algebraic_topology.simplicial_object | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

5ed51dc3

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

814d76e2

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
 import AlgebraicTopology.SimplexCategory
-import CategoryTheory.Arrow
+import CategoryTheory.Comma.Arrow
 import CategoryTheory.Limits.FunctorCategory
 import CategoryTheory.Opposites

814d76e2

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
-import Mathbin.AlgebraicTopology.SimplexCategory
-import Mathbin.CategoryTheory.Arrow
-import Mathbin.CategoryTheory.Limits.FunctorCategory
-import Mathbin.CategoryTheory.Opposites
+import AlgebraicTopology.SimplexCategory
+import CategoryTheory.Arrow
+import CategoryTheory.Limits.FunctorCategory
+import CategoryTheory.Opposites
 
 #align_import algebraic_topology.simplicial_object from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"

814d76e2

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module algebraic_topology.simplicial_object
-! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.SimplexCategory
 import Mathbin.CategoryTheory.Arrow
 import Mathbin.CategoryTheory.Limits.FunctorCategory
 import Mathbin.CategoryTheory.Opposites
 
+#align_import algebraic_topology.simplicial_object from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"
+
 /-!
 # Simplicial objects in a category.

814d76e2

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -52,7 +52,6 @@ deriving Category
 
 namespace SimplicialObject
 
--- mathport name: simplicial_object.at
 scoped[Simplicial]
   notation:1000 X " _[" n "]" =>
     (X : CategoryTheory.SimplicialObject hole!).obj (Opposite.op (SimplexCategory.mk n))
@@ -71,64 +70,85 @@ instance [HasColimits C] : HasColimits (SimplicialObject C) :=
 
 variable {C} (X : SimplicialObject C)
 
+#print CategoryTheory.SimplicialObject.δ /-
 /-- Face maps for a simplicial object. -/
 def δ {n} (i : Fin (n + 2)) : X _[n + 1] ⟶ X _[n] :=
   X.map (SimplexCategory.δ i).op
 #align category_theory.simplicial_object.δ CategoryTheory.SimplicialObject.δ
+-/
 
+#print CategoryTheory.SimplicialObject.σ /-
 /-- Degeneracy maps for a simplicial object. -/
 def σ {n} (i : Fin (n + 1)) : X _[n] ⟶ X _[n + 1] :=
   X.map (SimplexCategory.σ i).op
 #align category_theory.simplicial_object.σ CategoryTheory.SimplicialObject.σ
+-/
 
+#print CategoryTheory.SimplicialObject.eqToIso /-
 /-- Isomorphisms from identities in ℕ. -/
 def eqToIso {n m : ℕ} (h : n = m) : X _[n] ≅ X _[m] :=
   X.mapIso (eqToIso (by rw [h]))
 #align category_theory.simplicial_object.eq_to_iso CategoryTheory.SimplicialObject.eqToIso
+-/
 
+#print CategoryTheory.SimplicialObject.eqToIso_refl /-
 @[simp]
 theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by ext; simp [eq_to_iso]
 #align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_refl
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_δ /-
 /-- The generic case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
     X.δ j.succ ≫ X.δ i = X.δ i.cast_succ ≫ X.δ j := by dsimp [δ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_δ' /-
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ j ≫ X.δ i =
       X.δ i.cast_succ ≫ X.δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) :=
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_δ'' /-
 @[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ j.succ ≫ X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
       X.δ i ≫ X.δ j :=
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_δ_self /-
 /-- The special case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_δ_self' /-
 @[reassoc]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
     X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by subst H; rw [δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_of_le /-
 /-- The second simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
     X.σ j.succ ≫ X.δ i.cast_succ = X.δ i ≫ X.σ j := by dsimp [δ, σ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_self /-
 /-- The first part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 𝟙 _ :=
@@ -136,12 +156,16 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_self, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_self
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_self' /-
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by subst H; rw [δ_comp_σ_self]
 #align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_succ /-
 /-- The second part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _ :=
@@ -149,19 +173,25 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_succ, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_succ CategoryTheory.SimplicialObject.δ_comp_σ_succ
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_succ' /-
 @[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by subst H; rw [δ_comp_σ_succ]
 #align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_of_gt /-
 /-- The fourth simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
     X.σ j.cast_succ ≫ X.δ i.succ = X.δ i ≫ X.σ j := by dsimp [δ, σ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
+-/
 
+#print CategoryTheory.SimplicialObject.δ_comp_σ_of_gt' /-
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
@@ -174,27 +204,34 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
                 i.is_le))) :=
   by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'
+-/
 
+#print CategoryTheory.SimplicialObject.σ_comp_σ /-
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
     X.σ j ≫ X.σ i.cast_succ = X.σ i ≫ X.σ j.succ := by dsimp [δ, σ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σ
+-/
 
 open scoped Simplicial
 
+#print CategoryTheory.SimplicialObject.δ_naturality /-
 @[simp, reassoc]
 theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (op [n]) = f.app (op [n + 1]) ≫ X'.δ i :=
   f.naturality _
 #align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturality
+-/
 
+#print CategoryTheory.SimplicialObject.σ_naturality /-
 @[simp, reassoc]
 theorem σ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (op [n + 1]) = f.app (op [n]) ≫ X'.σ i :=
   f.naturality _
 #align category_theory.simplicial_object.σ_naturality CategoryTheory.SimplicialObject.σ_naturality
+-/
 
 variable (C)
 
@@ -314,6 +351,7 @@ def toArrow : Augmented C ⥤ Arrow C
 #align category_theory.simplicial_object.augmented.to_arrow CategoryTheory.SimplicialObject.Augmented.toArrow
 -/
 
+#print CategoryTheory.SimplicialObject.Augmented.w₀ /-
 /-- The compatibility of a morphism with the augmentation, on 0-simplices -/
 @[reassoc]
 theorem w₀ {X Y : Augmented C} (f : X ⟶ Y) :
@@ -321,6 +359,7 @@ theorem w₀ {X Y : Augmented C} (f : X ⟶ Y) :
       X.Hom.app (op (SimplexCategory.mk 0)) ≫ Augmented.point.map f :=
   by convert congr_app f.w (op (SimplexCategory.mk 0))
 #align category_theory.simplicial_object.augmented.w₀ CategoryTheory.SimplicialObject.Augmented.w₀
+-/
 
 variable (C)
 
@@ -367,6 +406,7 @@ variable {C}
 
 end Augmented
 
+#print CategoryTheory.SimplicialObject.augment /-
 /-- Augment a simplicial object with an object. -/
 @[simps]
 def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
@@ -382,12 +422,15 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
         rw [← g.op_unop]
         simpa only [← X.map_comp, ← category.assoc, category.comp_id, ← op_comp] using w _ _ _ }
 #align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augment
+-/
 
+#print CategoryTheory.SimplicialObject.augment_hom_zero /-
 @[simp]
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
     (X.augment X₀ f w).Hom.app (op [0]) = f := by dsimp;
   rw [SimplexCategory.hom_zero_zero ([0].const 0), op_id, X.map_id, category.id_comp]
 #align category_theory.simplicial_object.augment_hom_zero CategoryTheory.SimplicialObject.augment_hom_zero
+-/
 
 end SimplicialObject
 
@@ -402,7 +445,6 @@ deriving Category
 
 namespace CosimplicialObject
 
--- mathport name: cosimplicial_object.at
 scoped[Simplicial]
   notation:1000 X " _[" n "]" =>
     (X : CategoryTheory.CosimplicialObject hole!).obj (SimplexCategory.mk n)
@@ -421,64 +463,85 @@ instance [HasColimits C] : HasColimits (CosimplicialObject C) :=
 
 variable {C} (X : CosimplicialObject C)
 
+#print CategoryTheory.CosimplicialObject.δ /-
 /-- Coface maps for a cosimplicial object. -/
 def δ {n} (i : Fin (n + 2)) : X _[n] ⟶ X _[n + 1] :=
   X.map (SimplexCategory.δ i)
 #align category_theory.cosimplicial_object.δ CategoryTheory.CosimplicialObject.δ
+-/
 
+#print CategoryTheory.CosimplicialObject.σ /-
 /-- Codegeneracy maps for a cosimplicial object. -/
 def σ {n} (i : Fin (n + 1)) : X _[n + 1] ⟶ X _[n] :=
   X.map (SimplexCategory.σ i)
 #align category_theory.cosimplicial_object.σ CategoryTheory.CosimplicialObject.σ
+-/
 
+#print CategoryTheory.CosimplicialObject.eqToIso /-
 /-- Isomorphisms from identities in ℕ. -/
 def eqToIso {n m : ℕ} (h : n = m) : X _[n] ≅ X _[m] :=
   X.mapIso (eqToIso (by rw [h]))
 #align category_theory.cosimplicial_object.eq_to_iso CategoryTheory.CosimplicialObject.eqToIso
+-/
 
+#print CategoryTheory.CosimplicialObject.eqToIso_refl /-
 @[simp]
 theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by ext; simp [eq_to_iso]
 #align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_refl
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_δ /-
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
     X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ i.cast_succ := by dsimp [δ];
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_δ' /-
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ i ≫ X.δ j =
       X.δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ X.δ i.cast_succ :=
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_δ'' /-
 @[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
       X.δ j ≫ X.δ i :=
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_δ_self /-
 /-- The special case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.δ i ≫ X.δ i.succ := by
   dsimp [δ]; simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_δ_self' /-
 @[reassoc]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
     X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by subst H; rw [δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_of_le /-
 /-- The second cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
     X.δ i.cast_succ ≫ X.σ j.succ = X.σ j ≫ X.δ i := by dsimp [δ, σ];
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_self /-
 /-- The first part of the third cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 𝟙 _ :=
@@ -486,12 +549,16 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_self, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_self
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_self' /-
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by subst H; rw [δ_comp_σ_self]
 #align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_succ /-
 /-- The second part of the third cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _ :=
@@ -499,19 +566,25 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_succ, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ CategoryTheory.CosimplicialObject.δ_comp_σ_succ
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_succ' /-
 @[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by subst H; rw [δ_comp_σ_succ]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt /-
 /-- The fourth cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
     X.δ i.succ ≫ X.σ j.cast_succ = X.σ j ≫ X.δ i := by dsimp [δ, σ];
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt' /-
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.δ i ≫ X.σ j =
@@ -524,25 +597,32 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
         X.δ (i.pred fun hi => by simpa only [Fin.not_lt_zero, hi] using H) :=
   by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'
+-/
 
+#print CategoryTheory.CosimplicialObject.σ_comp_σ /-
 /-- The fifth cosimplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
     X.σ i.cast_succ ≫ X.σ j = X.σ j.succ ≫ X.σ i := by dsimp [δ, σ];
   simp only [← X.map_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σ
+-/
 
+#print CategoryTheory.CosimplicialObject.δ_naturality /-
 @[simp, reassoc]
 theorem δ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (SimplexCategory.mk (n + 1)) = f.app (SimplexCategory.mk n) ≫ X'.δ i :=
   f.naturality _
 #align category_theory.cosimplicial_object.δ_naturality CategoryTheory.CosimplicialObject.δ_naturality
+-/
 
+#print CategoryTheory.CosimplicialObject.σ_naturality /-
 @[simp, reassoc]
 theorem σ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (SimplexCategory.mk n) = f.app (SimplexCategory.mk (n + 1)) ≫ X'.σ i :=
   f.naturality _
 #align category_theory.cosimplicial_object.σ_naturality CategoryTheory.CosimplicialObject.σ_naturality
+-/
 
 variable (C)
 
@@ -709,6 +789,7 @@ end Augmented
 
 open scoped Simplicial
 
+#print CategoryTheory.CosimplicialObject.augment /-
 /-- Augment a cosimplicial object with an object. -/
 @[simps]
 def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
@@ -723,26 +804,33 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
         dsimp
         simpa [← X.map_comp] using w _ _ _ }
 #align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augment
+-/
 
+#print CategoryTheory.CosimplicialObject.augment_hom_zero /-
 @[simp]
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :
     (X.augment X₀ f w).Hom.app [0] = f := by dsimp;
   rw [SimplexCategory.hom_zero_zero ([0].const 0), X.map_id, category.comp_id]
 #align category_theory.cosimplicial_object.augment_hom_zero CategoryTheory.CosimplicialObject.augment_hom_zero
+-/
 
 end CosimplicialObject
 
+#print CategoryTheory.simplicialCosimplicialEquiv /-
 /-- The anti-equivalence between simplicial objects and cosimplicial objects. -/
 @[simps]
 def simplicialCosimplicialEquiv : (SimplicialObject C)ᵒᵖ ≌ CosimplicialObject Cᵒᵖ :=
   Functor.leftOpRightOpEquiv _ _
 #align category_theory.simplicial_cosimplicial_equiv CategoryTheory.simplicialCosimplicialEquiv
+-/
 
+#print CategoryTheory.cosimplicialSimplicialEquiv /-
 /-- The anti-equivalence between cosimplicial objects and simplicial objects. -/
 @[simps]
 def cosimplicialSimplicialEquiv : (CosimplicialObject C)ᵒᵖ ≌ SimplicialObject Cᵒᵖ :=
   Functor.opUnopEquiv _ _
 #align category_theory.cosimplicial_simplicial_equiv CategoryTheory.cosimplicialSimplicialEquiv
+-/
 
 variable {C}
 
@@ -832,6 +920,7 @@ def cosimplicialToSimplicialAugmented :
 #align category_theory.cosimplicial_to_simplicial_augmented CategoryTheory.cosimplicialToSimplicialAugmented
 -/
 
+#print CategoryTheory.simplicialCosimplicialAugmentedEquiv /-
 /-- The contravariant categorical equivalence between augmented simplicial
 objects and augmented cosimplicial objects in the opposite category. -/
 @[simps Functor inverse]
@@ -842,6 +931,7 @@ def simplicialCosimplicialAugmentedEquiv :
       rw [← f.op_unop]; simp_rw [← op_comp]; congr 1; tidy)
     ((NatIso.ofComponents fun X => X.leftOpRightOpIso) <| by tidy)
 #align category_theory.simplicial_cosimplicial_augmented_equiv CategoryTheory.simplicialCosimplicialAugmentedEquiv
+-/
 
 end CategoryTheory

814d76e2

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -45,7 +45,8 @@ variable (C : Type u) [Category.{v} C]
 This is the category of contravariant functors from `simplex_category` to `C`. -/
 @[nolint has_nonempty_instance]
 def SimplicialObject :=
-  SimplexCategoryᵒᵖ ⥤ C deriving Category
+  SimplexCategoryᵒᵖ ⥤ C
+deriving Category
 #align category_theory.simplicial_object CategoryTheory.SimplicialObject
 -/
 
@@ -209,7 +210,8 @@ def whiskering (D : Type _) [Category D] : (C ⥤ D) ⥤ SimplicialObject C ⥤
 /-- Truncated simplicial objects. -/
 @[nolint has_nonempty_instance]
 def Truncated (n : ℕ) :=
-  (SimplexCategory.Truncated n)ᵒᵖ ⥤ C deriving Category
+  (SimplexCategory.Truncated n)ᵒᵖ ⥤ C
+deriving Category
 #align category_theory.simplicial_object.truncated CategoryTheory.SimplicialObject.Truncated
 -/
 
@@ -267,7 +269,8 @@ abbrev const : C ⥤ SimplicialObject C :=
 /-- The category of augmented simplicial objects, defined as a comma category. -/
 @[nolint has_nonempty_instance]
 def Augmented :=
-  Comma (𝟭 (SimplicialObject C)) (const C)deriving Category
+  Comma (𝟭 (SimplicialObject C)) (const C)
+deriving Category
 #align category_theory.simplicial_object.augmented CategoryTheory.SimplicialObject.Augmented
 -/
 
@@ -392,7 +395,8 @@ end SimplicialObject
 /-- Cosimplicial objects. -/
 @[nolint has_nonempty_instance]
 def CosimplicialObject :=
-  SimplexCategory ⥤ C deriving Category
+  SimplexCategory ⥤ C
+deriving Category
 #align category_theory.cosimplicial_object CategoryTheory.CosimplicialObject
 -/
 
@@ -554,7 +558,8 @@ def whiskering (D : Type _) [Category D] : (C ⥤ D) ⥤ CosimplicialObject C 
 /-- Truncated cosimplicial objects. -/
 @[nolint has_nonempty_instance]
 def Truncated (n : ℕ) :=
-  SimplexCategory.Truncated n ⥤ C deriving Category
+  SimplexCategory.Truncated n ⥤ C
+deriving Category
 #align category_theory.cosimplicial_object.truncated CategoryTheory.CosimplicialObject.Truncated
 -/
 
@@ -612,7 +617,8 @@ abbrev const : C ⥤ CosimplicialObject C :=
 /-- Augmented cosimplicial objects. -/
 @[nolint has_nonempty_instance]
 def Augmented :=
-  Comma (const C) (𝟭 (CosimplicialObject C))deriving Category
+  Comma (const C) (𝟭 (CosimplicialObject C))
+deriving Category
 #align category_theory.cosimplicial_object.augmented CategoryTheory.CosimplicialObject.Augmented
 -/

814d76e2

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -169,7 +169,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
           (j.cast_lt
             ((add_lt_add_iff_right 1).mp
               (lt_of_lt_of_le
-                (by simpa only [[anonymous], ← Fin.val_succ] using fin.lt_iff_coe_lt_coe.mp H)
+                (by simpa only [Fin.val_eq_coe, ← Fin.val_succ] using fin.lt_iff_coe_lt_coe.mp H)
                 i.is_le))) :=
   by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'
@@ -515,7 +515,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
           (j.cast_lt
             ((add_lt_add_iff_right 1).mp
               (lt_of_lt_of_le
-                (by simpa only [[anonymous], ← Fin.val_succ] using fin.lt_iff_coe_lt_coe.mp H)
+                (by simpa only [Fin.val_eq_coe, ← Fin.val_succ] using fin.lt_iff_coe_lt_coe.mp H)
                 i.is_le))) ≫
         X.δ (i.pred fun hi => by simpa only [Fin.not_lt_zero, hi] using H) :=
   by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]

814d76e2

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -181,7 +181,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   simp only [← X.map_comp, ← op_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σ
 
-open Simplicial
+open scoped Simplicial
 
 @[simp, reassoc]
 theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
@@ -701,7 +701,7 @@ variable {C}
 
 end Augmented
 
-open Simplicial
+open scoped Simplicial
 
 /-- Augment a cosimplicial object with an object. -/
 @[simps]

814d76e2

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -70,52 +70,25 @@ instance [HasColimits C] : HasColimits (SimplicialObject C) :=
 
 variable {C} (X : SimplicialObject C)
 
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 /-- Face maps for a simplicial object. -/
 def δ {n} (i : Fin (n + 2)) : X _[n + 1] ⟶ X _[n] :=
   X.map (SimplexCategory.δ i).op
 #align category_theory.simplicial_object.δ CategoryTheory.SimplicialObject.δ
 
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 /-- Degeneracy maps for a simplicial object. -/
 def σ {n} (i : Fin (n + 1)) : X _[n] ⟶ X _[n + 1] :=
   X.map (SimplexCategory.σ i).op
 #align category_theory.simplicial_object.σ CategoryTheory.SimplicialObject.σ
 
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 /-- Isomorphisms from identities in ℕ. -/
 def eqToIso {n m : ℕ} (h : n = m) : X _[n] ≅ X _[m] :=
   X.mapIso (eqToIso (by rw [h]))
 #align category_theory.simplicial_object.eq_to_iso CategoryTheory.SimplicialObject.eqToIso
 
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 @[simp]
 theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by ext; simp [eq_to_iso]
 #align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_refl
 
-/- warning: category_theory.simplicial_object.δ_comp_δ -> CategoryTheory.SimplicialObject.δ_comp_δ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
@@ -123,9 +96,6 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
 
-/- warning: category_theory.simplicial_object.δ_comp_δ' -> CategoryTheory.SimplicialObject.δ_comp_δ' is a dubious translation:
-<too large>
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 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ j ≫ X.δ i =
@@ -133,9 +103,6 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
 
-/- warning: category_theory.simplicial_object.δ_comp_δ'' -> CategoryTheory.SimplicialObject.δ_comp_δ'' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ j.succ ≫ X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
@@ -143,26 +110,17 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''
 
-/- warning: category_theory.simplicial_object.δ_comp_δ_self -> CategoryTheory.SimplicialObject.δ_comp_δ_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
     X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by subst H; rw [δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'
 
-/- warning: category_theory.simplicial_object.δ_comp_σ_of_le -> CategoryTheory.SimplicialObject.δ_comp_σ_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
@@ -170,9 +128,6 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 𝟙 _ :=
@@ -181,20 +136,11 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_self, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_self
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by subst H; rw [δ_comp_σ_self]
 #align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'
 
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 /-- The second part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _ :=
@@ -203,20 +149,11 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_succ, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_succ CategoryTheory.SimplicialObject.δ_comp_σ_succ
 
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 @[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by subst H; rw [δ_comp_σ_succ]
 #align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'
 
-/- warning: category_theory.simplicial_object.δ_comp_σ_of_gt -> CategoryTheory.SimplicialObject.δ_comp_σ_of_gt is a dubious translation:
-<too large>
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 /-- The fourth simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
@@ -224,9 +161,6 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
@@ -240,9 +174,6 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
@@ -252,18 +183,12 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
 
 open Simplicial
 
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-<too large>
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 @[simp, reassoc]
 theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (op [n]) = f.app (op [n + 1]) ≫ X'.δ i :=
   f.naturality _
 #align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturality
 
-/- warning: category_theory.simplicial_object.σ_naturality -> CategoryTheory.SimplicialObject.σ_naturality is a dubious translation:
-<too large>
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 @[simp, reassoc]
 theorem σ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (op [n + 1]) = f.app (op [n]) ≫ X'.σ i :=
@@ -386,9 +311,6 @@ def toArrow : Augmented C ⥤ Arrow C
 #align category_theory.simplicial_object.augmented.to_arrow CategoryTheory.SimplicialObject.Augmented.toArrow
 -/
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augmented.w₀ CategoryTheory.SimplicialObject.Augmented.w₀ₓ'. -/
 /-- The compatibility of a morphism with the augmentation, on 0-simplices -/
 @[reassoc]
 theorem w₀ {X Y : Augmented C} (f : X ⟶ Y) :
@@ -442,9 +364,6 @@ variable {C}
 
 end Augmented
 
-/- warning: category_theory.simplicial_object.augment -> CategoryTheory.SimplicialObject.augment is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augmentₓ'. -/
 /-- Augment a simplicial object with an object. -/
 @[simps]
 def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
@@ -461,9 +380,6 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
         simpa only [← X.map_comp, ← category.assoc, category.comp_id, ← op_comp] using w _ _ _ }
 #align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augment
 
-/- warning: category_theory.simplicial_object.augment_hom_zero -> CategoryTheory.SimplicialObject.augment_hom_zero is a dubious translation:
-<too large>
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 @[simp]
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
     (X.augment X₀ f w).Hom.app (op [0]) = f := by dsimp;
@@ -501,52 +417,25 @@ instance [HasColimits C] : HasColimits (CosimplicialObject C) :=
 
 variable {C} (X : CosimplicialObject C)
 
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 /-- Coface maps for a cosimplicial object. -/
 def δ {n} (i : Fin (n + 2)) : X _[n] ⟶ X _[n + 1] :=
   X.map (SimplexCategory.δ i)
 #align category_theory.cosimplicial_object.δ CategoryTheory.CosimplicialObject.δ
 
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 /-- Codegeneracy maps for a cosimplicial object. -/
 def σ {n} (i : Fin (n + 1)) : X _[n + 1] ⟶ X _[n] :=
   X.map (SimplexCategory.σ i)
 #align category_theory.cosimplicial_object.σ CategoryTheory.CosimplicialObject.σ
 
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 /-- Isomorphisms from identities in ℕ. -/
 def eqToIso {n m : ℕ} (h : n = m) : X _[n] ≅ X _[m] :=
   X.mapIso (eqToIso (by rw [h]))
 #align category_theory.cosimplicial_object.eq_to_iso CategoryTheory.CosimplicialObject.eqToIso
 
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 @[simp]
 theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by ext; simp [eq_to_iso]
 #align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_refl
 
-/- warning: category_theory.cosimplicial_object.δ_comp_δ -> CategoryTheory.CosimplicialObject.δ_comp_δ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
@@ -554,9 +443,6 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ i ≫ X.δ j =
@@ -564,9 +450,6 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
 
-/- warning: category_theory.cosimplicial_object.δ_comp_δ'' -> CategoryTheory.CosimplicialObject.δ_comp_δ'' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
@@ -574,26 +457,17 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''
 
-/- warning: category_theory.cosimplicial_object.δ_comp_δ_self -> CategoryTheory.CosimplicialObject.δ_comp_δ_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.δ i ≫ X.δ i.succ := by
   dsimp [δ]; simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
     X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by subst H; rw [δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'
 
-/- warning: category_theory.cosimplicial_object.δ_comp_σ_of_le -> CategoryTheory.CosimplicialObject.δ_comp_σ_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
@@ -601,9 +475,6 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 𝟙 _ :=
@@ -612,20 +483,11 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_self, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_self
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by subst H; rw [δ_comp_σ_self]
 #align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'
 
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 /-- The second part of the third cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _ :=
@@ -634,20 +496,11 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_succ, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ CategoryTheory.CosimplicialObject.δ_comp_σ_succ
 
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 @[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by subst H; rw [δ_comp_σ_succ]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'
 
-/- warning: category_theory.cosimplicial_object.δ_comp_σ_of_gt -> CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt is a dubious translation:
-<too large>
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 /-- The fourth cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
@@ -655,9 +508,6 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
 
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-<too large>
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 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.δ i ≫ X.σ j =
@@ -671,9 +521,6 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth cosimplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
@@ -681,24 +528,12 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   simp only [← X.map_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σ
 
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 @[simp, reassoc]
 theorem δ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (SimplexCategory.mk (n + 1)) = f.app (SimplexCategory.mk n) ≫ X'.δ i :=
   f.naturality _
 #align category_theory.cosimplicial_object.δ_naturality CategoryTheory.CosimplicialObject.δ_naturality
 
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 @[simp, reassoc]
 theorem σ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (SimplexCategory.mk n) = f.app (SimplexCategory.mk (n + 1)) ≫ X'.σ i :=
@@ -868,12 +703,6 @@ end Augmented
 
 open Simplicial
 
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 /-- Augment a cosimplicial object with an object. -/
 @[simps]
 def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
@@ -889,9 +718,6 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
         simpa [← X.map_comp] using w _ _ _ }
 #align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augment
 
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 @[simp]
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :
     (X.augment X₀ f w).Hom.app [0] = f := by dsimp;
@@ -900,24 +726,12 @@ theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.o
 
 end CosimplicialObject
 
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 /-- The anti-equivalence between simplicial objects and cosimplicial objects. -/
 @[simps]
 def simplicialCosimplicialEquiv : (SimplicialObject C)ᵒᵖ ≌ CosimplicialObject Cᵒᵖ :=
   Functor.leftOpRightOpEquiv _ _
 #align category_theory.simplicial_cosimplicial_equiv CategoryTheory.simplicialCosimplicialEquiv
 
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-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u1 u2, max u1 u2} (Opposite.{succ (max u1 u2)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u1 u2} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{max (succ u2) (succ u1)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategorySimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
-Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_simplicial_equiv CategoryTheory.cosimplicialSimplicialEquivₓ'. -/
 /-- The anti-equivalence between cosimplicial objects and simplicial objects. -/
 @[simps]
 def cosimplicialSimplicialEquiv : (CosimplicialObject C)ᵒᵖ ≌ SimplicialObject Cᵒᵖ :=
@@ -1012,12 +826,6 @@ def cosimplicialToSimplicialAugmented :
 #align category_theory.cosimplicial_to_simplicial_augmented CategoryTheory.cosimplicialToSimplicialAugmented
 -/
 
-/- warning: category_theory.simplicial_cosimplicial_augmented_equiv -> CategoryTheory.simplicialCosimplicialAugmentedEquiv is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max (max u1 u2) u2 u1, max u1 u2} (Opposite.{succ (max (max u1 u2) u2 u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max (max u1 u2) u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.Augmented.category.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{max (succ u2) (succ u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.instCategoryAugmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
-Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_cosimplicial_augmented_equiv CategoryTheory.simplicialCosimplicialAugmentedEquivₓ'. -/
 /-- The contravariant categorical equivalence between augmented simplicial
 objects and augmented cosimplicial objects in the opposite category. -/
 @[simps Functor inverse]

814d76e2

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -57,19 +57,13 @@ scoped[Simplicial]
     (X : CategoryTheory.SimplicialObject hole!).obj (Opposite.op (SimplexCategory.mk n))
 
 instance {J : Type v} [SmallCategory J] [HasLimitsOfShape J C] :
-    HasLimitsOfShape J (SimplicialObject C) :=
-  by
-  dsimp [simplicial_object]
-  infer_instance
+    HasLimitsOfShape J (SimplicialObject C) := by dsimp [simplicial_object]; infer_instance
 
 instance [HasLimits C] : HasLimits (SimplicialObject C) :=
   ⟨inferInstance⟩
 
 instance {J : Type v} [SmallCategory J] [HasColimitsOfShape J C] :
-    HasColimitsOfShape J (SimplicialObject C) :=
-  by
-  dsimp [simplicial_object]
-  infer_instance
+    HasColimitsOfShape J (SimplicialObject C) := by dsimp [simplicial_object]; infer_instance
 
 instance [HasColimits C] : HasColimits (SimplicialObject C) :=
   ⟨inferInstance⟩
@@ -116,10 +110,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} (h : Eq.{1} Nat n n), Eq.{succ u1} (CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.SimplicialObject.eqToIso.{u1, u2} C _inst_1 X n n h) (CategoryTheory.Iso.refl.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_reflₓ'. -/
 @[simp]
-theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
-  by
-  ext
-  simp [eq_to_iso]
+theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by ext; simp [eq_to_iso]
 #align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_refl
 
 /- warning: category_theory.simplicial_object.δ_comp_δ -> CategoryTheory.SimplicialObject.δ_comp_δ is a dubious translation:
@@ -128,9 +119,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.simpli
 /-- The generic case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    X.δ j.succ ≫ X.δ i = X.δ i.cast_succ ≫ X.δ j :=
-  by
-  dsimp [δ]
+    X.δ j.succ ≫ X.δ i = X.δ i.cast_succ ≫ X.δ j := by dsimp [δ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
 
@@ -141,9 +130,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.simpli
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ j ≫ X.δ i =
       X.δ i.cast_succ ≫ X.δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) :=
-  by
-  dsimp [δ]
-  simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
+  by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
 
 /- warning: category_theory.simplicial_object.δ_comp_δ'' -> CategoryTheory.SimplicialObject.δ_comp_δ'' is a dubious translation:
@@ -153,9 +140,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.simpli
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ j.succ ≫ X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
       X.δ i ≫ X.δ j :=
-  by
-  dsimp [δ]
-  simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
+  by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''
 
 /- warning: category_theory.simplicial_object.δ_comp_δ_self -> CategoryTheory.SimplicialObject.δ_comp_δ_self is a dubious translation:
@@ -163,10 +148,8 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc]
-theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.δ i.succ ≫ X.δ i :=
-  by
-  dsimp [δ]
-  simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
+theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
+  dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
 
 /- warning: category_theory.simplicial_object.δ_comp_δ_self' -> CategoryTheory.SimplicialObject.δ_comp_δ_self' is a dubious translation:
@@ -174,9 +157,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
-    X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
-  subst H
-  rw [δ_comp_δ_self]
+    X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by subst H; rw [δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'
 
 /- warning: category_theory.simplicial_object.δ_comp_σ_of_le -> CategoryTheory.SimplicialObject.δ_comp_σ_of_le is a dubious translation:
@@ -185,9 +166,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.simpli
 /-- The second simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
-    X.σ j.succ ≫ X.δ i.cast_succ = X.δ i ≫ X.σ j :=
-  by
-  dsimp [δ, σ]
+    X.σ j.succ ≫ X.δ i.cast_succ = X.δ i ≫ X.σ j := by dsimp [δ, σ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
 
@@ -207,9 +186,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
-    X.σ i ≫ X.δ j = 𝟙 _ := by
-  subst H
-  rw [δ_comp_σ_self]
+    X.σ i ≫ X.δ j = 𝟙 _ := by subst H; rw [δ_comp_σ_self]
 #align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'
 
 /- warning: category_theory.simplicial_object.δ_comp_σ_succ -> CategoryTheory.SimplicialObject.δ_comp_σ_succ is a dubious translation:
@@ -234,9 +211,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
-    X.σ i ≫ X.δ j = 𝟙 _ := by
-  subst H
-  rw [δ_comp_σ_succ]
+    X.σ i ≫ X.δ j = 𝟙 _ := by subst H; rw [δ_comp_σ_succ]
 #align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'
 
 /- warning: category_theory.simplicial_object.δ_comp_σ_of_gt -> CategoryTheory.SimplicialObject.δ_comp_σ_of_gt is a dubious translation:
@@ -245,9 +220,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.simpli
 /-- The fourth simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
-    X.σ j.cast_succ ≫ X.δ i.succ = X.δ i ≫ X.σ j :=
-  by
-  dsimp [δ, σ]
+    X.σ j.cast_succ ≫ X.δ i.succ = X.δ i ≫ X.σ j := by dsimp [δ, σ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
 
@@ -264,9 +237,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
               (lt_of_lt_of_le
                 (by simpa only [[anonymous], ← Fin.val_succ] using fin.lt_iff_coe_lt_coe.mp H)
                 i.is_le))) :=
-  by
-  dsimp [δ, σ]
-  simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
+  by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'
 
 /- warning: category_theory.simplicial_object.σ_comp_σ -> CategoryTheory.SimplicialObject.σ_comp_σ is a dubious translation:
@@ -275,9 +246,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.simpli
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    X.σ j ≫ X.σ i.cast_succ = X.σ i ≫ X.σ j.succ :=
-  by
-  dsimp [δ, σ]
+    X.σ j ≫ X.σ i.cast_succ = X.σ i ≫ X.σ j.succ := by dsimp [δ, σ];
   simp only [← X.map_comp, ← op_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σ
 
@@ -324,19 +293,13 @@ variable {C}
 namespace Truncated
 
 instance {n} {J : Type v} [SmallCategory J] [HasLimitsOfShape J C] :
-    HasLimitsOfShape J (SimplicialObject.Truncated C n) :=
-  by
-  dsimp [truncated]
-  infer_instance
+    HasLimitsOfShape J (SimplicialObject.Truncated C n) := by dsimp [truncated]; infer_instance
 
 instance {n} [HasLimits C] : HasLimits (SimplicialObject.Truncated C n) :=
   ⟨inferInstance⟩
 
 instance {n} {J : Type v} [SmallCategory J] [HasColimitsOfShape J C] :
-    HasColimitsOfShape J (SimplicialObject.Truncated C n) :=
-  by
-  dsimp [truncated]
-  infer_instance
+    HasColimitsOfShape J (SimplicialObject.Truncated C n) := by dsimp [truncated]; infer_instance
 
 instance {n} [HasColimits C] : HasColimits (SimplicialObject.Truncated C n) :=
   ⟨inferInstance⟩
@@ -503,8 +466,7 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augment_hom_zero CategoryTheory.SimplicialObject.augment_hom_zeroₓ'. -/
 @[simp]
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
-    (X.augment X₀ f w).Hom.app (op [0]) = f := by
-  dsimp
+    (X.augment X₀ f w).Hom.app (op [0]) = f := by dsimp;
   rw [SimplexCategory.hom_zero_zero ([0].const 0), op_id, X.map_id, category.id_comp]
 #align category_theory.simplicial_object.augment_hom_zero CategoryTheory.SimplicialObject.augment_hom_zero
 
@@ -526,19 +488,13 @@ scoped[Simplicial]
     (X : CategoryTheory.CosimplicialObject hole!).obj (SimplexCategory.mk n)
 
 instance {J : Type v} [SmallCategory J] [HasLimitsOfShape J C] :
-    HasLimitsOfShape J (CosimplicialObject C) :=
-  by
-  dsimp [cosimplicial_object]
-  infer_instance
+    HasLimitsOfShape J (CosimplicialObject C) := by dsimp [cosimplicial_object]; infer_instance
 
 instance [HasLimits C] : HasLimits (CosimplicialObject C) :=
   ⟨inferInstance⟩
 
 instance {J : Type v} [SmallCategory J] [HasColimitsOfShape J C] :
-    HasColimitsOfShape J (CosimplicialObject C) :=
-  by
-  dsimp [cosimplicial_object]
-  infer_instance
+    HasColimitsOfShape J (CosimplicialObject C) := by dsimp [cosimplicial_object]; infer_instance
 
 instance [HasColimits C] : HasColimits (CosimplicialObject C) :=
   ⟨inferInstance⟩
@@ -585,10 +541,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} (h : Eq.{1} Nat n n), Eq.{succ u1} (CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CosimplicialObject.eqToIso.{u1, u2} C _inst_1 X n n h) (CategoryTheory.Iso.refl.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_reflₓ'. -/
 @[simp]
-theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
-  by
-  ext
-  simp [eq_to_iso]
+theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by ext; simp [eq_to_iso]
 #align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_refl
 
 /- warning: category_theory.cosimplicial_object.δ_comp_δ -> CategoryTheory.CosimplicialObject.δ_comp_δ is a dubious translation:
@@ -597,9 +550,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.cosimp
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ i.cast_succ :=
-  by
-  dsimp [δ]
+    X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ i.cast_succ := by dsimp [δ];
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
 
@@ -610,9 +561,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.cosimp
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ i ≫ X.δ j =
       X.δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ X.δ i.cast_succ :=
-  by
-  dsimp [δ]
-  simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
+  by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
 
 /- warning: category_theory.cosimplicial_object.δ_comp_δ'' -> CategoryTheory.CosimplicialObject.δ_comp_δ'' is a dubious translation:
@@ -622,9 +571,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.cosimp
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
       X.δ j ≫ X.δ i :=
-  by
-  dsimp [δ]
-  simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
+  by dsimp [δ]; simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''
 
 /- warning: category_theory.cosimplicial_object.δ_comp_δ_self -> CategoryTheory.CosimplicialObject.δ_comp_δ_self is a dubious translation:
@@ -632,10 +579,8 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.δ i ≫ X.δ i.succ :=
-  by
-  dsimp [δ]
-  simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
+theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.δ i ≫ X.δ i.succ := by
+  dsimp [δ]; simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
 
 /- warning: category_theory.cosimplicial_object.δ_comp_δ_self' -> CategoryTheory.CosimplicialObject.δ_comp_δ_self' is a dubious translation:
@@ -643,9 +588,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
-    X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by
-  subst H
-  rw [δ_comp_δ_self]
+    X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by subst H; rw [δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'
 
 /- warning: category_theory.cosimplicial_object.δ_comp_σ_of_le -> CategoryTheory.CosimplicialObject.δ_comp_σ_of_le is a dubious translation:
@@ -654,9 +597,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.cosimp
 /-- The second cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
-    X.δ i.cast_succ ≫ X.σ j.succ = X.σ j ≫ X.δ i :=
-  by
-  dsimp [δ, σ]
+    X.δ i.cast_succ ≫ X.σ j.succ = X.σ j ≫ X.δ i := by dsimp [δ, σ];
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
 
@@ -676,9 +617,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
-    X.δ j ≫ X.σ i = 𝟙 _ := by
-  subst H
-  rw [δ_comp_σ_self]
+    X.δ j ≫ X.σ i = 𝟙 _ := by subst H; rw [δ_comp_σ_self]
 #align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'
 
 /- warning: category_theory.cosimplicial_object.δ_comp_σ_succ -> CategoryTheory.CosimplicialObject.δ_comp_σ_succ is a dubious translation:
@@ -703,9 +642,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
-    X.δ j ≫ X.σ i = 𝟙 _ := by
-  subst H
-  rw [δ_comp_σ_succ]
+    X.δ j ≫ X.σ i = 𝟙 _ := by subst H; rw [δ_comp_σ_succ]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'
 
 /- warning: category_theory.cosimplicial_object.δ_comp_σ_of_gt -> CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt is a dubious translation:
@@ -714,9 +651,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.cosimp
 /-- The fourth cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
-    X.δ i.succ ≫ X.σ j.cast_succ = X.σ j ≫ X.δ i :=
-  by
-  dsimp [δ, σ]
+    X.δ i.succ ≫ X.σ j.cast_succ = X.σ j ≫ X.δ i := by dsimp [δ, σ];
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
 
@@ -733,9 +668,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
                 (by simpa only [[anonymous], ← Fin.val_succ] using fin.lt_iff_coe_lt_coe.mp H)
                 i.is_le))) ≫
         X.δ (i.pred fun hi => by simpa only [Fin.not_lt_zero, hi] using H) :=
-  by
-  dsimp [δ, σ]
-  simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
+  by dsimp [δ, σ]; simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'
 
 /- warning: category_theory.cosimplicial_object.σ_comp_σ -> CategoryTheory.CosimplicialObject.σ_comp_σ is a dubious translation:
@@ -744,9 +677,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.cosimp
 /-- The fifth cosimplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    X.σ i.cast_succ ≫ X.σ j = X.σ j.succ ≫ X.σ i :=
-  by
-  dsimp [δ, σ]
+    X.σ i.cast_succ ≫ X.σ j = X.σ j.succ ≫ X.σ i := by dsimp [δ, σ];
   simp only [← X.map_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σ
 
@@ -797,19 +728,13 @@ variable {C}
 namespace Truncated
 
 instance {n} {J : Type v} [SmallCategory J] [HasLimitsOfShape J C] :
-    HasLimitsOfShape J (CosimplicialObject.Truncated C n) :=
-  by
-  dsimp [truncated]
-  infer_instance
+    HasLimitsOfShape J (CosimplicialObject.Truncated C n) := by dsimp [truncated]; infer_instance
 
 instance {n} [HasLimits C] : HasLimits (CosimplicialObject.Truncated C n) :=
   ⟨inferInstance⟩
 
 instance {n} {J : Type v} [SmallCategory J] [HasColimitsOfShape J C] :
-    HasColimitsOfShape J (CosimplicialObject.Truncated C n) :=
-  by
-  dsimp [truncated]
-  infer_instance
+    HasColimitsOfShape J (CosimplicialObject.Truncated C n) := by dsimp [truncated]; infer_instance
 
 instance {n} [HasColimits C] : HasColimits (CosimplicialObject.Truncated C n) :=
   ⟨inferInstance⟩
@@ -969,8 +894,7 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.augment_hom_zero CategoryTheory.CosimplicialObject.augment_hom_zeroₓ'. -/
 @[simp]
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :
-    (X.augment X₀ f w).Hom.app [0] = f := by
-  dsimp
+    (X.augment X₀ f w).Hom.app [0] = f := by dsimp;
   rw [SimplexCategory.hom_zero_zero ([0].const 0), X.map_id, category.comp_id]
 #align category_theory.cosimplicial_object.augment_hom_zero CategoryTheory.CosimplicialObject.augment_hom_zero
 
@@ -1100,13 +1024,8 @@ objects and augmented cosimplicial objects in the opposite category. -/
 def simplicialCosimplicialAugmentedEquiv :
     (SimplicialObject.Augmented C)ᵒᵖ ≌ CosimplicialObject.Augmented Cᵒᵖ :=
   Equivalence.mk (simplicialToCosimplicialAugmented _) (cosimplicialToSimplicialAugmented _)
-    (NatIso.ofComponents (fun X => X.unop.rightOpLeftOpIso.op) fun X Y f =>
-      by
-      dsimp
-      rw [← f.op_unop]
-      simp_rw [← op_comp]
-      congr 1
-      tidy)
+    (NatIso.ofComponents (fun X => X.unop.rightOpLeftOpIso.op) fun X Y f => by dsimp;
+      rw [← f.op_unop]; simp_rw [← op_comp]; congr 1; tidy)
     ((NatIso.ofComponents fun X => X.leftOpRightOpIso) <| by tidy)
 #align category_theory.simplicial_cosimplicial_augmented_equiv CategoryTheory.simplicialCosimplicialAugmentedEquiv

814d76e2

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -123,10 +123,7 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
 #align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_refl
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 @[reassoc]
@@ -138,10 +135,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
 
 /- warning: category_theory.simplicial_object.δ_comp_δ' -> CategoryTheory.SimplicialObject.δ_comp_δ' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
@@ -153,10 +147,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
@@ -168,10 +159,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 #align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''
 
 /- warning: category_theory.simplicial_object.δ_comp_δ_self -> CategoryTheory.SimplicialObject.δ_comp_δ_self is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc]
@@ -182,10 +170,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
@@ -195,10 +180,7 @@ theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast
 #align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc]
@@ -210,10 +192,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc]
@@ -224,10 +203,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
 #align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_self
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
@@ -264,10 +240,7 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 #align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc]
@@ -279,10 +252,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
@@ -300,10 +270,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 #align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc]
@@ -317,10 +284,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
 open Simplicial
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturalityₓ'. -/
 @[simp, reassoc]
 theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
@@ -329,10 +293,7 @@ theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i :
 #align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturality
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_naturality CategoryTheory.SimplicialObject.σ_naturalityₓ'. -/
 @[simp, reassoc]
 theorem σ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
@@ -463,10 +424,7 @@ def toArrow : Augmented C ⥤ Arrow C
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augmented.w₀ CategoryTheory.SimplicialObject.Augmented.w₀ₓ'. -/
 /-- The compatibility of a morphism with the augmentation, on 0-simplices -/
 @[reassoc]
@@ -522,10 +480,7 @@ variable {C}
 end Augmented
 
 /- warning: category_theory.simplicial_object.augment -> CategoryTheory.SimplicialObject.augment is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augmentₓ'. -/
 /-- Augment a simplicial object with an object. -/
 @[simps]
@@ -544,10 +499,7 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
 #align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augment
 
 /- warning: category_theory.simplicial_object.augment_hom_zero -> CategoryTheory.SimplicialObject.augment_hom_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augment_hom_zero CategoryTheory.SimplicialObject.augment_hom_zeroₓ'. -/
 @[simp]
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
@@ -640,10 +592,7 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
 #align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_refl
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc]
@@ -655,10 +604,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
 
 /- warning: category_theory.cosimplicial_object.δ_comp_δ' -> CategoryTheory.CosimplicialObject.δ_comp_δ' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
@@ -670,10 +616,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
@@ -685,10 +628,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 #align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
 @[reassoc]
@@ -699,10 +639,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
@@ -712,10 +649,7 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast
 #align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second cosimplicial identity -/
 @[reassoc]
@@ -727,10 +661,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third cosimplicial identity -/
 @[reassoc]
@@ -741,10 +672,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
 #align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_self
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
@@ -781,10 +709,7 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 #align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth cosimplicial identity -/
 @[reassoc]
@@ -796,10 +721,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
@@ -817,10 +739,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth cosimplicial identity -/
 @[reassoc]
@@ -1046,10 +965,7 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
 #align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augment
 
 /- warning: category_theory.cosimplicial_object.augment_hom_zero -> CategoryTheory.CosimplicialObject.augment_hom_zero is a dubious translation:
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(CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Comma.right.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)))) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Comma.right.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) f
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.augment_hom_zero CategoryTheory.CosimplicialObject.augment_hom_zeroₓ'. -/
 @[simp]
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :

814d76e2

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -129,7 +129,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat 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(instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
     X.δ j.succ ≫ X.δ i = X.δ i.cast_succ ≫ X.δ j :=
   by
@@ -143,7 +143,7 @@ lean 3 declaration is
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ j ≫ X.δ i =
       X.δ i.cast_succ ≫ X.δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) :=
@@ -158,7 +158,7 @@ lean 3 declaration is
 but is expected to have type
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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j)) H) (Fin.is_lt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ j.succ ≫ X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
       X.δ i ≫ X.δ j :=
@@ -174,7 +174,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) 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x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 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C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.δ i.succ ≫ X.δ i :=
   by
   dsimp [δ]
@@ -187,7 +187,7 @@ lean 3 declaration is
 but is expected to have type
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Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
     X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   subst H
@@ -201,7 +201,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 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(instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} 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x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C 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(CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} 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(OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
     X.σ j.succ ≫ X.δ i.cast_succ = X.δ i ≫ X.σ j :=
   by
@@ -216,7 +216,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i))) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 𝟙 _ :=
   by
   dsimp [δ, σ]
@@ -229,7 +229,7 @@ lean 3 declaration is
 but is expected to have type
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Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by
   subst H
@@ -243,7 +243,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_succ CategoryTheory.SimplicialObject.δ_comp_σ_succₓ'. -/
 /-- The second part of the third simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _ :=
   by
   dsimp [δ, σ]
@@ -256,7 +256,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by
   subst H
@@ -270,7 +270,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LT.lt.{0} ((fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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(x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) 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Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j) i) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) 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(CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
     X.σ j.cast_succ ≫ X.δ i.succ = X.δ i ≫ X.σ j :=
   by
@@ -284,7 +284,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} (H : LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) i), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory 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Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n (Fin.pred (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i (fun (hi : Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) => False.elim.{0} False (Eq.mp.{0} (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) i) False (Eq.trans.{1} Prop (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) i) (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) False (congrArg.{1, 1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) Prop i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)) hi) (Mathlib.AlgebraicTopology.SimplicialObject._auxLemma.2 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) H)))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n (Fin.castLT (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j (Iff.mp (LT.lt.{0} Nat instLTNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (add_lt_add_iff_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) (OrderedCancelAddCommMonoid.to_contravariantClass_right.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.val (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) H (Fin.is_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i))))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
       X.δ (i.pred fun hi => by simpa only [Fin.not_lt_zero, hi] using H) ≫
@@ -306,7 +306,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
     X.σ j ≫ X.σ i.cast_succ = X.σ i ≫ X.σ j.succ :=
   by
@@ -322,7 +322,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X' : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1} {X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1} (f : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) X X') {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X X' f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X X' f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X' n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (op [n]) = f.app (op [n + 1]) ≫ X'.δ i :=
   f.naturality _
@@ -334,7 +334,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X' : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1} {X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1} (f : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) X X') {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X X' f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X X' f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X' n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_naturality CategoryTheory.SimplicialObject.σ_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem σ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (op [n + 1]) = f.app (op [n]) ≫ X'.σ i :=
   f.naturality _
@@ -469,7 +469,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1} {Y : CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1} (f : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1))) X Y), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.Augmented.drop.{u1, u2} C _inst_1)) X)) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) Y))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.Augmented.drop.{u1, u2} C _inst_1)) X)) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.Augmented.drop.{u1, u2} C _inst_1)) Y)) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) Y))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} 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(CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Comma.left.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) Y)) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) Y)) (CategoryTheory.Comma.hom.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) 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(CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) X))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Prefunctor.obj.{succ u1, succ u1, max u2 u1, u2} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, u2} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.Augmented.point.{u1, u2} C _inst_1)) Y) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Comma.left.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) X)) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) X)) (CategoryTheory.Comma.hom.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Prefunctor.map.{succ u1, succ u1, max u2 u1, u2} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, u2} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.Augmented.point.{u1, u2} C _inst_1)) X Y f))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augmented.w₀ CategoryTheory.SimplicialObject.Augmented.w₀ₓ'. -/
 /-- The compatibility of a morphism with the augmentation, on 0-simplices -/
-@[reassoc.1]
+@[reassoc]
 theorem w₀ {X Y : Augmented C} (f : X ⟶ Y) :
     (Augmented.drop.map f).app (op (SimplexCategory.mk 0)) ≫ Y.Hom.app (op (SimplexCategory.mk 0)) =
       X.Hom.app (op (SimplexCategory.mk 0)) ≫ Augmented.point.map f :=
@@ -646,7 +646,7 @@ but is expected to have type
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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C 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0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 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 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
     X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ i.cast_succ :=
   by
@@ -660,7 +660,7 @@ lean 3 declaration is
 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ i ≫ X.δ j =
       X.δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ X.δ i.cast_succ :=
@@ -675,7 +675,7 @@ lean 3 declaration is
 but is expected to have type
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1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 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(instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j)) H) (Fin.is_lt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
       X.δ j ≫ X.δ i :=
@@ -691,7 +691,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.δ i ≫ X.δ i.succ :=
   by
   dsimp [δ]
@@ -704,7 +704,7 @@ lean 3 declaration is
 but is expected to have type
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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
     X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by
   subst H
@@ -718,7 +718,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
     X.δ i.cast_succ ≫ X.σ j.succ = X.σ j ≫ X.δ i :=
   by
@@ -733,7 +733,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 𝟙 _ :=
   by
   dsimp [δ, σ]
@@ -746,7 +746,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by
   subst H
@@ -760,7 +760,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_succ CategoryTheory.CosimplicialObject.δ_comp_σ_succₓ'. -/
 /-- The second part of the third cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _ :=
   by
   dsimp [δ, σ]
@@ -773,7 +773,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by
   subst H
@@ -787,7 +787,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LT.lt.{0} ((fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
     X.δ i.succ ≫ X.σ j.cast_succ = X.σ j ≫ X.δ i :=
   by
@@ -801,7 +801,7 @@ lean 3 declaration is
 but is expected to have type
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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)) hi) (Mathlib.AlgebraicTopology.SimplicialObject._auxLemma.2 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) H)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.δ i ≫ X.σ j =
       X.σ
@@ -823,7 +823,7 @@ but is expected to have type
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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth cosimplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
     X.σ i.cast_succ ≫ X.σ j = X.σ j.succ ≫ X.σ i :=
   by
@@ -837,7 +837,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X' : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1} {X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1} (f : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) X X') {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X X' f (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X X' f (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X' n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_naturality CategoryTheory.CosimplicialObject.δ_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem δ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (SimplexCategory.mk (n + 1)) = f.app (SimplexCategory.mk n) ≫ X'.δ i :=
   f.naturality _
@@ -849,7 +849,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X' : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1} {X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1} (f : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) X X') {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X X' f (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X') (SimplexCategory.mk n)) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X X' f (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X' n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_naturality CategoryTheory.CosimplicialObject.σ_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem σ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (SimplexCategory.mk n) = f.app (SimplexCategory.mk (n + 1)) ≫ X'.σ i :=
   f.naturality _

814d76e2

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -126,7 +126,7 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) j)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} 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 but is expected to have type
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(Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 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(instOfNatNat 2)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 @[reassoc.1]
@@ -141,7 +141,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} (H : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n 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 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
@@ -156,7 +156,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 lean 3 declaration is
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(CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
@@ -171,7 +171,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 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Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc.1]
@@ -185,7 +185,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.
 lean 3 declaration is
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Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} 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(Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 but is expected to have type
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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) j (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 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(instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
@@ -198,7 +198,7 @@ theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast
 lean 3 declaration is
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(OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc.1]
@@ -213,7 +213,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 lean 3 declaration is
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 but is expected to have type
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SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} 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(CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i))) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc.1]
@@ -227,7 +227,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
 lean 3 declaration is
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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
 but is expected to have type
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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
@@ -267,7 +267,7 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 lean 3 declaration is
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(OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin 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Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) j) i) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 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(CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LT.lt.{0} ((fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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(instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc.1]
@@ -303,7 +303,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 lean 3 declaration is
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Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) j))))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) 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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc.1]
@@ -643,7 +643,7 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
 lean 3 declaration is
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 but is expected to have type
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} 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instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 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(x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc.1]
@@ -658,7 +658,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 lean 3 declaration is
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x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
@@ -673,7 +673,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 lean 3 declaration is
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x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j)) H) (Fin.is_lt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
@@ -688,7 +688,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) 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(CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) 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Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat 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 but is expected to have type
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(CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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(instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory 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(instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
 @[reassoc.1]
@@ -702,7 +702,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.
 lean 3 declaration is
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) j (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, 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(SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
@@ -715,7 +715,7 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast
 lean 3 declaration is
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(instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second cosimplicial identity -/
 @[reassoc.1]
@@ -730,7 +730,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 lean 3 declaration is
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 but is expected to have type
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) 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(x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third cosimplicial identity -/
 @[reassoc.1]
@@ -744,7 +744,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
 lean 3 declaration is
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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n))))
 but is expected to have type
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n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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(instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
@@ -784,7 +784,7 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 lean 3 declaration is
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n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth cosimplicial identity -/
 @[reassoc.1]
@@ -820,7 +820,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory 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(CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth cosimplicial identity -/
 @[reassoc.1]

814d76e2

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -280,7 +280,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
 
 /- warning: category_theory.simplicial_object.δ_comp_σ_of_gt' -> CategoryTheory.SimplicialObject.δ_comp_σ_of_gt' is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (add_lt_add_iff_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) (OrderedCancelAddCommMonoid.to_contravariantClass_right.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 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 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
@@ -797,7 +797,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
 
 /- warning: category_theory.cosimplicial_object.δ_comp_σ_of_gt' -> CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt' is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} (H : LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) i), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n (Fin.castLT (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j (Iff.mp (LT.lt.{0} Nat instLTNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (add_lt_add_iff_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) (OrderedCancelAddCommMonoid.to_contravariantClass_right.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.val (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) H (Fin.is_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n (Fin.pred (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i (fun (hi : Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) => False.elim.{0} False (Eq.mp.{0} (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) i) False (Eq.trans.{1} Prop (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) i) (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) False (congrArg.{1, 1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) Prop i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (LT.lt.{0} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (instLTFin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)) hi) (Mathlib.AlgebraicTopology.SimplicialObject._auxLemma.2 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) H)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'ₓ'. -/

814d76e2

bump to nightly-2023-04-20-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

fbfe5c3e

Diff

@@ -126,7 +126,7 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) 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 but is expected to have type
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 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(instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 @[reassoc.1]
@@ -141,7 +141,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} (H : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 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(OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 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 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
@@ -156,7 +156,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} (H : LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n 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(Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
@@ -171,7 +171,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} 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Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc.1]
@@ -185,7 +185,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) j (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 but is expected to have type
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u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, 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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
@@ -198,7 +198,7 @@ theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast
 lean 3 declaration is
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 but is expected to have type
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SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} 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_inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc.1]
@@ -213,7 +213,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i))) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) i))) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory 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(CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc.1]
@@ -227,7 +227,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
 lean 3 declaration is
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 but is expected to have type
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(x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
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(instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) 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SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
@@ -267,7 +267,7 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 lean 3 declaration is
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Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 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 but is expected to have type
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(CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc.1]
@@ -303,7 +303,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n j) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) j))))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} 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(CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X n i) (CategoryTheory.SimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j))))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc.1]
@@ -643,7 +643,7 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc.1]
@@ -658,7 +658,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 lean 3 declaration is
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 but is expected to have type
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n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 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Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))) H)))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
@@ -673,7 +673,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 lean 3 declaration is
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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j)) H) (Fin.is_lt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j)))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
@@ -688,7 +688,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) 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(CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) 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Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat 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 but is expected to have type
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(CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
 @[reassoc.1]
@@ -702,7 +702,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) j (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) i))))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) j (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun 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 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
@@ -715,7 +715,7 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast
 lean 3 declaration is
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instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second cosimplicial identity -/
 @[reassoc.1]
@@ -730,7 +730,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)))
 but is expected to have type
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LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third cosimplicial identity -/
 @[reassoc.1]
@@ -744,7 +744,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
 lean 3 declaration is
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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, 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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.δ.{u1, u2} C _inst_1 X n j) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
@@ -784,7 +784,7 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin 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 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth cosimplicial identity -/
 @[reassoc.1]
@@ -820,7 +820,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ 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 but is expected to have type
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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C 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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i j) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CategoryStruct.comp.{u1, u2} C 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CosimplicialObject.σ.{u1, u2} C _inst_1 X n i)))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth cosimplicial identity -/
 @[reassoc.1]

814d76e2

bump to nightly-2023-04-18-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

c37d1701

Diff

@@ -1064,7 +1064,7 @@ end CosimplicialObject
 lean 3 declaration is
   forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u1 u2, max u1 u2} (Opposite.{succ (max u1 u2)} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
 but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{succ (max u2 u1)} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{max (succ u2) (succ u1)} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_cosimplicial_equiv CategoryTheory.simplicialCosimplicialEquivₓ'. -/
 /-- The anti-equivalence between simplicial objects and cosimplicial objects. -/
 @[simps]
@@ -1076,7 +1076,7 @@ def simplicialCosimplicialEquiv : (SimplicialObject C)ᵒᵖ ≌ CosimplicialObj
 lean 3 declaration is
   forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u1 u2, max u1 u2} (Opposite.{succ (max u1 u2)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u1 u2} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
 but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{succ (max u2 u1)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategorySimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{max (succ u2) (succ u1)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategorySimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
 Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_simplicial_equiv CategoryTheory.cosimplicialSimplicialEquivₓ'. -/
 /-- The anti-equivalence between cosimplicial objects and simplicial objects. -/
 @[simps]
@@ -1176,7 +1176,7 @@ def cosimplicialToSimplicialAugmented :
 lean 3 declaration is
   forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max (max u1 u2) u2 u1, max u1 u2} (Opposite.{succ (max (max u1 u2) u2 u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max (max u1 u2) u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.Augmented.category.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
 but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{succ (max u2 u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.instCategoryAugmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{max (succ u2) (succ u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.instCategoryAugmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
 Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_cosimplicial_augmented_equiv CategoryTheory.simplicialCosimplicialAugmentedEquivₓ'. -/
 /-- The contravariant categorical equivalence between augmented simplicial
 objects and augmented cosimplicial objects in the opposite category. -/

814d76e2

bump to nightly-2023-04-13-02

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

bd75793a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module algebraic_topology.simplicial_object
-! leanprover-community/mathlib commit 5ed51dc37c6b891b79314ee11a50adc2b1df6fd6
+! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.Opposites
 /-!
 # Simplicial objects in a category.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A simplicial object in a category `C` is a `C`-valued presheaf on `simplex_category`.
 (Similarly a cosimplicial object is functor `simplex_category ⥤ C`.)

5ed51dc3

bump to nightly-2023-04-11-14

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

34188197

Diff

@@ -37,12 +37,14 @@ namespace CategoryTheory
 
 variable (C : Type u) [Category.{v} C]
 
+#print CategoryTheory.SimplicialObject /-
 /-- The category of simplicial objects valued in a category `C`.
 This is the category of contravariant functors from `simplex_category` to `C`. -/
 @[nolint has_nonempty_instance]
 def SimplicialObject :=
   SimplexCategoryᵒᵖ ⥤ C deriving Category
 #align category_theory.simplicial_object CategoryTheory.SimplicialObject
+-/
 
 namespace SimplicialObject
 
@@ -71,21 +73,45 @@ instance [HasColimits C] : HasColimits (SimplicialObject C) :=
 
 variable {C} (X : SimplicialObject C)
 
+/- warning: category_theory.simplicial_object.δ -> CategoryTheory.SimplicialObject.δ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ CategoryTheory.SimplicialObject.δₓ'. -/
 /-- Face maps for a simplicial object. -/
 def δ {n} (i : Fin (n + 2)) : X _[n + 1] ⟶ X _[n] :=
   X.map (SimplexCategory.δ i).op
 #align category_theory.simplicial_object.δ CategoryTheory.SimplicialObject.δ
 
+/- warning: category_theory.simplicial_object.σ -> CategoryTheory.SimplicialObject.σ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ CategoryTheory.SimplicialObject.σₓ'. -/
 /-- Degeneracy maps for a simplicial object. -/
 def σ {n} (i : Fin (n + 1)) : X _[n] ⟶ X _[n + 1] :=
   X.map (SimplexCategory.σ i).op
 #align category_theory.simplicial_object.σ CategoryTheory.SimplicialObject.σ
 
+/- warning: category_theory.simplicial_object.eq_to_iso -> CategoryTheory.SimplicialObject.eqToIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {m : Nat}, (Eq.{1} Nat n m) -> (CategoryTheory.Iso.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk m))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} {m : Nat}, (Eq.{1} Nat n m) -> (CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk m))))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.eq_to_iso CategoryTheory.SimplicialObject.eqToIsoₓ'. -/
 /-- Isomorphisms from identities in ℕ. -/
 def eqToIso {n m : ℕ} (h : n = m) : X _[n] ≅ X _[m] :=
   X.mapIso (eqToIso (by rw [h]))
 #align category_theory.simplicial_object.eq_to_iso CategoryTheory.SimplicialObject.eqToIso
 
+/- warning: category_theory.simplicial_object.eq_to_iso_refl -> CategoryTheory.SimplicialObject.eqToIso_refl is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} (h : Eq.{1} Nat n n), Eq.{succ u1} (CategoryTheory.Iso.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.SimplicialObject.eqToIso.{u1, u2} C _inst_1 X n n h) (CategoryTheory.Iso.refl.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) {n : Nat} (h : Eq.{1} Nat n n), Eq.{succ u1} (CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))) (CategoryTheory.SimplicialObject.eqToIso.{u1, u2} C _inst_1 X n n h) (CategoryTheory.Iso.refl.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_reflₓ'. -/
 @[simp]
 theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
   by
@@ -93,6 +119,12 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
   simp [eq_to_iso]
 #align category_theory.simplicial_object.eq_to_iso_refl CategoryTheory.SimplicialObject.eqToIso_refl
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
@@ -102,6 +134,12 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
 
+/- warning: category_theory.simplicial_object.δ_comp_δ' -> CategoryTheory.SimplicialObject.δ_comp_δ' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ j ≫ X.δ i =
@@ -111,6 +149,12 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
 
+/- warning: category_theory.simplicial_object.δ_comp_δ'' -> CategoryTheory.SimplicialObject.δ_comp_δ'' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ j.succ ≫ X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
@@ -120,6 +164,12 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.simplicial_object.δ_comp_δ'' CategoryTheory.SimplicialObject.δ_comp_δ''
 
+/- warning: category_theory.simplicial_object.δ_comp_δ_self -> CategoryTheory.SimplicialObject.δ_comp_δ_self is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.δ i.succ ≫ X.δ i :=
@@ -128,6 +178,12 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i.cast_succ ≫ X.δ i = X.
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast_succ) :
     X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
@@ -135,6 +191,12 @@ theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = i.cast
   rw [δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self' CategoryTheory.SimplicialObject.δ_comp_δ_self'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
@@ -144,6 +206,12 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 𝟙 _ :=
@@ -152,6 +220,12 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.cast_succ = 
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_self, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_self
 
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(CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by
@@ -159,6 +233,12 @@ theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast
   rw [δ_comp_σ_self]
 #align category_theory.simplicial_object.δ_comp_σ_self' CategoryTheory.SimplicialObject.δ_comp_σ_self'
 
+/- warning: category_theory.simplicial_object.δ_comp_σ_succ -> CategoryTheory.SimplicialObject.δ_comp_σ_succ is a dubious translation:
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(Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_succ CategoryTheory.SimplicialObject.δ_comp_σ_succₓ'. -/
 /-- The second part of the third simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _ :=
@@ -167,6 +247,12 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ i.succ = 𝟙 _
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_succ, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_succ CategoryTheory.SimplicialObject.δ_comp_σ_succ
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.σ i ≫ X.δ j = 𝟙 _ := by
@@ -174,6 +260,12 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
   rw [δ_comp_σ_succ]
 #align category_theory.simplicial_object.δ_comp_σ_succ' CategoryTheory.SimplicialObject.δ_comp_σ_succ'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
@@ -183,6 +275,12 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
@@ -198,6 +296,12 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt' CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'
 
+/- warning: category_theory.simplicial_object.σ_comp_σ -> CategoryTheory.SimplicialObject.σ_comp_σ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc.1]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
@@ -209,12 +313,24 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
 
 open Simplicial
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturalityₓ'. -/
 @[simp, reassoc.1]
 theorem δ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (op [n]) = f.app (op [n + 1]) ≫ X'.δ i :=
   f.naturality _
 #align category_theory.simplicial_object.δ_naturality CategoryTheory.SimplicialObject.δ_naturality
 
+/- warning: category_theory.simplicial_object.σ_naturality -> CategoryTheory.SimplicialObject.σ_naturality is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.σ_naturality CategoryTheory.SimplicialObject.σ_naturalityₓ'. -/
 @[simp, reassoc.1]
 theorem σ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (op [n + 1]) = f.app (op [n]) ≫ X'.σ i :=
@@ -223,17 +339,21 @@ theorem σ_naturality {X' X : SimplicialObject C} (f : X ⟶ X') {n : ℕ} (i :
 
 variable (C)
 
+#print CategoryTheory.SimplicialObject.whiskering /-
 /-- Functor composition induces a functor on simplicial objects. -/
 @[simps]
 def whiskering (D : Type _) [Category D] : (C ⥤ D) ⥤ SimplicialObject C ⥤ SimplicialObject D :=
   whiskeringRight _ _ _
 #align category_theory.simplicial_object.whiskering CategoryTheory.SimplicialObject.whiskering
+-/
 
+#print CategoryTheory.SimplicialObject.Truncated /-
 /-- Truncated simplicial objects. -/
 @[nolint has_nonempty_instance]
 def Truncated (n : ℕ) :=
   (SimplexCategory.Truncated n)ᵒᵖ ⥤ C deriving Category
 #align category_theory.simplicial_object.truncated CategoryTheory.SimplicialObject.Truncated
+-/
 
 variable {C}
 
@@ -259,11 +379,13 @@ instance {n} [HasColimits C] : HasColimits (SimplicialObject.Truncated C n) :=
 
 variable (C)
 
+#print CategoryTheory.SimplicialObject.Truncated.whiskering /-
 /-- Functor composition induces a functor on truncated simplicial objects. -/
 @[simps]
 def whiskering {n} (D : Type _) [Category D] : (C ⥤ D) ⥤ Truncated C n ⥤ Truncated D n :=
   whiskeringRight _ _ _
 #align category_theory.simplicial_object.truncated.whiskering CategoryTheory.SimplicialObject.Truncated.whiskering
+-/
 
 variable {C}
 
@@ -271,42 +393,53 @@ end Truncated
 
 section Skeleton
 
+#print CategoryTheory.SimplicialObject.sk /-
 /-- The skeleton functor from simplicial objects to truncated simplicial objects. -/
 def sk (n : ℕ) : SimplicialObject C ⥤ SimplicialObject.Truncated C n :=
   (whiskeringLeft _ _ _).obj SimplexCategory.Truncated.inclusion.op
 #align category_theory.simplicial_object.sk CategoryTheory.SimplicialObject.sk
+-/
 
 end Skeleton
 
 variable (C)
 
+#print CategoryTheory.SimplicialObject.const /-
 /-- The constant simplicial object is the constant functor. -/
 abbrev const : C ⥤ SimplicialObject C :=
   CategoryTheory.Functor.const _
 #align category_theory.simplicial_object.const CategoryTheory.SimplicialObject.const
+-/
 
+#print CategoryTheory.SimplicialObject.Augmented /-
 /-- The category of augmented simplicial objects, defined as a comma category. -/
 @[nolint has_nonempty_instance]
 def Augmented :=
   Comma (𝟭 (SimplicialObject C)) (const C)deriving Category
 #align category_theory.simplicial_object.augmented CategoryTheory.SimplicialObject.Augmented
+-/
 
 variable {C}
 
 namespace Augmented
 
+#print CategoryTheory.SimplicialObject.Augmented.drop /-
 /-- Drop the augmentation. -/
 @[simps]
 def drop : Augmented C ⥤ SimplicialObject C :=
   Comma.fst _ _
 #align category_theory.simplicial_object.augmented.drop CategoryTheory.SimplicialObject.Augmented.drop
+-/
 
+#print CategoryTheory.SimplicialObject.Augmented.point /-
 /-- The point of the augmentation. -/
 @[simps]
 def point : Augmented C ⥤ C :=
   Comma.snd _ _
 #align category_theory.simplicial_object.augmented.point CategoryTheory.SimplicialObject.Augmented.point
+-/
 
+#print CategoryTheory.SimplicialObject.Augmented.toArrow /-
 /-- The functor from augmented objects to arrows. -/
 @[simps]
 def toArrow : Augmented C ⥤ Arrow C
@@ -324,7 +457,14 @@ def toArrow : Augmented C ⥤ Arrow C
         erw [η.w]
         rfl }
 #align category_theory.simplicial_object.augmented.to_arrow CategoryTheory.SimplicialObject.Augmented.toArrow
+-/
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augmented.w₀ CategoryTheory.SimplicialObject.Augmented.w₀ₓ'. -/
 /-- The compatibility of a morphism with the augmentation, on 0-simplices -/
 @[reassoc.1]
 theorem w₀ {X Y : Augmented C} (f : X ⟶ Y) :
@@ -335,6 +475,7 @@ theorem w₀ {X Y : Augmented C} (f : X ⟶ Y) :
 
 variable (C)
 
+#print CategoryTheory.SimplicialObject.Augmented.whiskeringObj /-
 /-- Functor composition induces a functor on augmented simplicial objects. -/
 @[simp]
 def whiskeringObj (D : Type _) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augmented D
@@ -353,7 +494,9 @@ def whiskeringObj (D : Type _) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augm
         erw [η.w]
         rfl }
 #align category_theory.simplicial_object.augmented.whiskering_obj CategoryTheory.SimplicialObject.Augmented.whiskeringObj
+-/
 
+#print CategoryTheory.SimplicialObject.Augmented.whiskering /-
 /-- Functor composition induces a functor on augmented simplicial objects. -/
 @[simps]
 def whiskering (D : Type u') [Category.{v'} D] : (C ⥤ D) ⥤ Augmented C ⥤ Augmented D
@@ -369,11 +512,18 @@ def whiskering (D : Type u') [Category.{v'} D] : (C ⥤ D) ⥤ Augmented C ⥤ A
             dsimp
             rw [category.comp_id, category.comp_id, η.naturality] } }
 #align category_theory.simplicial_object.augmented.whiskering CategoryTheory.SimplicialObject.Augmented.whiskering
+-/
 
 variable {C}
 
 end Augmented
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augmentₓ'. -/
 /-- Augment a simplicial object with an object. -/
 @[simps]
 def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
@@ -390,6 +540,12 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
         simpa only [← X.map_comp, ← category.assoc, category.comp_id, ← op_comp] using w _ _ _ }
 #align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augment
 
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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory i)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) X₀ (CategoryTheory.Functor.map.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory i) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Quiver.Hom.op.{0, 1} SimplexCategory 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(CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, max u1 u2, u2, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (CategoryTheory.Functor.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, 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(CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, max u1 u2, u2, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (CategoryTheory.Comma.hom.{u1, u1, u1, max u1 u2, u2, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) f
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (X₀ : C) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) X₀) (w : forall (i : SimplexCategory) (g₁ : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) i) (g₂ : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) i), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory i)) X₀) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory i)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) X₀ (Prefunctor.map.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory i) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) i g₁)) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory i)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) X₀ (Prefunctor.map.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory i) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) i g₂)) f)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Comma.left.{u1, u1, u1, max u2 u1, u2, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) C _inst_1 (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Prefunctor.obj.{1, succ u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} 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u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} 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(CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) f
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_object.augment_hom_zero CategoryTheory.SimplicialObject.augment_hom_zeroₓ'. -/
 @[simp]
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
     (X.augment X₀ f w).Hom.app (op [0]) = f := by
@@ -399,11 +555,13 @@ theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X
 
 end SimplicialObject
 
+#print CategoryTheory.CosimplicialObject /-
 /-- Cosimplicial objects. -/
 @[nolint has_nonempty_instance]
 def CosimplicialObject :=
   SimplexCategory ⥤ C deriving Category
 #align category_theory.cosimplicial_object CategoryTheory.CosimplicialObject
+-/
 
 namespace CosimplicialObject
 
@@ -432,21 +590,45 @@ instance [HasColimits C] : HasColimits (CosimplicialObject C) :=
 
 variable {C} (X : CosimplicialObject C)
 
+/- warning: category_theory.cosimplicial_object.δ -> CategoryTheory.CosimplicialObject.δ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ CategoryTheory.CosimplicialObject.δₓ'. -/
 /-- Coface maps for a cosimplicial object. -/
 def δ {n} (i : Fin (n + 2)) : X _[n] ⟶ X _[n + 1] :=
   X.map (SimplexCategory.δ i)
 #align category_theory.cosimplicial_object.δ CategoryTheory.CosimplicialObject.δ
 
+/- warning: category_theory.cosimplicial_object.σ -> CategoryTheory.CosimplicialObject.σ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ CategoryTheory.CosimplicialObject.σₓ'. -/
 /-- Codegeneracy maps for a cosimplicial object. -/
 def σ {n} (i : Fin (n + 1)) : X _[n + 1] ⟶ X _[n] :=
   X.map (SimplexCategory.σ i)
 #align category_theory.cosimplicial_object.σ CategoryTheory.CosimplicialObject.σ
 
+/- warning: category_theory.cosimplicial_object.eq_to_iso -> CategoryTheory.CosimplicialObject.eqToIso is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} {m : Nat}, (Eq.{1} Nat n m) -> (CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk m)))
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.eq_to_iso CategoryTheory.CosimplicialObject.eqToIsoₓ'. -/
 /-- Isomorphisms from identities in ℕ. -/
 def eqToIso {n m : ℕ} (h : n = m) : X _[n] ≅ X _[m] :=
   X.mapIso (eqToIso (by rw [h]))
 #align category_theory.cosimplicial_object.eq_to_iso CategoryTheory.CosimplicialObject.eqToIso
 
+/- warning: category_theory.cosimplicial_object.eq_to_iso_refl -> CategoryTheory.CosimplicialObject.eqToIso_refl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) {n : Nat} (h : Eq.{1} Nat n n), Eq.{succ u1} (CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))) (CategoryTheory.CosimplicialObject.eqToIso.{u1, u2} C _inst_1 X n n h) (CategoryTheory.Iso.refl.{u1, u2} C _inst_1 (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)))
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_reflₓ'. -/
 @[simp]
 theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
   by
@@ -454,6 +636,12 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ :=
   simp [eq_to_iso]
 #align category_theory.cosimplicial_object.eq_to_iso_refl CategoryTheory.CosimplicialObject.eqToIso_refl
 
+/- warning: category_theory.cosimplicial_object.δ_comp_δ -> CategoryTheory.CosimplicialObject.δ_comp_δ is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δₓ'. -/
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc.1]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
@@ -463,6 +651,12 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     X.δ i ≫ X.δ j =
@@ -472,6 +666,12 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
 
+/- warning: category_theory.cosimplicial_object.δ_comp_δ'' -> CategoryTheory.CosimplicialObject.δ_comp_δ'' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     X.δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
@@ -481,6 +681,12 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ'' H]
 #align category_theory.cosimplicial_object.δ_comp_δ'' CategoryTheory.CosimplicialObject.δ_comp_δ''
 
+/- warning: category_theory.cosimplicial_object.δ_comp_δ_self -> CategoryTheory.CosimplicialObject.δ_comp_δ_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first cosimplicial identity -/
 @[reassoc.1]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.δ i ≫ X.δ i.succ :=
@@ -489,6 +695,12 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : X.δ i ≫ X.δ i.cast_succ = X.
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
     X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by
@@ -496,6 +708,12 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast
   rw [δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self' CategoryTheory.CosimplicialObject.δ_comp_δ_self'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_leₓ'. -/
 /-- The second cosimplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.cast_succ) :
@@ -505,6 +723,12 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third cosimplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 𝟙 _ :=
@@ -513,6 +737,12 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ i.cast_succ ≫ X.σ i = 
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_self, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_self
 
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u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n))))
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by
@@ -520,6 +750,12 @@ theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast
   rw [δ_comp_σ_self]
 #align category_theory.cosimplicial_object.δ_comp_σ_self' CategoryTheory.CosimplicialObject.δ_comp_σ_self'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_succ CategoryTheory.CosimplicialObject.δ_comp_σ_succₓ'. -/
 /-- The second part of the third cosimplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _ :=
@@ -528,6 +764,12 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : X.δ i.succ ≫ X.σ i = 𝟙 _
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_succ, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ CategoryTheory.CosimplicialObject.δ_comp_σ_succ
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ) :
     X.δ j ≫ X.σ i = 𝟙 _ := by
@@ -535,6 +777,12 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
   rw [δ_comp_σ_succ]
 #align category_theory.cosimplicial_object.δ_comp_σ_succ' CategoryTheory.CosimplicialObject.δ_comp_σ_succ'
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth cosimplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
@@ -544,6 +792,12 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'ₓ'. -/
 @[reassoc.1]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.δ i ≫ X.σ j =
@@ -559,6 +813,12 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   simpa only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σₓ'. -/
 /-- The fifth cosimplicial identity -/
 @[reassoc.1]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
@@ -568,12 +828,24 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   simp only [← X.map_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σ
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.δ_naturality CategoryTheory.CosimplicialObject.δ_naturalityₓ'. -/
 @[simp, reassoc.1]
 theorem δ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 2)) :
     X.δ i ≫ f.app (SimplexCategory.mk (n + 1)) = f.app (SimplexCategory.mk n) ≫ X'.δ i :=
   f.naturality _
 #align category_theory.cosimplicial_object.δ_naturality CategoryTheory.CosimplicialObject.δ_naturality
 
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X' : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1} {X : CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1} (f : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) X X') {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory 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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.σ_naturality CategoryTheory.CosimplicialObject.σ_naturalityₓ'. -/
 @[simp, reassoc.1]
 theorem σ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ f.app (SimplexCategory.mk n) = f.app (SimplexCategory.mk (n + 1)) ≫ X'.σ i :=
@@ -582,17 +854,21 @@ theorem σ_naturality {X' X : CosimplicialObject C} (f : X ⟶ X') {n : ℕ} (i
 
 variable (C)
 
+#print CategoryTheory.CosimplicialObject.whiskering /-
 /-- Functor composition induces a functor on cosimplicial objects. -/
 @[simps]
 def whiskering (D : Type _) [Category D] : (C ⥤ D) ⥤ CosimplicialObject C ⥤ CosimplicialObject D :=
   whiskeringRight _ _ _
 #align category_theory.cosimplicial_object.whiskering CategoryTheory.CosimplicialObject.whiskering
+-/
 
+#print CategoryTheory.CosimplicialObject.Truncated /-
 /-- Truncated cosimplicial objects. -/
 @[nolint has_nonempty_instance]
 def Truncated (n : ℕ) :=
   SimplexCategory.Truncated n ⥤ C deriving Category
 #align category_theory.cosimplicial_object.truncated CategoryTheory.CosimplicialObject.Truncated
+-/
 
 variable {C}
 
@@ -618,11 +894,13 @@ instance {n} [HasColimits C] : HasColimits (CosimplicialObject.Truncated C n) :=
 
 variable (C)
 
+#print CategoryTheory.CosimplicialObject.Truncated.whiskering /-
 /-- Functor composition induces a functor on truncated cosimplicial objects. -/
 @[simps]
 def whiskering {n} (D : Type _) [Category D] : (C ⥤ D) ⥤ Truncated C n ⥤ Truncated D n :=
   whiskeringRight _ _ _
 #align category_theory.cosimplicial_object.truncated.whiskering CategoryTheory.CosimplicialObject.Truncated.whiskering
+-/
 
 variable {C}
 
@@ -630,42 +908,53 @@ end Truncated
 
 section Skeleton
 
+#print CategoryTheory.CosimplicialObject.sk /-
 /-- The skeleton functor from cosimplicial objects to truncated cosimplicial objects. -/
 def sk (n : ℕ) : CosimplicialObject C ⥤ CosimplicialObject.Truncated C n :=
   (whiskeringLeft _ _ _).obj SimplexCategory.Truncated.inclusion
 #align category_theory.cosimplicial_object.sk CategoryTheory.CosimplicialObject.sk
+-/
 
 end Skeleton
 
 variable (C)
 
+#print CategoryTheory.CosimplicialObject.const /-
 /-- The constant cosimplicial object. -/
 abbrev const : C ⥤ CosimplicialObject C :=
   CategoryTheory.Functor.const _
 #align category_theory.cosimplicial_object.const CategoryTheory.CosimplicialObject.const
+-/
 
+#print CategoryTheory.CosimplicialObject.Augmented /-
 /-- Augmented cosimplicial objects. -/
 @[nolint has_nonempty_instance]
 def Augmented :=
   Comma (const C) (𝟭 (CosimplicialObject C))deriving Category
 #align category_theory.cosimplicial_object.augmented CategoryTheory.CosimplicialObject.Augmented
+-/
 
 variable {C}
 
 namespace Augmented
 
+#print CategoryTheory.CosimplicialObject.Augmented.drop /-
 /-- Drop the augmentation. -/
 @[simps]
 def drop : Augmented C ⥤ CosimplicialObject C :=
   Comma.snd _ _
 #align category_theory.cosimplicial_object.augmented.drop CategoryTheory.CosimplicialObject.Augmented.drop
+-/
 
+#print CategoryTheory.CosimplicialObject.Augmented.point /-
 /-- The point of the augmentation. -/
 @[simps]
 def point : Augmented C ⥤ C :=
   Comma.fst _ _
 #align category_theory.cosimplicial_object.augmented.point CategoryTheory.CosimplicialObject.Augmented.point
+-/
 
+#print CategoryTheory.CosimplicialObject.Augmented.toArrow /-
 /-- The functor from augmented objects to arrows. -/
 @[simps]
 def toArrow : Augmented C ⥤ Arrow C
@@ -683,9 +972,11 @@ def toArrow : Augmented C ⥤ Arrow C
         erw [← η.w]
         rfl }
 #align category_theory.cosimplicial_object.augmented.to_arrow CategoryTheory.CosimplicialObject.Augmented.toArrow
+-/
 
 variable (C)
 
+#print CategoryTheory.CosimplicialObject.Augmented.whiskeringObj /-
 /-- Functor composition induces a functor on augmented cosimplicial objects. -/
 @[simp]
 def whiskeringObj (D : Type _) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augmented D
@@ -704,7 +995,9 @@ def whiskeringObj (D : Type _) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augm
         erw [← η.w]
         rfl }
 #align category_theory.cosimplicial_object.augmented.whiskering_obj CategoryTheory.CosimplicialObject.Augmented.whiskeringObj
+-/
 
+#print CategoryTheory.CosimplicialObject.Augmented.whiskering /-
 /-- Functor composition induces a functor on augmented cosimplicial objects. -/
 @[simps]
 def whiskering (D : Type u') [Category.{v'} D] : (C ⥤ D) ⥤ Augmented C ⥤ Augmented D
@@ -720,6 +1013,7 @@ def whiskering (D : Type u') [Category.{v'} D] : (C ⥤ D) ⥤ Augmented C ⥤ A
             dsimp
             rw [category.id_comp, category.id_comp, η.naturality] } }
 #align category_theory.cosimplicial_object.augmented.whiskering CategoryTheory.CosimplicialObject.Augmented.whiskering
+-/
 
 variable {C}
 
@@ -727,6 +1021,12 @@ end Augmented
 
 open Simplicial
 
+/- warning: category_theory.cosimplicial_object.augment -> CategoryTheory.CosimplicialObject.augment is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augmentₓ'. -/
 /-- Augment a cosimplicial object with an object. -/
 @[simps]
 def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
@@ -742,6 +1042,12 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
         simpa [← X.map_comp] using w _ _ _ }
 #align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augment
 
+/- warning: category_theory.cosimplicial_object.augment_hom_zero -> CategoryTheory.CosimplicialObject.augment_hom_zero is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1))) (CategoryTheory.Comma.right.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w))) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, max u2 u1, max u2 u1} C _inst_1 (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.const.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.augment.{u1, u2} C _inst_1 X X₀ f w)) (SimplexCategory.mk (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) f
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_object.augment_hom_zero CategoryTheory.CosimplicialObject.augment_hom_zeroₓ'. -/
 @[simp]
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :
     (X.augment X₀ f w).Hom.app [0] = f := by
@@ -751,12 +1057,24 @@ theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.o
 
 end CosimplicialObject
 
+/- warning: category_theory.simplicial_cosimplicial_equiv -> CategoryTheory.simplicialCosimplicialEquiv is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u1 u2, max u1 u2} (Opposite.{succ (max u1 u2)} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u1 u2} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{succ (max u2 u1)} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_cosimplicial_equiv CategoryTheory.simplicialCosimplicialEquivₓ'. -/
 /-- The anti-equivalence between simplicial objects and cosimplicial objects. -/
 @[simps]
 def simplicialCosimplicialEquiv : (SimplicialObject C)ᵒᵖ ≌ CosimplicialObject Cᵒᵖ :=
   Functor.leftOpRightOpEquiv _ _
 #align category_theory.simplicial_cosimplicial_equiv CategoryTheory.simplicialCosimplicialEquiv
 
+/- warning: category_theory.cosimplicial_simplicial_equiv -> CategoryTheory.cosimplicialSimplicialEquiv is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u1 u2, max u1 u2} (Opposite.{succ (max u1 u2)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u1 u2} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.CosimplicialObject.category.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{succ (max u2 u1)} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.SimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.CosimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategoryCosimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.instCategorySimplicialObject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+Case conversion may be inaccurate. Consider using '#align category_theory.cosimplicial_simplicial_equiv CategoryTheory.cosimplicialSimplicialEquivₓ'. -/
 /-- The anti-equivalence between cosimplicial objects and simplicial objects. -/
 @[simps]
 def cosimplicialSimplicialEquiv : (CosimplicialObject C)ᵒᵖ ≌ SimplicialObject Cᵒᵖ :=
@@ -765,6 +1083,7 @@ def cosimplicialSimplicialEquiv : (CosimplicialObject C)ᵒᵖ ≌ SimplicialObj
 
 variable {C}
 
+#print CategoryTheory.SimplicialObject.Augmented.rightOp /-
 /-- Construct an augmented cosimplicial object in the opposite
 category from an augmented simplicial object. -/
 @[simps]
@@ -775,7 +1094,9 @@ def SimplicialObject.Augmented.rightOp (X : SimplicialObject.Augmented C) :
   right := X.left.rightOp
   Hom := X.Hom.rightOp
 #align category_theory.simplicial_object.augmented.right_op CategoryTheory.SimplicialObject.Augmented.rightOp
+-/
 
+#print CategoryTheory.CosimplicialObject.Augmented.leftOp /-
 /-- Construct an augmented simplicial object from an augmented cosimplicial
 object in the opposite category. -/
 @[simps]
@@ -785,7 +1106,9 @@ def CosimplicialObject.Augmented.leftOp (X : CosimplicialObject.Augmented Cᵒ
   right := X.left.unop
   Hom := X.Hom.leftOp
 #align category_theory.cosimplicial_object.augmented.left_op CategoryTheory.CosimplicialObject.Augmented.leftOp
+-/
 
+#print CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso /-
 /-- Converting an augmented simplicial object to an augmented cosimplicial
 object and back is isomorphic to the given object. -/
 @[simps]
@@ -793,7 +1116,9 @@ def SimplicialObject.Augmented.rightOpLeftOpIso (X : SimplicialObject.Augmented
     X.rightOp.leftOp ≅ X :=
   Comma.isoMk X.left.rightOpLeftOpIso (eqToIso <| by simp) (by tidy)
 #align category_theory.simplicial_object.augmented.right_op_left_op_iso CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso
+-/
 
+#print CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso /-
 /-- Converting an augmented cosimplicial object to an augmented simplicial
 object and back is isomorphic to the given object. -/
 @[simps]
@@ -801,9 +1126,11 @@ def CosimplicialObject.Augmented.leftOpRightOpIso (X : CosimplicialObject.Augmen
     X.leftOp.rightOp ≅ X :=
   Comma.isoMk (eqToIso <| by simp) X.right.leftOpRightOpIso (by tidy)
 #align category_theory.cosimplicial_object.augmented.left_op_right_op_iso CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso
+-/
 
 variable (C)
 
+#print CategoryTheory.simplicialToCosimplicialAugmented /-
 /-- A functorial version of `simplicial_object.augmented.right_op`. -/
 @[simps]
 def simplicialToCosimplicialAugmented :
@@ -820,7 +1147,9 @@ def simplicialToCosimplicialAugmented :
         congr 1
         exact (congr_app f.unop.w (op x)).symm }
 #align category_theory.simplicial_to_cosimplicial_augmented CategoryTheory.simplicialToCosimplicialAugmented
+-/
 
+#print CategoryTheory.cosimplicialToSimplicialAugmented /-
 /-- A functorial version of `cosimplicial_object.augmented.left_op`. -/
 @[simps]
 def cosimplicialToSimplicialAugmented :
@@ -838,7 +1167,14 @@ def cosimplicialToSimplicialAugmented :
           congr 1
           exact (congr_app f.w x.unop).symm }
 #align category_theory.cosimplicial_to_simplicial_augmented CategoryTheory.cosimplicialToSimplicialAugmented
+-/
 
+/- warning: category_theory.simplicial_cosimplicial_augmented_equiv -> CategoryTheory.simplicialCosimplicialAugmentedEquiv is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max (max u1 u2) u2 u1, max u1 u2} (Opposite.{succ (max (max u1 u2) u2 u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max (max u1 u2) u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.Augmented.category.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.category.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C], CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (Opposite.{succ (max u2 u1)} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.Augmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (CategoryTheory.Category.opposite.{u1, max u2 u1} (CategoryTheory.SimplicialObject.Augmented.{u1, u2} C _inst_1) (CategoryTheory.SimplicialObject.instCategoryAugmented.{u1, u2} C _inst_1)) (CategoryTheory.CosimplicialObject.instCategoryAugmented.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))
+Case conversion may be inaccurate. Consider using '#align category_theory.simplicial_cosimplicial_augmented_equiv CategoryTheory.simplicialCosimplicialAugmentedEquivₓ'. -/
 /-- The contravariant categorical equivalence between augmented simplicial
 objects and augmented cosimplicial objects in the opposite category. -/
 @[simps Functor inverse]

5ed51dc3

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

5ed51dc3

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -33,7 +33,7 @@ namespace CategoryTheory
 
 variable (C : Type u) [Category.{v} C]
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- The category of simplicial objects valued in a category `C`.
 This is the category of contravariant functors from `SimplexCategory` to `C`. -/
 def SimplicialObject :=
@@ -224,7 +224,7 @@ def whiskering (D : Type*) [Category D] : (C ⥤ D) ⥤ SimplicialObject C ⥤ S
   whiskeringRight _ _ _
 #align category_theory.simplicial_object.whiskering CategoryTheory.SimplicialObject.whiskering
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- Truncated simplicial objects. -/
 def Truncated (n : ℕ) :=
   (SimplexCategory.Truncated n)ᵒᵖ ⥤ C
@@ -282,7 +282,7 @@ abbrev const : C ⥤ SimplicialObject C :=
   CategoryTheory.Functor.const _
 #align category_theory.simplicial_object.const CategoryTheory.SimplicialObject.const
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- The category of augmented simplicial objects, defined as a comma category. -/
 def Augmented :=
   Comma (𝟭 (SimplicialObject C)) (const C)
@@ -403,7 +403,7 @@ theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X
 
 end SimplicialObject
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- Cosimplicial objects. -/
 def CosimplicialObject :=
   SimplexCategory ⥤ C
@@ -593,7 +593,7 @@ def whiskering (D : Type*) [Category D] : (C ⥤ D) ⥤ CosimplicialObject C ⥤
   whiskeringRight _ _ _
 #align category_theory.cosimplicial_object.whiskering CategoryTheory.CosimplicialObject.whiskering
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- Truncated cosimplicial objects. -/
 def Truncated (n : ℕ) :=
   SimplexCategory.Truncated n ⥤ C
@@ -651,7 +651,7 @@ abbrev const : C ⥤ CosimplicialObject C :=
   CategoryTheory.Functor.const _
 #align category_theory.cosimplicial_object.const CategoryTheory.CosimplicialObject.const
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- Augmented cosimplicial objects. -/
 def Augmented :=
   Comma (const C) (𝟭 (CosimplicialObject C))

5ed51dc3

chore: remove mathport name: <expression> lines (#11928)

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

11431c65

Diff

@@ -416,7 +416,6 @@ instance : Category (CosimplicialObject C) := by
 
 namespace CosimplicialObject
 
--- mathport name: cosimplicial_object.at
 set_option quotPrecheck false in
 /-- `X _[n]` denotes the `n`th-term of the cosimplicial object X -/
 scoped[Simplicial]

5ed51dc3

chore: prevent API leakage on SimplexCategory (#11395)

This PR removes the simps attribute in the definition of the category structure on SimplexCategory so as to prevent API leakage. Better suited simp lemmas are added. The definition of SimplexCategory.const is also generalized in order to describe any constant map in SimplexCategory.

27d3439f

Diff

@@ -388,7 +388,7 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
   left := X
   right := X₀
   hom :=
-    { app := fun i => X.map (SimplexCategory.const i.unop 0).op ≫ f
+    { app := fun i => X.map (SimplexCategory.const _ _ 0).op ≫ f
       naturality := by
         intro i j g
         dsimp
@@ -398,9 +398,7 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
 
 -- Porting note: removed @[simp] as the linter complains
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
-    (X.augment X₀ f w).hom.app (op [0]) = f := by
-  dsimp
-  rw [SimplexCategory.hom_zero_zero ([0].const 0), op_id, X.map_id, Category.id_comp]
+    (X.augment X₀ f w).hom.app (op [0]) = f := by simp
 #align category_theory.simplicial_object.augment_hom_zero CategoryTheory.SimplicialObject.augment_hom_zero
 
 end SimplicialObject
@@ -753,18 +751,16 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
   left := X₀
   right := X
   hom :=
-    { app := fun i => f ≫ X.map (SimplexCategory.const i 0)
+    { app := fun i => f ≫ X.map (SimplexCategory.const _ _ 0)
       naturality := by
         intro i j g
         dsimp
-        simpa [← X.map_comp] using w _ _ _ }
+        rw [Category.id_comp, Category.assoc, ← X.map_comp, w] }
 #align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augment
 
 -- Porting note: removed @[simp] as the linter complains
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :
-    (X.augment X₀ f w).hom.app [0] = f := by
-  dsimp
-  rw [SimplexCategory.hom_zero_zero ([0].const 0), X.map_id, Category.comp_id]
+    (X.augment X₀ f w).hom.app [0] = f := by simp
 #align category_theory.cosimplicial_object.augment_hom_zero CategoryTheory.CosimplicialObject.augment_hom_zero
 
 end CosimplicialObject

5ed51dc3

chore: remove more autoImplicit (#11336)

... or reduce its scope (the full removal is not as obvious).

59f72a90

Diff

@@ -21,9 +21,6 @@ Use the notation `X _[n]` in the `Simplicial` locale to obtain the `n`-th term o
 
 -/
 
-set_option autoImplicit true
-
-
 open Opposite
 
 open CategoryTheory
@@ -233,7 +230,7 @@ def Truncated (n : ℕ) :=
   (SimplexCategory.Truncated n)ᵒᵖ ⥤ C
 #align category_theory.simplicial_object.truncated CategoryTheory.SimplicialObject.Truncated
 
-instance : Category (Truncated C n) := by
+instance {n : ℕ} : Category (Truncated C n) := by
   dsimp [Truncated]
   infer_instance
 
@@ -605,7 +602,7 @@ def Truncated (n : ℕ) :=
   SimplexCategory.Truncated n ⥤ C
 #align category_theory.cosimplicial_object.truncated CategoryTheory.CosimplicialObject.Truncated
 
-instance : Category (Truncated C n) := by
+instance {n : ℕ} : Category (Truncated C n) := by
   dsimp [Truncated]
   infer_instance

5ed51dc3

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -399,7 +399,7 @@ def augment (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀)
         simpa only [← X.map_comp, ← Category.assoc, Category.comp_id, ← op_comp] using w _ _ _ }
 #align category_theory.simplicial_object.augment CategoryTheory.SimplicialObject.augment
 
--- porting note: removed @[simp] as the linter complains
+-- Porting note: removed @[simp] as the linter complains
 theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X₀) (w) :
     (X.augment X₀ f w).hom.app (op [0]) = f := by
   dsimp
@@ -763,7 +763,7 @@ def augment (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0])
         simpa [← X.map_comp] using w _ _ _ }
 #align category_theory.cosimplicial_object.augment CategoryTheory.CosimplicialObject.augment
 
--- porting note: removed @[simp] as the linter complains
+-- Porting note: removed @[simp] as the linter complains
 theorem augment_hom_zero (X : CosimplicialObject C) (X₀ : C) (f : X₀ ⟶ X.obj [0]) (w) :
     (X.augment X₀ f w).hom.app [0] = f := by
   dsimp

5ed51dc3

chore: classify removed @[nolint has_nonempty_instance] porting notes (#10929)

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

2599c3bb

Diff

@@ -36,7 +36,7 @@ namespace CategoryTheory
 
 variable (C : Type u) [Category.{v} C]
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- The category of simplicial objects valued in a category `C`.
 This is the category of contravariant functors from `SimplexCategory` to `C`. -/
 def SimplicialObject :=
@@ -227,7 +227,7 @@ def whiskering (D : Type*) [Category D] : (C ⥤ D) ⥤ SimplicialObject C ⥤ S
   whiskeringRight _ _ _
 #align category_theory.simplicial_object.whiskering CategoryTheory.SimplicialObject.whiskering
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- Truncated simplicial objects. -/
 def Truncated (n : ℕ) :=
   (SimplexCategory.Truncated n)ᵒᵖ ⥤ C
@@ -285,7 +285,7 @@ abbrev const : C ⥤ SimplicialObject C :=
   CategoryTheory.Functor.const _
 #align category_theory.simplicial_object.const CategoryTheory.SimplicialObject.const
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- The category of augmented simplicial objects, defined as a comma category. -/
 def Augmented :=
   Comma (𝟭 (SimplicialObject C)) (const C)
@@ -408,7 +408,7 @@ theorem augment_hom_zero (X : SimplicialObject C) (X₀ : C) (f : X _[0] ⟶ X
 
 end SimplicialObject
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- Cosimplicial objects. -/
 def CosimplicialObject :=
   SimplexCategory ⥤ C
@@ -599,7 +599,7 @@ def whiskering (D : Type*) [Category D] : (C ⥤ D) ⥤ CosimplicialObject C ⥤
   whiskeringRight _ _ _
 #align category_theory.cosimplicial_object.whiskering CategoryTheory.CosimplicialObject.whiskering
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- Truncated cosimplicial objects. -/
 def Truncated (n : ℕ) :=
   SimplexCategory.Truncated n ⥤ C
@@ -657,7 +657,7 @@ abbrev const : C ⥤ CosimplicialObject C :=
   CategoryTheory.Functor.const _
 #align category_theory.cosimplicial_object.const CategoryTheory.CosimplicialObject.const
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- Augmented cosimplicial objects. -/
 def Augmented :=
   Comma (const C) (𝟭 (CosimplicialObject C))

5ed51dc3

chore: classify added to ease automation porting notes (#10689)

Classifies by adding issue number (#10688) to porting notes claiming anything semantically equivalent to added to ease automation.
Enforce singular convention converting "porting notes" to "porting note".

b06068c3

Diff

@@ -76,7 +76,7 @@ instance [HasColimits C] : HasColimits (SimplicialObject C) :=
 
 variable {C}
 
--- porting note: added to ease automation
+-- Porting note (#10688): added to ease automation
 @[ext]
 lemma hom_ext {X Y : SimplicialObject C} (f g : X ⟶ Y)
     (h : ∀ (n : SimplexCategoryᵒᵖ), f.app n = g.app n) : f = g :=
@@ -300,7 +300,7 @@ variable {C}
 
 namespace Augmented
 
--- porting note: added to ease automation
+-- Porting note (#10688): added to ease automation
 @[ext]
 lemma hom_ext {X Y : Augmented C} (f g : X ⟶ Y) (h₁ : f.left = g.left) (h₂ : f.right = g.right) :
     f = g :=
@@ -446,7 +446,7 @@ instance [HasColimits C] : HasColimits (CosimplicialObject C) :=
 
 variable {C}
 
--- porting note: added to ease automation
+-- Porting note (#10688): added to ease automation
 @[ext]
 lemma hom_ext {X Y : CosimplicialObject C} (f g : X ⟶ Y)
     (h : ∀ (n : SimplexCategory), f.app n = g.app n) : f = g :=
@@ -672,7 +672,7 @@ variable {C}
 
 namespace Augmented
 
--- porting note: added to ease automation
+-- Porting note (#10688): added to ease automation
 @[ext]
 lemma hom_ext {X Y : Augmented C} (f g : X ⟶ Y) (h₁ : f.left = g.left) (h₂ : f.right = g.right) :
     f = g :=

5ed51dc3

refactor: create folder CategoryTheory/Comma (#10108)

38cd7278

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
 import Mathlib.AlgebraicTopology.SimplexCategory
-import Mathlib.CategoryTheory.Arrow
+import Mathlib.CategoryTheory.Comma.Arrow
 import Mathlib.CategoryTheory.Limits.FunctorCategory
 import Mathlib.CategoryTheory.Opposites

5ed51dc3

feat(AlgebraicTopology/Quasicategory): alternative statement of hornfilling condition (#9360)

7cade347

Diff

@@ -53,7 +53,7 @@ namespace SimplicialObject
 set_option quotPrecheck false in
 /-- `X _[n]` denotes the `n`th-term of the simplicial object X -/
 scoped[Simplicial]
-  notation:1000 X " _[" n "]" =>
+  notation3:1000 X " _[" n "]" =>
     (X : CategoryTheory.SimplicialObject _).obj (Opposite.op (SimplexCategory.mk n))
 
 open Simplicial

5ed51dc3

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -117,7 +117,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
     X.δ j ≫ X.δ i =
       X.δ (Fin.castSucc i) ≫
-        X.δ (j.pred <| fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) := by
+        X.δ (j.pred fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
@@ -191,7 +191,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
-      X.δ (i.pred <| fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) ≫
+      X.δ (i.pred fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) ≫
         X.σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
@@ -488,7 +488,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
     X.δ i ≫ X.δ j =
-      X.δ (j.pred <| fun (hj : j = 0) => by simp only [hj, Fin.not_lt_zero] at H) ≫
+      X.δ (j.pred fun (hj : j = 0) => by simp only [hj, Fin.not_lt_zero] at H) ≫
         X.δ (Fin.castSucc i) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]

5ed51dc3

chore: exactly 4 spaces in theorems (#7328)

Co-authored-by: Moritz Firsching <firsching@google.com>

d3263b23

Diff

@@ -79,7 +79,7 @@ variable {C}
 -- porting note: added to ease automation
 @[ext]
 lemma hom_ext {X Y : SimplicialObject C} (f g : X ⟶ Y)
-  (h : ∀ (n : SimplexCategoryᵒᵖ), f.app n = g.app n) : f = g :=
+    (h : ∀ (n : SimplexCategoryᵒᵖ), f.app n = g.app n) : f = g :=
   NatTrans.ext _ _ (by ext; apply h)
 
 variable (X : SimplicialObject C)
@@ -449,7 +449,7 @@ variable {C}
 -- porting note: added to ease automation
 @[ext]
 lemma hom_ext {X Y : CosimplicialObject C} (f g : X ⟶ Y)
-  (h : ∀ (n : SimplexCategory), f.app n = g.app n) : f = g :=
+    (h : ∀ (n : SimplexCategory), f.app n = g.app n) : f = g :=
   NatTrans.ext _ _ (by ext; apply h)
 
 variable (X : CosimplicialObject C)

5ed51dc3

fix: disable autoImplicit globally (#6528)

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

Assuming variables are in scope, but pasting the lemma in the wrong section
Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

0c24f831

Diff

@@ -21,6 +21,8 @@ Use the notation `X _[n]` in the `Simplicial` locale to obtain the `n`-th term o
 
 -/
 
+set_option autoImplicit true
+
 
 open Opposite

5ed51dc3

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -221,7 +221,7 @@ variable (C)
 
 /-- Functor composition induces a functor on simplicial objects. -/
 @[simps!]
-def whiskering (D : Type _) [Category D] : (C ⥤ D) ⥤ SimplicialObject C ⥤ SimplicialObject D :=
+def whiskering (D : Type*) [Category D] : (C ⥤ D) ⥤ SimplicialObject C ⥤ SimplicialObject D :=
   whiskeringRight _ _ _
 #align category_theory.simplicial_object.whiskering CategoryTheory.SimplicialObject.whiskering
 
@@ -259,7 +259,7 @@ variable (C)
 
 /-- Functor composition induces a functor on truncated simplicial objects. -/
 @[simps!]
-def whiskering {n} (D : Type _) [Category D] : (C ⥤ D) ⥤ Truncated C n ⥤ Truncated D n :=
+def whiskering {n} (D : Type*) [Category D] : (C ⥤ D) ⥤ Truncated C n ⥤ Truncated D n :=
   whiskeringRight _ _ _
 #align category_theory.simplicial_object.truncated.whiskering CategoryTheory.SimplicialObject.Truncated.whiskering
 
@@ -345,7 +345,7 @@ variable (C)
 
 /-- Functor composition induces a functor on augmented simplicial objects. -/
 @[simp]
-def whiskeringObj (D : Type _) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augmented D where
+def whiskeringObj (D : Type*) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augmented D where
   obj X :=
     { left := ((whiskering _ _).obj F).obj (drop.obj X)
       right := F.obj (point.obj X)
@@ -593,7 +593,7 @@ variable (C)
 
 /-- Functor composition induces a functor on cosimplicial objects. -/
 @[simps!]
-def whiskering (D : Type _) [Category D] : (C ⥤ D) ⥤ CosimplicialObject C ⥤ CosimplicialObject D :=
+def whiskering (D : Type*) [Category D] : (C ⥤ D) ⥤ CosimplicialObject C ⥤ CosimplicialObject D :=
   whiskeringRight _ _ _
 #align category_theory.cosimplicial_object.whiskering CategoryTheory.CosimplicialObject.whiskering
 
@@ -631,7 +631,7 @@ variable (C)
 
 /-- Functor composition induces a functor on truncated cosimplicial objects. -/
 @[simps!]
-def whiskering {n} (D : Type _) [Category D] : (C ⥤ D) ⥤ Truncated C n ⥤ Truncated D n :=
+def whiskering {n} (D : Type*) [Category D] : (C ⥤ D) ⥤ Truncated C n ⥤ Truncated D n :=
   whiskeringRight _ _ _
 #align category_theory.cosimplicial_object.truncated.whiskering CategoryTheory.CosimplicialObject.Truncated.whiskering
 
@@ -709,7 +709,7 @@ variable (C)
 
 /-- Functor composition induces a functor on augmented cosimplicial objects. -/
 @[simp]
-def whiskeringObj (D : Type _) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augmented D where
+def whiskeringObj (D : Type*) [Category D] (F : C ⥤ D) : Augmented C ⥤ Augmented D where
   obj X :=
     { left := F.obj (point.obj X)
       right := ((whiskering _ _).obj F).obj (drop.obj X)

5ed51dc3

chore: bump to nightly-2023-07-15 (#5992)

Various adaptations to changes when Fin API was moved to Std. One notable change is that many lemmas are now stated in terms of i ≠ 0 (for i : Fin n) rather then i.1 ≠ 0, and as a consequence many Fin.vne_of_ne applications have been added or removed, mostly removed.

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

24924f96

Diff

@@ -115,7 +115,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
     X.δ j ≫ X.δ i =
       X.δ (Fin.castSucc i) ≫
-        X.δ (j.pred <| Fin.vne_of_ne fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) := by
+        X.δ (j.pred <| fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
@@ -189,7 +189,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
-      X.δ (i.pred <| Fin.vne_of_ne fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) ≫
+      X.δ (i.pred <| fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) ≫
         X.σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
@@ -486,7 +486,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
 @[reassoc]
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
     X.δ i ≫ X.δ j =
-      X.δ (j.pred <| Fin.vne_of_ne fun (hj : j = 0) => by simp only [hj, Fin.not_lt_zero] at H) ≫
+      X.δ (j.pred <| fun (hj : j = 0) => by simp only [hj, Fin.not_lt_zero] at H) ≫
         X.δ (Fin.castSucc i) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
@@ -563,7 +563,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.δ i ≫ X.σ j =
       X.σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
-        X.δ (i.pred <| Fin.vne_of_ne
+        X.δ (i.pred <|
           fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]

5ed51dc3

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module algebraic_topology.simplicial_object
-! leanprover-community/mathlib commit 5ed51dc37c6b891b79314ee11a50adc2b1df6fd6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.SimplexCategory
 import Mathlib.CategoryTheory.Arrow
 import Mathlib.CategoryTheory.Limits.FunctorCategory
 import Mathlib.CategoryTheory.Opposites
 
+#align_import algebraic_topology.simplicial_object from "leanprover-community/mathlib"@"5ed51dc37c6b891b79314ee11a50adc2b1df6fd6"
+
 /-!
 # Simplicial objects in a category.

5ed51dc3

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -109,20 +109,21 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by
 /-- The generic case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    X.δ j.succ ≫ X.δ i = X.δ (Fin.castSuccEmb i) ≫ X.δ j := by
+    X.δ j.succ ≫ X.δ i = X.δ (Fin.castSucc i) ≫ X.δ j := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
 
 @[reassoc]
-theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSuccEmb i < j) :
+theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
     X.δ j ≫ X.δ i =
-      X.δ (Fin.castSuccEmb i) ≫ X.δ (j.pred fun hj => by simp [hj, Fin.not_lt_zero] at H) := by
+      X.δ (Fin.castSucc i) ≫
+        X.δ (j.pred <| Fin.vne_of_ne fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
 @[reassoc]
-theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSuccEmb j) :
+theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSucc j) :
     X.δ j.succ ≫ X.δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
       X.δ i ≫ X.δ j := by
   dsimp [δ]
@@ -132,13 +133,13 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.cast
 /-- The special case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} :
-    X.δ (Fin.castSuccEmb i) ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
+    X.δ (Fin.castSucc i) ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
 
 @[reassoc]
-theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = Fin.castSuccEmb i) :
+theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = Fin.castSucc i) :
     X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   subst H
   rw [δ_comp_δ_self]
@@ -146,21 +147,21 @@ theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = Fin.ca
 
 /-- The second simplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSuccEmb j) :
-    X.σ j.succ ≫ X.δ (Fin.castSuccEmb i) = X.δ i ≫ X.σ j := by
+theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSucc j) :
+    X.σ j.succ ≫ X.δ (Fin.castSucc i) = X.δ i ≫ X.σ j := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
 
 /-- The first part of the third simplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ (Fin.castSuccEmb i) = 𝟙 _ := by
+theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ (Fin.castSucc i) = 𝟙 _ := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_self, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_self
 
 @[reassoc]
-theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSuccEmb i) :
+theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSucc i) :
     X.σ i ≫ X.δ j = 𝟙 _ := by
   subst H
   rw [δ_comp_σ_self]
@@ -182,8 +183,8 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 
 /-- The fourth simplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSuccEmb j < i) :
-    X.σ (Fin.castSuccEmb j) ≫ X.δ i.succ = X.δ i ≫ X.σ j := by
+theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSucc j < i) :
+    X.σ (Fin.castSucc j) ≫ X.δ i.succ = X.δ i ≫ X.σ j := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
@@ -191,7 +192,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
 @[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.σ j ≫ X.δ i =
-      X.δ (i.pred fun hi => by simp only [Fin.not_lt_zero, hi] at H) ≫
+      X.δ (i.pred <| Fin.vne_of_ne fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) ≫
         X.σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
@@ -200,7 +201,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    X.σ j ≫ X.σ (Fin.castSuccEmb i) = X.σ i ≫ X.σ j.succ := by
+    X.σ j ≫ X.σ (Fin.castSucc i) = X.σ i ≫ X.σ j.succ := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σ
@@ -480,22 +481,22 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ (Fin.castSuccEmb i) := by
+    X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ (Fin.castSucc i) := by
   dsimp [δ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
 
 @[reassoc]
-theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSuccEmb i < j) :
+theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
     X.δ i ≫ X.δ j =
-      X.δ (j.pred fun hj => by simp only [hj, Fin.not_lt_zero] at H) ≫
-        X.δ (Fin.castSuccEmb i) := by
+      X.δ (j.pred <| Fin.vne_of_ne fun (hj : j = 0) => by simp only [hj, Fin.not_lt_zero] at H) ≫
+        X.δ (Fin.castSucc i) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
 
 @[reassoc]
-theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSuccEmb j) :
+theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSucc j) :
     X.δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
       X.δ j ≫ X.δ i := by
   dsimp [δ]
@@ -505,13 +506,13 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.cast
 /-- The special case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} :
-    X.δ i ≫ X.δ (Fin.castSuccEmb i) = X.δ i ≫ X.δ i.succ := by
+    X.δ i ≫ X.δ (Fin.castSucc i) = X.δ i ≫ X.δ i.succ := by
   dsimp [δ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
 
 @[reassoc]
-theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.castSuccEmb i) :
+theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.castSucc i) :
     X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by
   subst H
   rw [δ_comp_δ_self]
@@ -519,21 +520,21 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.ca
 
 /-- The second cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSuccEmb j) :
-    X.δ (Fin.castSuccEmb i) ≫ X.σ j.succ = X.σ j ≫ X.δ i := by
+theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSucc j) :
+    X.δ (Fin.castSucc i) ≫ X.σ j.succ = X.σ j ≫ X.δ i := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
 
 /-- The first part of the third cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ (Fin.castSuccEmb i) ≫ X.σ i = 𝟙 _ := by
+theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ (Fin.castSucc i) ≫ X.σ i = 𝟙 _ := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_self, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_self
 
 @[reassoc]
-theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSuccEmb i) :
+theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSucc i) :
     X.δ j ≫ X.σ i = 𝟙 _ := by
   subst H
   rw [δ_comp_σ_self]
@@ -555,8 +556,8 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 
 /-- The fourth cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSuccEmb j < i) :
-    X.δ i.succ ≫ X.σ (Fin.castSuccEmb j) = X.σ j ≫ X.δ i := by
+theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSucc j < i) :
+    X.δ i.succ ≫ X.σ (Fin.castSucc j) = X.σ j ≫ X.δ i := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
@@ -565,7 +566,8 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     X.δ i ≫ X.σ j =
       X.σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
-        X.δ (i.pred fun hi => by simp only [Fin.not_lt_zero, hi] at H) := by
+        X.δ (i.pred <| Fin.vne_of_ne
+          fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt' H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt' CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'
@@ -573,7 +575,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 /-- The fifth cosimplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    X.σ (Fin.castSuccEmb i) ≫ X.σ j = X.σ j.succ ≫ X.σ i := by
+    X.σ (Fin.castSucc i) ≫ X.σ j = X.σ j.succ ≫ X.σ i := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σ

5ed51dc3

chore: rename Fin.castSucc to Fin.castSuccEmb (#5729)

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

f4e42872

Diff

@@ -109,20 +109,20 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by
 /-- The generic case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    X.δ j.succ ≫ X.δ i = X.δ (Fin.castSucc i) ≫ X.δ j := by
+    X.δ j.succ ≫ X.δ i = X.δ (Fin.castSuccEmb i) ≫ X.δ j := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.simplicial_object.δ_comp_δ CategoryTheory.SimplicialObject.δ_comp_δ
 
 @[reassoc]
-theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
+theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSuccEmb i < j) :
     X.δ j ≫ X.δ i =
-      X.δ (Fin.castSucc i) ≫ X.δ (j.pred fun hj => by simp [hj, Fin.not_lt_zero] at H) := by
+      X.δ (Fin.castSuccEmb i) ≫ X.δ (j.pred fun hj => by simp [hj, Fin.not_lt_zero] at H) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.simplicial_object.δ_comp_δ' CategoryTheory.SimplicialObject.δ_comp_δ'
 @[reassoc]
-theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSucc j) :
+theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSuccEmb j) :
     X.δ j.succ ≫ X.δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) =
       X.δ i ≫ X.δ j := by
   dsimp [δ]
@@ -132,13 +132,13 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.cast
 /-- The special case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} :
-    X.δ (Fin.castSucc i) ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
+    X.δ (Fin.castSuccEmb i) ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.simplicial_object.δ_comp_δ_self CategoryTheory.SimplicialObject.δ_comp_δ_self
 
 @[reassoc]
-theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = Fin.castSucc i) :
+theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = Fin.castSuccEmb i) :
     X.δ j ≫ X.δ i = X.δ i.succ ≫ X.δ i := by
   subst H
   rw [δ_comp_δ_self]
@@ -146,21 +146,21 @@ theorem δ_comp_δ_self' {n} {j : Fin (n + 3)} {i : Fin (n + 2)} (H : j = Fin.ca
 
 /-- The second simplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSucc j) :
-    X.σ j.succ ≫ X.δ (Fin.castSucc i) = X.δ i ≫ X.σ j := by
+theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSuccEmb j) :
+    X.σ j.succ ≫ X.δ (Fin.castSuccEmb i) = X.δ i ≫ X.σ j := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.simplicial_object.δ_comp_σ_of_le CategoryTheory.SimplicialObject.δ_comp_σ_of_le
 
 /-- The first part of the third simplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ (Fin.castSucc i) = 𝟙 _ := by
+theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.σ i ≫ X.δ (Fin.castSuccEmb i) = 𝟙 _ := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_self, op_id, X.map_id]
 #align category_theory.simplicial_object.δ_comp_σ_self CategoryTheory.SimplicialObject.δ_comp_σ_self
 
 @[reassoc]
-theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSucc i) :
+theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSuccEmb i) :
     X.σ i ≫ X.δ j = 𝟙 _ := by
   subst H
   rw [δ_comp_σ_self]
@@ -182,8 +182,8 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 
 /-- The fourth simplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSucc j < i) :
-    X.σ (Fin.castSucc j) ≫ X.δ i.succ = X.δ i ≫ X.σ j := by
+theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSuccEmb j < i) :
+    X.σ (Fin.castSuccEmb j) ≫ X.δ i.succ = X.δ i ≫ X.σ j := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.simplicial_object.δ_comp_σ_of_gt CategoryTheory.SimplicialObject.δ_comp_σ_of_gt
@@ -200,7 +200,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    X.σ j ≫ X.σ (Fin.castSucc i) = X.σ i ≫ X.σ j.succ := by
+    X.σ j ≫ X.σ (Fin.castSuccEmb i) = X.σ i ≫ X.σ j.succ := by
   dsimp [δ, σ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.simplicial_object.σ_comp_σ CategoryTheory.SimplicialObject.σ_comp_σ
@@ -480,21 +480,22 @@ theorem eqToIso_refl {n : ℕ} (h : n = n) : X.eqToIso h = Iso.refl _ := by
 /-- The generic case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ (Fin.castSucc i) := by
+    X.δ i ≫ X.δ j.succ = X.δ j ≫ X.δ (Fin.castSuccEmb i) := by
   dsimp [δ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ H]
 #align category_theory.cosimplicial_object.δ_comp_δ CategoryTheory.CosimplicialObject.δ_comp_δ
 
 @[reassoc]
-theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
+theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSuccEmb i < j) :
     X.δ i ≫ X.δ j =
-      X.δ (j.pred fun hj => by simp only [hj, Fin.not_lt_zero] at H) ≫ X.δ (Fin.castSucc i) := by
+      X.δ (j.pred fun hj => by simp only [hj, Fin.not_lt_zero] at H) ≫
+        X.δ (Fin.castSuccEmb i) := by
   dsimp [δ]
   simp only [← X.map_comp, ← op_comp, SimplexCategory.δ_comp_δ' H]
 #align category_theory.cosimplicial_object.δ_comp_δ' CategoryTheory.CosimplicialObject.δ_comp_δ'
 
 @[reassoc]
-theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSucc j) :
+theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSuccEmb j) :
     X.δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ X.δ j.succ =
       X.δ j ≫ X.δ i := by
   dsimp [δ]
@@ -504,13 +505,13 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.cast
 /-- The special case of the first cosimplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} :
-    X.δ i ≫ X.δ (Fin.castSucc i) = X.δ i ≫ X.δ i.succ := by
+    X.δ i ≫ X.δ (Fin.castSuccEmb i) = X.δ i ≫ X.δ i.succ := by
   dsimp [δ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_δ_self]
 #align category_theory.cosimplicial_object.δ_comp_δ_self CategoryTheory.CosimplicialObject.δ_comp_δ_self
 
 @[reassoc]
-theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.castSucc i) :
+theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.castSuccEmb i) :
     X.δ i ≫ X.δ j = X.δ i ≫ X.δ i.succ := by
   subst H
   rw [δ_comp_δ_self]
@@ -518,21 +519,21 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.ca
 
 /-- The second cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSucc j) :
-    X.δ (Fin.castSucc i) ≫ X.σ j.succ = X.σ j ≫ X.δ i := by
+theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSuccEmb j) :
+    X.δ (Fin.castSuccEmb i) ≫ X.σ j.succ = X.σ j ≫ X.δ i := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_le H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_le CategoryTheory.CosimplicialObject.δ_comp_σ_of_le
 
 /-- The first part of the third cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ (Fin.castSucc i) ≫ X.σ i = 𝟙 _ := by
+theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : X.δ (Fin.castSuccEmb i) ≫ X.σ i = 𝟙 _ := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_self, X.map_id]
 #align category_theory.cosimplicial_object.δ_comp_σ_self CategoryTheory.CosimplicialObject.δ_comp_σ_self
 
 @[reassoc]
-theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSucc i) :
+theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = Fin.castSuccEmb i) :
     X.δ j ≫ X.σ i = 𝟙 _ := by
   subst H
   rw [δ_comp_σ_self]
@@ -554,8 +555,8 @@ theorem δ_comp_σ_succ' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.succ
 
 /-- The fourth cosimplicial identity -/
 @[reassoc]
-theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSucc j < i) :
-    X.δ i.succ ≫ X.σ (Fin.castSucc j) = X.σ j ≫ X.δ i := by
+theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSuccEmb j < i) :
+    X.δ i.succ ≫ X.σ (Fin.castSuccEmb j) = X.σ j ≫ X.δ i := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.δ_comp_σ_of_gt H]
 #align category_theory.cosimplicial_object.δ_comp_σ_of_gt CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt
@@ -572,7 +573,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 /-- The fifth cosimplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    X.σ (Fin.castSucc i) ≫ X.σ j = X.σ j.succ ≫ X.σ i := by
+    X.σ (Fin.castSuccEmb i) ≫ X.σ j = X.σ j.succ ≫ X.σ i := by
   dsimp [δ, σ]
   simp only [← X.map_comp, SimplexCategory.σ_comp_σ H]
 #align category_theory.cosimplicial_object.σ_comp_σ CategoryTheory.CosimplicialObject.σ_comp_σ

5ed51dc3

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

5b958613

Diff

@@ -809,7 +809,7 @@ object and back is isomorphic to the given object. -/
 @[simps!]
 def SimplicialObject.Augmented.rightOpLeftOpIso (X : SimplicialObject.Augmented C) :
     X.rightOp.leftOp ≅ X :=
-  Comma.isoMk X.left.rightOpLeftOpIso (CategoryTheory.eqToIso <| by aesop_cat) (by aesop_cat)
+  Comma.isoMk X.left.rightOpLeftOpIso (CategoryTheory.eqToIso <| by aesop_cat)
 #align category_theory.simplicial_object.augmented.right_op_left_op_iso CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso
 
 /-- Converting an augmented cosimplicial object to an augmented simplicial
@@ -817,7 +817,7 @@ object and back is isomorphic to the given object. -/
 @[simps!]
 def CosimplicialObject.Augmented.leftOpRightOpIso (X : CosimplicialObject.Augmented Cᵒᵖ) :
     X.leftOp.rightOp ≅ X :=
-  Comma.isoMk (CategoryTheory.eqToIso <| by simp) X.right.leftOpRightOpIso (by aesop_cat)
+  Comma.isoMk (CategoryTheory.eqToIso <| by simp) X.right.leftOpRightOpIso
 #align category_theory.cosimplicial_object.augmented.left_op_right_op_iso CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso
 
 variable (C)
@@ -867,7 +867,7 @@ def simplicialCosimplicialAugmentedEquiv :
       simp_rw [← op_comp]
       congr 1
       aesop_cat)
-    ((NatIso.ofComponents fun X => X.leftOpRightOpIso) <| by aesop_cat)
+    (NatIso.ofComponents fun X => X.leftOpRightOpIso)
 #align category_theory.simplicial_cosimplicial_augmented_equiv CategoryTheory.simplicialCosimplicialAugmentedEquiv
 
 end CategoryTheory

5ed51dc3

chore: made Opposite a structure (#3193)

The opposite category is no longer a type synonym, but a structure.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net>

d090d0a8

Diff

@@ -80,8 +80,8 @@ variable {C}
 -- porting note: added to ease automation
 @[ext]
 lemma hom_ext {X Y : SimplicialObject C} (f g : X ⟶ Y)
-  (h : ∀ (n : SimplexCategory), f.app n = g.app n) : f = g :=
-  NatTrans.ext _ _ (by ext ; apply h)
+  (h : ∀ (n : SimplexCategoryᵒᵖ), f.app n = g.app n) : f = g :=
+  NatTrans.ext _ _ (by ext; apply h)
 
 variable (X : SimplicialObject C)
 
@@ -450,7 +450,7 @@ variable {C}
 @[ext]
 lemma hom_ext {X Y : CosimplicialObject C} (f g : X ⟶ Y)
   (h : ∀ (n : SimplexCategory), f.app n = g.app n) : f = g :=
-  NatTrans.ext _ _ (by ext ; apply h)
+  NatTrans.ext _ _ (by ext; apply h)
 
 variable (X : CosimplicialObject C)

5ed51dc3

feat: port AlgebraicTopology.SimplicialObject (#3302)

d462f81d

`algebraic_topology.simplicial_object` ⟷ `Mathlib.AlgebraicTopology.SimplicialObject`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 6 + 301

algebraic_topology.simplicial_object ⟷ Mathlib.AlgebraicTopology.SimplicialObject

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 6 + 301

`algebraic_topology.simplicial_object` ⟷ `Mathlib.AlgebraicTopology.SimplicialObject`