sum_mul_le_sum_mul_comp_perm -> Antivary.sum_mul_le_sum_mul_comp_perm is a dubious translation:
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+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_permₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
@@ -503,6 +761,12 @@ theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
   hfg.sum_smul_le_sum_smul_comp_perm
 #align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_perm
 
+/- warning: antivary.sum_mul_eq_sum_mul_comp_perm_iff -> Antivary.sum_mul_eq_sum_mul_comp_perm_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_eq_sum_mul_comp_perm_iff Antivary.sum_mul_eq_sum_mul_comp_perm_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f` and `g ∘ σ` antivary
 together. Stated by permuting the entries of `g`. -/
@@ -511,6 +775,12 @@ theorem Antivary.sum_mul_eq_sum_mul_comp_perm_iff (hfg : Antivary f g) :
   hfg.sum_smul_eq_sum_smul_comp_perm_iff
 #align antivary.sum_mul_eq_sum_mul_comp_perm_iff Antivary.sum_mul_eq_sum_mul_comp_perm_iff
 
+/- warning: antivary.sum_mul_lt_sum_mul_comp_perm_iff -> Antivary.sum_mul_lt_sum_mul_comp_perm_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g 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) => SMul.smul.{u2, u2} α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (StrictOrderedRing.toRing.{u2} α (LinearOrderedRing.toStrictOrderedRing.{u2} α _inst_1))))) (f i) (g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i))))) (Not (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 (Function.comp.{succ u1, succ u1, succ u2} ι ι α g (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)))))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g 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) => HSMul.hSMul.{u1, u1, u1} α α α (instHSMul.{u1, u1} α α (SMulZeroClass.toSMul.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (SMulWithZero.toSMulZeroClass.{u1, u1} α α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))) (MulZeroClass.toSMulWithZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))))))) (f i) (g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i))))) (Not (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 (Function.comp.{succ u2, succ u2, succ u1} ι ι α g (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f` and `g ∘ σ` do not antivary together. Stated by permuting the entries of `g`. -/
@@ -519,6 +789,12 @@ theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
   hfg.sum_smul_lt_sum_smul_comp_perm_iff
 #align antivary.sum_mul_lt_sum_mul_comp_perm_iff Antivary.sum_mul_lt_sum_mul_comp_perm_iff
 
+/- warning: antivary.sum_mul_le_sum_comp_perm_mul -> Antivary.sum_mul_le_sum_comp_perm_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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))))) (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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i))))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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)))) (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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i))))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mulₓ'. -/
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
@@ -526,6 +802,12 @@ theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
   hfg.sum_smul_le_sum_comp_perm_smul
 #align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mul
 
+/- warning: antivary.sum_mul_eq_sum_comp_perm_mul_iff -> Antivary.sum_mul_eq_sum_comp_perm_mul_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (Eq.{succ u2} α (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g 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) => 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)))) (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (Eq.{succ u1} α (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g 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) => 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)))) (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_eq_sum_comp_perm_mul_iff Antivary.sum_mul_eq_sum_comp_perm_mul_iffₓ'. -/
 /-- **Equality case of the Rearrangement Inequality**: Pointwise multiplication of `f` and `g`,
 which antivary together, is unchanged by a permutation if and only if `f ∘ σ` and `g` antivary
 together. Stated by permuting the entries of `f`. -/
@@ -534,6 +816,12 @@ theorem Antivary.sum_mul_eq_sum_comp_perm_mul_iff (hfg : Antivary f g) :
   hfg.sum_smul_eq_sum_comp_perm_smul_iff
 #align antivary.sum_mul_eq_sum_comp_perm_mul_iff Antivary.sum_mul_eq_sum_comp_perm_mul_iff
 
+/- warning: antivary.sum_mul_lt_sum_comp_perm_mul_iff -> Antivary.sum_mul_lt_sum_comp_perm_mul_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : LinearOrderedRing.{u2} α] {σ : Equiv.Perm.{succ u1} ι} {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) -> (Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (StrictOrderedRing.toOrderedAddCommGroup.{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) => 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))) (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 (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ i)) (g i)))) (Not (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)))) (Function.comp.{succ u1, succ u1, succ u2} ι ι α f (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} ι) (fun (_x : Equiv.{succ u1, succ u1} ι ι) => ι -> ι) (Equiv.hasCoeToFun.{succ u1, succ u1} ι ι) σ)) g)))
+but is expected to have type
+  forall {ι : Type.{u2}} {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] {σ : Equiv.Perm.{succ u2} ι} {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) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{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) => 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))) (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 (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ i)) (g i)))) (Not (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))) (Function.comp.{succ u2, succ u2, succ u1} ι ι α f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} ι) ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} ι ι) σ)) g)))
+Case conversion may be inaccurate. Consider using '#align antivary.sum_mul_lt_sum_comp_perm_mul_iff Antivary.sum_mul_lt_sum_comp_perm_mul_iffₓ'. -/
 /-- **Strict inequality case of the Rearrangement Inequality**: Pointwise multiplication of
 `f` and `g`, which antivary together, is strictly decreased by a permutation if and only if
 `f ∘ σ` and `g` do not antivary together. Stated by permuting the entries of `f`. -/

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

@@ -153,8 +153,7 @@ theorem MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 theorem MonovaryOn.sum_comp_perm_smul_le_sum_smul (hfg : MonovaryOn f g s)
     (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f (σ i) • g i) ≤ ∑ i in s, f i • g i :=
   by
-  convert
-    hfg.sum_smul_comp_perm_le_sum_smul
+  convert hfg.sum_smul_comp_perm_le_sum_smul
       (show { x | σ⁻¹ x ≠ x } ⊆ s by simp only [set_support_inv_eq, hσ]) using
     1
   exact σ.sum_comp' s (fun i j => f i • g j) hσ

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

@@ -74,7 +74,7 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
     set τ : Perm ι := σ.trans (swap a (σ a)) with hτ
     have hτs : { x | τ x ≠ x } ⊆ s := by
       intro x hx
-      simp only [τ, Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx
+      simp only [τ, Ne, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx
       split_ifs at hx with h₁ h₂
       · obtain rfl | hax := eq_or_ne x a
         · contradiction
@@ -87,7 +87,7 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
     obtain hσa | hσa := eq_or_ne a (σ a)
     · rw [hτ, ← hσa, swap_self, trans_refl]
     have h1s : σ⁻¹ a ∈ s := by
-      rw [Ne.def, ← inv_eq_iff_eq] at hσa
+      rw [Ne, ← inv_eq_iff_eq] at hσa
       refine' mem_of_mem_insert_of_ne (hσ fun h ↦ hσa _) hσa
       rwa [apply_inv_self, eq_comm] at h
     simp only [← s.sum_erase_add _ h1s, add_comm]
@@ -104,7 +104,7 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
       cases' hamax with hamax hamax
       · exact hamax.le
       · exact hamax.1.le
-    · rw [mem_erase, Ne.def, eq_inv_iff_eq] at hx
+    · rw [mem_erase, Ne, eq_inv_iff_eq] at hx
       rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
       rintro rfl
       exact has hx.2

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

@@ -74,7 +74,7 @@ theorem MonovaryOn.sum_smul_comp_perm_le_sum_smul (hfg : MonovaryOn f g s)
     set τ : Perm ι := σ.trans (swap a (σ a)) with hτ
     have hτs : { x | τ x ≠ x } ⊆ s := by
       intro x hx
-      simp only [Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx
+      simp only [τ, Ne.def, Set.mem_setOf_eq, Equiv.coe_trans, Equiv.swap_comp_apply] at hx
       split_ifs at hx with h₁ h₂
       · obtain rfl | hax := eq_or_ne x a
         · contradiction
@@ -128,7 +128,8 @@ theorem MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff (hfg : MonovaryOn f g s)
       refine' ((hfg.sum_smul_comp_perm_le_sum_smul hτs).trans_lt' _).ne
       obtain rfl | hxy := eq_or_ne x y
       · cases lt_irrefl _ hfxy
-      simp only [← s.sum_erase_add _ hx, ← (s.erase x).sum_erase_add _ (mem_erase.2 ⟨hxy.symm, hy⟩),
+      simp only [τ, ← s.sum_erase_add _ hx,
+        ← (s.erase x).sum_erase_add _ (mem_erase.2 ⟨hxy.symm, hy⟩),
         add_assoc, Equiv.coe_trans, Function.comp_apply, swap_apply_right, swap_apply_left]
       refine' add_lt_add_of_le_of_lt (Finset.sum_congr rfl fun z hz ↦ _).le
         (smul_add_smul_lt_smul_add_smul hfxy hgxy)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,7 +5,9 @@ Authors: Mantas Bakšys
 -/
 import Mathlib.Algebra.BigOperators.Basic
 import Mathlib.Algebra.Order.Module.OrderedSMul
+import Mathlib.Algebra.Order.Group.Instances
 import Mathlib.Data.Prod.Lex
+import Mathlib.Data.Set.Image
 import Mathlib.GroupTheory.Perm.Support
 import Mathlib.Order.Monotone.Monovary
 import Mathlib.Tactic.Abel

• Merge Function.left_id and Function.comp.left_id into Function.id_comp.
• Merge Function.right_id and Function.comp.right_id into Function.comp_id.
• Merge Function.comp_const_right and Function.comp_const into Function.comp_const, use explicit arguments.
• Move Function.const_comp to Mathlib.Init.Function, use explicit arguments.

@@ -167,10 +167,10 @@ theorem MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff (hfg : MonovaryOn f g s)
     rw [σ.sum_comp' s (fun i j ↦ f i • g j) hσ]
     congr
   · convert h.comp_right σ
-    · rw [comp.assoc, inv_def, symm_comp_self, comp.right_id]
+    · rw [comp.assoc, inv_def, symm_comp_self, comp_id]
     · rw [σ.eq_preimage_iff_image_eq, Set.image_perm hσ]
   · convert h.comp_right σ.symm
-    · rw [comp.assoc, self_comp_symm, comp.right_id]
+    · rw [comp.assoc, self_comp_symm, comp_id]
     · rw [σ.symm.eq_preimage_iff_image_eq]
       exact Set.image_perm hσinv
 #align monovary_on.sum_comp_perm_smul_eq_sum_smul_iff MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff

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

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
 -/
 import Mathlib.Algebra.BigOperators.Basic
-import Mathlib.Algebra.Order.Module
+import Mathlib.Algebra.Order.Module.OrderedSMul
 import Mathlib.Data.Prod.Lex
 import Mathlib.GroupTheory.Perm.Support
 import Mathlib.Order.Monotone.Monovary

Normalising to naming convention rule number 6.

@@ -52,7 +52,7 @@ 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}
@@ -331,7 +331,7 @@ theorem Antivary.sum_smul_lt_sum_comp_perm_smul_iff (hfg : Antivary f g) :
   simp [(hfg.antivaryOn _).sum_smul_lt_sum_comp_perm_smul_iff fun _ _ ↦ mem_univ _]
 #align antivary.sum_smul_lt_sum_comp_perm_smul_iff Antivary.sum_smul_lt_sum_comp_perm_smul_iff
 
-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.

@@ -47,7 +47,7 @@ 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>

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Mantas Bakšys. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
-
-! This file was ported from Lean 3 source module algebra.order.rearrangement
-! leanprover-community/mathlib commit b3f25363ae62cb169e72cd6b8b1ac97bacf21ca7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Basic
 import Mathlib.Algebra.Order.Module
@@ -15,6 +10,8 @@ import Mathlib.GroupTheory.Perm.Support
 import Mathlib.Order.Monotone.Monovary
 import Mathlib.Tactic.Abel
 
+#align_import algebra.order.rearrangement from "leanprover-community/mathlib"@"b3f25363ae62cb169e72cd6b8b1ac97bacf21ca7"
+
 /-!
 # Rearrangement inequality
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -191,7 +191,7 @@ theorem MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff (hfg : MonovaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_smul_le_sum_smul_comp_perm (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f i • g (σ i) :=
+    (hσ : { x | σ x ≠ x } ⊆ s) : ∑ i in s, f i • g i ≤ ∑ i in s, f i • g (σ i) :=
   hfg.dual_right.sum_smul_comp_perm_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_smul_comp_perm AntivaryOn.sum_smul_le_sum_smul_comp_perm
 
@@ -217,7 +217,7 @@ theorem AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff (hfg : AntivaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_smul_le_sum_comp_perm_smul (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i • g i) ≤ ∑ i in s, f (σ i) • g i :=
+    (hσ : { x | σ x ≠ x } ⊆ s) : ∑ i in s, f i • g i ≤ ∑ i in s, f (σ i) • g i :=
   hfg.dual_right.sum_comp_perm_smul_le_sum_smul hσ
 #align antivary_on.sum_smul_le_sum_comp_perm_smul AntivaryOn.sum_smul_le_sum_comp_perm_smul
 
@@ -291,7 +291,7 @@ theorem Monovary.sum_comp_perm_smul_lt_sum_smul_iff (hfg : Monovary f g) :
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_smul_le_sum_smul_comp_perm (hfg : Antivary f g) :
-    (∑ i, f i • g i) ≤ ∑ i, f i • g (σ i) :=
+    ∑ i, f i • g i ≤ ∑ i, f i • g (σ i) :=
   (hfg.antivaryOn _).sum_smul_le_sum_smul_comp_perm fun _ _ ↦ mem_univ _
 #align antivary.sum_smul_le_sum_smul_comp_perm Antivary.sum_smul_le_sum_smul_comp_perm
 
@@ -314,7 +314,7 @@ theorem Antivary.sum_smul_lt_sum_smul_comp_perm_iff (hfg : Antivary f g) :
 /-- **Rearrangement Inequality**: Pointwise scalar multiplication of `f` and `g` is minimized when
 `f` and `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_smul_le_sum_comp_perm_smul (hfg : Antivary f g) :
-    (∑ i, f i • g i) ≤ ∑ i, f (σ i) • g i :=
+    ∑ i, f i • g i ≤ ∑ i, f (σ i) • g i :=
   (hfg.antivaryOn _).sum_smul_le_sum_comp_perm_smul fun _ _ ↦ mem_univ _
 #align antivary.sum_smul_le_sum_comp_perm_smul Antivary.sum_smul_le_sum_comp_perm_smul
 
@@ -401,7 +401,7 @@ theorem MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff (hfg : MonovaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem AntivaryOn.sum_mul_le_sum_mul_comp_perm (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i * g i) ≤ ∑ i in s, f i * g (σ i) :=
+    (hσ : { x | σ x ≠ x } ⊆ s) : ∑ i in s, f i * g i ≤ ∑ i in s, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm hσ
 #align antivary_on.sum_mul_le_sum_mul_comp_perm AntivaryOn.sum_mul_le_sum_mul_comp_perm
 
@@ -426,7 +426,7 @@ theorem AntivaryOn.sum_mul_lt_sum_mul_comp_perm_iff (hfg : AntivaryOn f g s)
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem AntivaryOn.sum_mul_le_sum_comp_perm_mul (hfg : AntivaryOn f g s)
-    (hσ : { x | σ x ≠ x } ⊆ s) : (∑ i in s, f i * g i) ≤ ∑ i in s, f (σ i) * g i :=
+    (hσ : { x | σ x ≠ x } ⊆ s) : ∑ i in s, f i * g i ≤ ∑ i in s, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul hσ
 #align antivary_on.sum_mul_le_sum_comp_perm_mul AntivaryOn.sum_mul_le_sum_comp_perm_mul
 
@@ -499,7 +499,7 @@ theorem Monovary.sum_comp_perm_mul_lt_sum_mul_iff (hfg : Monovary f g) :
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `g`. -/
 theorem Antivary.sum_mul_le_sum_mul_comp_perm (hfg : Antivary f g) :
-    (∑ i, f i * g i) ≤ ∑ i, f i * g (σ i) :=
+    ∑ i, f i * g i ≤ ∑ i, f i * g (σ i) :=
   hfg.sum_smul_le_sum_smul_comp_perm
 #align antivary.sum_mul_le_sum_mul_comp_perm Antivary.sum_mul_le_sum_mul_comp_perm
 
@@ -522,7 +522,7 @@ theorem Antivary.sum_mul_lt_sum_mul_comp_perm_iff (hfg : Antivary f g) :
 /-- **Rearrangement Inequality**: Pointwise multiplication of `f` and `g` is minimized when `f` and
 `g` antivary together. Stated by permuting the entries of `f`. -/
 theorem Antivary.sum_mul_le_sum_comp_perm_mul (hfg : Antivary f g) :
-    (∑ i, f i * g i) ≤ ∑ i, f (σ i) * g i :=
+    ∑ i, f i * g i ≤ ∑ i, f (σ i) * g i :=
   hfg.sum_smul_le_sum_comp_perm_smul
 #align antivary.sum_mul_le_sum_comp_perm_mul Antivary.sum_mul_le_sum_comp_perm_mul
 

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>

@@ -345,7 +345,6 @@ Special cases of the above when scalar multiplication is actually multiplication
 
 section Mul
 
-set_option synthInstance.etaExperiment true
 
 variable [LinearOrderedRing α] {s : Finset ι} {σ : Perm ι} {f g : ι → α}
 

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>