algebraic_topology.simplex_category ⟷ Mathlib.AlgebraicTopology.SimplexCategory

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

@@ -524,19 +524,19 @@ theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ =>
 
 namespace SkeletalFunctor
 
-instance : Full skeletalFunctor.{v}
+instance : CategoryTheory.Functor.Full skeletalFunctor.{v}
     where
   Preimage a b f :=
     SimplexCategory.Hom.mk ⟨fun i => (f (ULift.up i)).down, fun i j h => f.Monotone h⟩
   witness' := by intro m n f; dsimp at *; ext1 ⟨i⟩; ext1; ext1; cases x; simp
 
-instance : Faithful skeletalFunctor.{v}
+instance : CategoryTheory.Functor.Faithful skeletalFunctor.{v}
     where map_injective' m n f g h := by
     ext1; ext1; ext1 i; apply ULift.up.inj
     change (skeletal_functor.map f) ⟨i⟩ = (skeletal_functor.map g) ⟨i⟩
     rw [h]
 
-instance : EssSurj skeletalFunctor.{v}
+instance : CategoryTheory.Functor.EssSurj skeletalFunctor.{v}
     where mem_essImage X :=
     ⟨mk (Fintype.card X - 1 : ℕ),
       ⟨by
@@ -556,8 +556,8 @@ instance : EssSurj skeletalFunctor.{v}
         · ext1; ext1 i; exact f.apply_symm_apply i⟩⟩
 
 #print SimplexCategory.SkeletalFunctor.isEquivalence /-
-noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
-  Equivalence.ofFullyFaithfullyEssSurj skeletalFunctor
+noncomputable instance isEquivalence : CategoryTheory.Functor.IsEquivalence skeletalFunctor.{v} :=
+  CategoryTheory.Functor.IsEquivalence.ofFullyFaithfullyEssSurj skeletalFunctor
 #align simplex_category.skeletal_functor.is_equivalence SimplexCategory.SkeletalFunctor.isEquivalence
 -/
 
@@ -602,7 +602,7 @@ simplex category.
 -/
 def inclusion {n : ℕ} : SimplexCategory.Truncated n ⥤ SimplexCategory :=
   fullSubcategoryInclusion _
-deriving Full, Faithful
+deriving CategoryTheory.Functor.Full, CategoryTheory.Functor.Faithful
 #align simplex_category.truncated.inclusion SimplexCategory.Truncated.inclusion
 -/
 
@@ -701,7 +701,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
     rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
-instance : ReflectsIsomorphisms (forget SimplexCategory) :=
+instance : CategoryTheory.Functor.ReflectsIsomorphisms (forget SimplexCategory) :=
   ⟨by
     intro x y f
     intro

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

@@ -7,7 +7,7 @@ import Mathbin.Tactic.Linarith.Default
 import CategoryTheory.Skeletal
 import Data.Fintype.Sort
 import Order.Category.NonemptyFinLinOrd
-import CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.Functor.ReflectsIso
 
 #align_import algebraic_topology.simplex_category from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 

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

@@ -324,7 +324,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_le_mk, Fin.castSucc_mk] at H 
+  simp only [Fin.mk_le_mk, Fin.castSucc_mk] at H
   dsimp
   split_ifs
   -- Most of the goals can now be handled by `linarith`,
@@ -399,7 +399,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_lt_mk, Fin.castSucc_mk] at H 
+  simp only [Fin.mk_lt_mk, Fin.castSucc_mk] at H
   suffices
     ite (_ < ite (k < i + 1) _ _) _ _ = ite _ (ite (j < k) (k - 1) k) (ite (j < k) (k - 1) k + 1) by
     simpa [apply_dite Fin.castSuccEmb, Fin.predAbove, push_cast]
@@ -407,22 +407,22 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   -- Most of the goals can now be handled by `linarith`,
   -- but we have to deal with three of them by hand.
   swap
-  · simp only [Fin.mk_lt_mk] at h_1 
-    simp only [not_lt] at h_2 
+  · simp only [Fin.mk_lt_mk] at h_1
+    simp only [not_lt] at h_2
     simp only [self_eq_add_right, one_ne_zero]
     exact
       lt_irrefl (k - 1)
         (lt_of_lt_of_le (Nat.pred_lt (ne_of_lt (lt_of_le_of_lt (zero_le _) h_1)).symm)
           (le_trans (Nat.le_of_lt_succ h) h_2))
   pick_goal 4
-  · simp only [Fin.mk_lt_mk] at h_1 
-    simp only [not_lt] at h 
+  · simp only [Fin.mk_lt_mk] at h_1
+    simp only [not_lt] at h
     simp only [Nat.add_succ_sub_one, add_zero]
     exfalso
     exact lt_irrefl _ (lt_of_le_of_lt (Nat.le_pred_of_lt (Nat.lt_of_succ_le h)) h_3)
   pick_goal 4
-  · simp only [Fin.mk_lt_mk] at h_1 
-    simp only [not_lt] at h_3 
+  · simp only [Fin.mk_lt_mk] at h_1
+    simp only [not_lt] at h_3
     simp only [Nat.add_succ_sub_one, add_zero]
     exact (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) h_2)).symm
   -- Hope for the best from `linarith`:
@@ -461,7 +461,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_le_mk] at H 
+  simp only [Fin.mk_le_mk] at H
   -- At this point `simp with push_cast` makes good progress, but neither `simp?` nor `squeeze_simp`
   -- return usable sets of lemmas.
   -- To avoid using a non-terminal simp, we make a `suffices` statement indicating the shape
@@ -474,14 +474,14 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ
   -- Most of them are dealt with `by simp at *; linarith`,
   -- but we pull out two harder ones to do by hand.
   pick_goal 3
-  · simp only [not_lt] at h_2 
+  · simp only [not_lt] at h_2
     exact
       False.elim
         (lt_irrefl (k - 1)
           (lt_of_lt_of_le (Nat.pred_lt (id (ne_of_lt (lt_of_le_of_lt (zero_le i) h)).symm))
             (le_trans h_2 (Nat.succ_le_of_lt h_1))))
   pick_goal 3
-  · simp only [Subtype.mk_lt_mk, not_lt] at h_1 
+  · simp only [Subtype.mk_lt_mk, not_lt] at h_1
     exact False.elim (lt_irrefl j (lt_of_lt_of_le (Nat.pred_lt_pred (Nat.succ_ne_zero j) h_2) h_1))
   -- Deal with the rest automatically.
   all_goals simp at * <;> linarith
@@ -697,7 +697,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
     simp only [Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
     rw [Fin.predAbove_of_castSucc_lt i b.succ _, Fin.pred_succ]
-    rw [not_le] at h 
+    rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
@@ -716,8 +716,8 @@ instance : ReflectsIsomorphisms (forget SimplexCategory) :=
                   · by_contra h''
                     have eq := fun i => congr_hom (iso.inv_hom_id (as_iso ((forget _).map f))) i
                     have ineq := f.to_order_hom.monotone' (le_of_not_ge h'')
-                    dsimp at ineq 
-                    erw [Eq, Eq] at ineq 
+                    dsimp at ineq
+                    erw [Eq, Eq] at ineq
                     exact not_le.mpr h' ineq
                   · rw [eq_of_le_of_not_lt h h'] }
           hom_inv_id' := by ext1; ext1; exact iso.hom_inv_id (as_iso ((forget _).map f))
@@ -780,12 +780,12 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     erw [Fin.succAbove_of_castSucc_lt i.succ x.cast_pred _]; swap
     · rwa [Eq, ← Fin.le_castSucc_iff]
     rw [Eq]
-  · simp only [not_le] at h' 
+  · simp only [not_le] at h'
     let y :=
       x.pred
         (by
           intro h
-          rw [h] at h' 
+          rw [h] at h'
           simpa only [Fin.lt_iff_val_lt_val, Nat.not_lt_zero, Fin.val_zero] using h')
     simp only [show x = y.succ by rw [Fin.succ_pred]] at h' ⊢
     rw [Fin.predAbove_of_castSucc_lt i y.succ h', Fin.pred_succ]
@@ -800,8 +800,8 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       cases' Nat.le.dest h' with c hc
       cases c
       · exfalso
-        rw [add_zero] at hc 
-        rw [hc] at h'' 
+        rw [add_zero] at hc
+        rw [hc] at h''
         exact h'' rfl
       · rw [← hc]
         simp only [add_le_add_iff_left, Nat.succ_eq_add_one, le_add_iff_nonneg_left, zero_le]
@@ -812,7 +812,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
 theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (hθ : ¬Function.Injective θ.toOrderHom) : ∃ (i : Fin (n + 1)) (θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' :=
   by
-  simp only [Function.Injective, exists_prop, Classical.not_forall] at hθ 
+  simp only [Function.Injective, exists_prop, Classical.not_forall] at hθ
   -- as θ is not injective, there exists `x<y` such that `θ x = θ y`
   -- and then, `θ x = θ (x+1)`
   have hθ₂ : ∃ x y : Fin (n + 2), (hom.to_order_hom θ) x = (hom.to_order_hom θ) y ∧ x < y :=
@@ -829,9 +829,9 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   let z := x.cast_pred
   use z
   simp only [←
-    show z.cast_succ = x from Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂ 
+    show z.cast_succ = x from Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSucc_lt_iff_succ_le] at h₂ 
+  rw [Fin.castSucc_lt_iff_succ_le] at h₂
   apply le_antisymm
   · exact θ.to_order_hom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
   · rw [h₁]
@@ -859,7 +859,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
             (fin.lt_iff_coe_lt_coe.mp ((Ne.le_iff_lt (hi x)).mp h'))
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
-    · simp only [not_le] at h' 
+    · simp only [not_le] at h'
       simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk,
         Fin.predAbove_of_castSucc_lt (Fin.castPred i) (θ.to_order_hom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]

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

@@ -693,10 +693,10 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
   simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk]
   by_cases b ≤ i
   · use b
-    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
+    rw [Fin.predAbove_of_le_castSucc i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
-    rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
+    rw [Fin.predAbove_of_castSucc_lt i b.succ _, Fin.pred_succ]
     rw [not_le] at h 
     rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
@@ -775,9 +775,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
     small_category_comp, σ, mk_hom, OrderHom.coe_mk]
   by_cases h' : x ≤ i.cast_succ
-  · rw [Fin.predAbove_below i x h']
+  · rw [Fin.predAbove_of_le_castSucc i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
-    erw [Fin.succAbove_below i.succ x.cast_pred _]; swap
+    erw [Fin.succAbove_of_castSucc_lt i.succ x.cast_pred _]; swap
     · rwa [Eq, ← Fin.le_castSucc_iff]
     rw [Eq]
   · simp only [not_le] at h' 
@@ -788,13 +788,13 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
           rw [h] at h' 
           simpa only [Fin.lt_iff_val_lt_val, Nat.not_lt_zero, Fin.val_zero] using h')
     simp only [show x = y.succ by rw [Fin.succ_pred]] at h' ⊢
-    rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
+    rw [Fin.predAbove_of_castSucc_lt i y.succ h', Fin.pred_succ]
     by_cases h'' : y = i
     · rw [h'']
       convert hi.symm
-      erw [Fin.succAbove_below i.succ _]
+      erw [Fin.succAbove_of_castSucc_lt i.succ _]
       exact Fin.lt_succ
-    · erw [Fin.succAbove_above i.succ _]
+    · erw [Fin.succAbove_of_le_castSucc i.succ _]
       simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
         Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
@@ -850,9 +850,9 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       small_category_comp]
     by_cases h' : θ.to_order_hom x ≤ i
     · simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk]
-      rw [Fin.predAbove_below (Fin.castPred i) (θ.to_order_hom x)
+      rw [Fin.predAbove_of_le_castSucc (Fin.castPred i) (θ.to_order_hom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
-      erw [Fin.succAbove_below i]; swap
+      erw [Fin.succAbove_of_castSucc_lt i]; swap
       · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
         exact
           lt_of_le_of_lt (Fin.coe_castPred_le_self _)
@@ -861,9 +861,9 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h' 
       simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk,
-        Fin.predAbove_above (Fin.castPred i) (θ.to_order_hom x)
+        Fin.predAbove_of_castSucc_lt (Fin.castPred i) (θ.to_order_hom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
-      erw [Fin.succAbove_above i _, Fin.succ_pred]
+      erw [Fin.succAbove_of_le_castSucc i _, Fin.succ_pred]
       simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_pred_of_lt (fin.lt_iff_coe_lt_coe.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)

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

@@ -40,7 +40,7 @@ universe v
 
 open CategoryTheory CategoryTheory.Limits
 
-/- ./././Mathport/Syntax/Translate/Command.lean:333:31: unsupported: @[derive, irreducible] def -/
+/- ./././Mathport/Syntax/Translate/Command.lean:336:31: unsupported: @[derive, irreducible] def -/
 #print SimplexCategory /-
 /-- The simplex category:
 * objects are natural numbers `n : ℕ`

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

@@ -40,7 +40,7 @@ universe v
 
 open CategoryTheory CategoryTheory.Limits
 
-/- ./././Mathport/Syntax/Translate/Command.lean:323:31: unsupported: @[derive, irreducible] def -/
+/- ./././Mathport/Syntax/Translate/Command.lean:333:31: unsupported: @[derive, irreducible] def -/
 #print SimplexCategory /-
 /-- The simplex category:
 * objects are natural numbers `n : ℕ`

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -812,7 +812,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
 theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (hθ : ¬Function.Injective θ.toOrderHom) : ∃ (i : Fin (n + 1)) (θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' :=
   by
-  simp only [Function.Injective, exists_prop, not_forall] at hθ 
+  simp only [Function.Injective, exists_prop, Classical.not_forall] at hθ 
   -- as θ is not injective, there exists `x<y` such that `θ x = θ y`
   -- and then, `θ x = θ (x+1)`
   have hθ₂ : ∃ x y : Fin (n + 2), (hom.to_order_hom θ) x = (hom.to_order_hom θ) y ∧ x < y :=

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

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
 import Mathbin.Tactic.Linarith.Default
-import Mathbin.CategoryTheory.Skeletal
-import Mathbin.Data.Fintype.Sort
-import Mathbin.Order.Category.NonemptyFinLinOrd
-import Mathbin.CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.Skeletal
+import Data.Fintype.Sort
+import Order.Category.NonemptyFinLinOrd
+import CategoryTheory.Functor.ReflectsIsomorphisms
 
 #align_import algebraic_topology.simplex_category from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 
@@ -496,9 +496,9 @@ section Skeleton
 /-- The functor that exhibits `simplex_category` as skeleton
 of `NonemptyFinLinOrd` -/
 @[simps obj map]
-def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v}
+def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrd.{v}
     where
-  obj a := NonemptyFinLinOrdCat.of <| ULift (Fin (a.len + 1))
+  obj a := NonemptyFinLinOrd.of <| ULift (Fin (a.len + 1))
   map a b f := ⟨fun i => ULift.up (f.toOrderHom i.down), fun i j h => f.toOrderHom.Monotone h⟩
   map_id' a := by ext; simp
   map_comp' a b c f g := by ext; simp
@@ -566,7 +566,7 @@ end SkeletalFunctor
 #print SimplexCategory.skeletalEquivalence /-
 /-- The equivalence that exhibits `simplex_category` as skeleton
 of `NonemptyFinLinOrd` -/
-noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrdCat.{v} :=
+noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrd.{v} :=
   Functor.asEquivalence skeletalFunctor
 #align simplex_category.skeletal_equivalence SimplexCategory.skeletalEquivalence
 -/
@@ -576,8 +576,7 @@ end Skeleton
 #print SimplexCategory.isSkeletonOf /-
 /-- `simplex_category` is a skeleton of `NonemptyFinLinOrd`.
 -/
-noncomputable def isSkeletonOf :
-    IsSkeletonOf NonemptyFinLinOrdCat SimplexCategory skeletalFunctor.{v}
+noncomputable def isSkeletonOf : IsSkeletonOf NonemptyFinLinOrd SimplexCategory skeletalFunctor.{v}
     where
   skel := skeletal
   eqv := SkeletalFunctor.isEquivalence
@@ -630,7 +629,7 @@ theorem mono_iff_injective {n m : SimplexCategory} {f : n ⟶ m} :
   by
   rw [← functor.mono_map_iff_mono skeletal_equivalence.Functor]
   dsimp only [skeletal_equivalence, functor.as_equivalence_functor]
-  rw [NonemptyFinLinOrdCat.mono_iff_injective, skeletal_functor.coe_map,
+  rw [NonemptyFinLinOrd.mono_iff_injective, skeletal_functor.coe_map,
     Function.Injective.of_comp_iff ULift.up_injective,
     Function.Injective.of_comp_iff' _ ULift.down_bijective]
 #align simplex_category.mono_iff_injective SimplexCategory.mono_iff_injective
@@ -644,7 +643,7 @@ theorem epi_iff_surjective {n m : SimplexCategory} {f : n ⟶ m} :
   by
   rw [← functor.epi_map_iff_epi skeletal_equivalence.Functor]
   dsimp only [skeletal_equivalence, functor.as_equivalence_functor]
-  rw [NonemptyFinLinOrdCat.epi_iff_surjective, skeletal_functor.coe_map,
+  rw [NonemptyFinLinOrd.epi_iff_surjective, skeletal_functor.coe_map,
     Function.Surjective.of_comp_iff' ULift.up_bijective,
     Function.Surjective.of_comp_iff _ ULift.down_surjective]
 #align simplex_category.epi_iff_surjective SimplexCategory.epi_iff_surjective
@@ -1000,9 +999,8 @@ to the category attached to the ordered set `{0, 1, ..., n}` -/
 @[simps obj map]
 def toCat : SimplexCategory ⥤ Cat.{0} :=
   SimplexCategory.skeletalFunctor ⋙
-    forget₂ NonemptyFinLinOrdCat LinOrdCat ⋙
-      forget₂ LinOrdCat LatCat ⋙
-        forget₂ LatCat PartOrdCat ⋙ forget₂ PartOrdCat PreordCat ⋙ preordCatToCat
+    forget₂ NonemptyFinLinOrd LinOrd ⋙
+      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrd ⋙ forget₂ PartOrd Preord ⋙ preordToCat
 #align simplex_category.to_Cat SimplexCategory.toCat
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -691,7 +691,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
   by
   rw [epi_iff_surjective]
   intro b
-  simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
+  simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk]
   by_cases b ≤ i
   · use b
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
@@ -774,7 +774,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   use δ i.succ ≫ θ
   ext1; ext1; ext1 x
   simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
-    small_category_comp, σ, mk_hom, OrderHom.coe_fun_mk]
+    small_category_comp, σ, mk_hom, OrderHom.coe_mk]
   by_cases h' : x ≤ i.cast_succ
   · rw [Fin.predAbove_below i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
@@ -850,7 +850,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
       small_category_comp]
     by_cases h' : θ.to_order_hom x ≤ i
-    · simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
+    · simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.to_order_hom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
       erw [Fin.succAbove_below i]; swap
@@ -861,7 +861,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h' 
-      simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk,
+      simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.to_order_hom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
       erw [Fin.succAbove_above i _, Fin.succ_pred]
@@ -871,7 +871,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     use θ ≫ σ (Fin.last _)
     ext1; ext1; ext1 x
     simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
-      small_category_comp, σ, δ, mk_hom, OrderHom.coe_fun_mk, OrderEmbedding.toOrderHom_coe,
+      small_category_comp, σ, δ, mk_hom, OrderHom.coe_mk, OrderEmbedding.toOrderHom_coe,
       Fin.predAbove_last, Fin.succAbove_last,
       Fin.castSucc_castPred ((Ne.le_iff_lt (hi x)).mp (Fin.le_last _))]
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 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.simplex_category
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Tactic.Linarith.Default
 import Mathbin.CategoryTheory.Skeletal
@@ -14,6 +9,8 @@ import Mathbin.Data.Fintype.Sort
 import Mathbin.Order.Category.NonemptyFinLinOrd
 import Mathbin.CategoryTheory.Functor.ReflectsIsomorphisms
 
+#align_import algebraic_topology.simplex_category from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-! # The simplex category
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

@@ -240,7 +240,7 @@ one given by the following generators and relations.
 #print SimplexCategory.δ /-
 /-- The `i`-th face map from `[n]` to `[n+1]` -/
 def δ {n} (i : Fin (n + 2)) : [n] ⟶ [n + 1] :=
-  mkHom (Fin.succAbove i).toOrderHom
+  mkHom (Fin.succAboveEmb i).toOrderHom
 #align simplex_category.δ SimplexCategory.δ
 -/
 
@@ -258,7 +258,7 @@ def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
   by
   ext k
-  dsimp [δ, Fin.succAbove]
+  dsimp [δ, Fin.succAboveEmb]
   simp only [OrderEmbedding.toOrderHom_coe, OrderEmbedding.coe_ofStrictMono, Function.comp_apply,
     SimplexCategory.Hom.toOrderHom_mk, OrderHom.comp_coe]
   rcases i with ⟨i, _⟩
@@ -321,13 +321,13 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
           i)
         (ite (j.cast_succ < k) (k - 1) k) (ite (j.cast_succ < k) (k - 1) k + 1)
     by
-    dsimp [δ, σ, Fin.succAbove, Fin.predAbove]
+    dsimp [δ, σ, Fin.succAboveEmb, Fin.predAbove]
     simp [Fin.predAbove, push_cast]
     convert rfl
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_le_mk, Fin.castSuccEmb_mk] at H 
+  simp only [Fin.mk_le_mk, Fin.castSucc_mk] at H 
   dsimp
   split_ifs
   -- Most of the goals can now be handled by `linarith`,
@@ -356,7 +356,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
     ite (Fin.castSuccEmb i < ite (j < i) (Fin.castSuccEmb j) j.succ)
         (ite (j < i) (j : ℕ) (j + 1) - 1) (ite (j < i) j (j + 1)) =
       j
-    by dsimp [δ, σ, Fin.succAbove, Fin.predAbove]; simpa [Fin.predAbove, push_cast]
+    by dsimp [δ, σ, Fin.succAboveEmb, Fin.predAbove]; simpa [Fin.predAbove, push_cast]
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   dsimp
@@ -379,7 +379,7 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 [n] :=
   ext j
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
-  dsimp [δ, σ, Fin.succAbove, Fin.predAbove]
+  dsimp [δ, σ, Fin.succAboveEmb, Fin.predAbove]
   simp [Fin.predAbove, push_cast]
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_σ_succ SimplexCategory.δ_comp_σ_succ
@@ -398,11 +398,11 @@ theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_succ < i) :
     δ i.succ ≫ σ j.cast_succ = σ j ≫ δ i := by
   ext k
-  dsimp [δ, σ, Fin.succAbove, Fin.predAbove]
+  dsimp [δ, σ, Fin.succAboveEmb, Fin.predAbove]
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_lt_mk, Fin.castSuccEmb_mk] at H 
+  simp only [Fin.mk_lt_mk, Fin.castSucc_mk] at H 
   suffices
     ite (_ < ite (k < i + 1) _ _) _ _ = ite _ (ite (j < k) (k - 1) k) (ite (j < k) (k - 1) k + 1) by
     simpa [apply_dite Fin.castSuccEmb, Fin.predAbove, push_cast]
@@ -447,7 +447,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   by
   rw [← δ_comp_σ_of_gt]
   · simpa only [Fin.succ_pred]
-  · rw [Fin.castSuccEmb_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
+  · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'
 -/
@@ -697,13 +697,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
   simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
   by_cases b ≤ i
   · use b
-    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSuccEmb] using h)]
-    simp only [Fin.coe_eq_castSuccEmb, Fin.castPred_castSuccEmb]
+    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
+    simp only [Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h 
     rw [Fin.lt_iff_val_lt_val] at h ⊢
-    simpa only [Fin.val_succ, Fin.coe_castSuccEmb] using Nat.lt.step h
+    simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
 instance : ReflectsIsomorphisms (forget SimplexCategory) :=
   ⟨by
@@ -780,9 +780,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     small_category_comp, σ, mk_hom, OrderHom.coe_fun_mk]
   by_cases h' : x ≤ i.cast_succ
   · rw [Fin.predAbove_below i x h']
-    have eq := Fin.castSuccEmb_castPred (gt_of_gt_of_ge (Fin.castSuccEmb_lt_last i) h')
+    have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
     erw [Fin.succAbove_below i.succ x.cast_pred _]; swap
-    · rwa [Eq, ← Fin.le_castSuccEmb_iff]
+    · rwa [Eq, ← Fin.le_castSucc_iff]
     rw [Eq]
   · simp only [not_le] at h' 
     let y :=
@@ -799,7 +799,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       erw [Fin.succAbove_below i.succ _]
       exact Fin.lt_succ
     · erw [Fin.succAbove_above i.succ _]
-      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSuccEmb,
+      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
         Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
       cases c
@@ -833,11 +833,11 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   let z := x.cast_pred
   use z
   simp only [←
-    show z.cast_succ = x from Fin.castSuccEmb_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂ 
+    show z.cast_succ = x from Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂ 
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSuccEmb_lt_iff_succ_le] at h₂ 
+  rw [Fin.castSucc_lt_iff_succ_le] at h₂ 
   apply le_antisymm
-  · exact θ.to_order_hom.monotone (le_of_lt (Fin.castSuccEmb_lt_succ z))
+  · exact θ.to_order_hom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
   · rw [h₁]
     exact θ.to_order_hom.monotone h₂
 #align simplex_category.eq_σ_comp_of_not_injective SimplexCategory.eq_σ_comp_of_not_injective
@@ -855,20 +855,20 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     by_cases h' : θ.to_order_hom x ≤ i
     · simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.to_order_hom x)
-          (by simpa [Fin.castSuccEmb_castPred h] using h')]
+          (by simpa [Fin.castSucc_castPred h] using h')]
       erw [Fin.succAbove_below i]; swap
-      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb]
+      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
         exact
           lt_of_le_of_lt (Fin.coe_castPred_le_self _)
             (fin.lt_iff_coe_lt_coe.mp ((Ne.le_iff_lt (hi x)).mp h'))
-      rw [Fin.castSuccEmb_castPred]
+      rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h' 
       simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.to_order_hom x)
-          (by simpa only [Fin.castSuccEmb_castPred h] using h')]
+          (by simpa only [Fin.castSucc_castPred h] using h')]
       erw [Fin.succAbove_above i _, Fin.succ_pred]
-      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSuccEmb, Fin.coe_pred] using
+      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_pred_of_lt (fin.lt_iff_coe_lt_coe.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
@@ -876,7 +876,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
       small_category_comp, σ, δ, mk_hom, OrderHom.coe_fun_mk, OrderEmbedding.toOrderHom_coe,
       Fin.predAbove_last, Fin.succAbove_last,
-      Fin.castSuccEmb_castPred ((Ne.le_iff_lt (hi x)).mp (Fin.le_last _))]
+      Fin.castSucc_castPred ((Ne.le_iff_lt (hi x)).mp (Fin.le_last _))]
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

@@ -327,7 +327,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_le_mk, Fin.castSucc_mk] at H 
+  simp only [Fin.mk_le_mk, Fin.castSuccEmb_mk] at H 
   dsimp
   split_ifs
   -- Most of the goals can now be handled by `linarith`,
@@ -353,8 +353,8 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
   by
   ext j
   suffices
-    ite (Fin.castSucc i < ite (j < i) (Fin.castSucc j) j.succ) (ite (j < i) (j : ℕ) (j + 1) - 1)
-        (ite (j < i) j (j + 1)) =
+    ite (Fin.castSuccEmb i < ite (j < i) (Fin.castSuccEmb j) j.succ)
+        (ite (j < i) (j : ℕ) (j + 1) - 1) (ite (j < i) j (j + 1)) =
       j
     by dsimp [δ, σ, Fin.succAbove, Fin.predAbove]; simpa [Fin.predAbove, push_cast]
   rcases i with ⟨i, _⟩
@@ -402,10 +402,10 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_lt_mk, Fin.castSucc_mk] at H 
+  simp only [Fin.mk_lt_mk, Fin.castSuccEmb_mk] at H 
   suffices
     ite (_ < ite (k < i + 1) _ _) _ _ = ite _ (ite (j < k) (k - 1) k) (ite (j < k) (k - 1) k + 1) by
-    simpa [apply_dite Fin.castSucc, Fin.predAbove, push_cast]
+    simpa [apply_dite Fin.castSuccEmb, Fin.predAbove, push_cast]
   split_ifs
   -- Most of the goals can now be handled by `linarith`,
   -- but we have to deal with three of them by hand.
@@ -447,7 +447,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   by
   rw [← δ_comp_σ_of_gt]
   · simpa only [Fin.succ_pred]
-  · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
+  · rw [Fin.castSuccEmb_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'
 -/
@@ -697,13 +697,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
   simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
   by_cases b ≤ i
   · use b
-    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
-    simp only [Fin.coe_eq_castSucc, Fin.castPred_castSucc]
+    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSuccEmb] using h)]
+    simp only [Fin.coe_eq_castSuccEmb, Fin.castPred_castSuccEmb]
   · use b.succ
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h 
     rw [Fin.lt_iff_val_lt_val] at h ⊢
-    simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
+    simpa only [Fin.val_succ, Fin.coe_castSuccEmb] using Nat.lt.step h
 
 instance : ReflectsIsomorphisms (forget SimplexCategory) :=
   ⟨by
@@ -780,9 +780,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     small_category_comp, σ, mk_hom, OrderHom.coe_fun_mk]
   by_cases h' : x ≤ i.cast_succ
   · rw [Fin.predAbove_below i x h']
-    have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
+    have eq := Fin.castSuccEmb_castPred (gt_of_gt_of_ge (Fin.castSuccEmb_lt_last i) h')
     erw [Fin.succAbove_below i.succ x.cast_pred _]; swap
-    · rwa [Eq, ← Fin.le_castSucc_iff]
+    · rwa [Eq, ← Fin.le_castSuccEmb_iff]
     rw [Eq]
   · simp only [not_le] at h' 
     let y :=
@@ -799,7 +799,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       erw [Fin.succAbove_below i.succ _]
       exact Fin.lt_succ
     · erw [Fin.succAbove_above i.succ _]
-      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
+      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSuccEmb,
         Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
       cases c
@@ -833,11 +833,11 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   let z := x.cast_pred
   use z
   simp only [←
-    show z.cast_succ = x from Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂ 
+    show z.cast_succ = x from Fin.castSuccEmb_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂ 
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSucc_lt_iff_succ_le] at h₂ 
+  rw [Fin.castSuccEmb_lt_iff_succ_le] at h₂ 
   apply le_antisymm
-  · exact θ.to_order_hom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
+  · exact θ.to_order_hom.monotone (le_of_lt (Fin.castSuccEmb_lt_succ z))
   · rw [h₁]
     exact θ.to_order_hom.monotone h₂
 #align simplex_category.eq_σ_comp_of_not_injective SimplexCategory.eq_σ_comp_of_not_injective
@@ -855,20 +855,20 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     by_cases h' : θ.to_order_hom x ≤ i
     · simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.to_order_hom x)
-          (by simpa [Fin.castSucc_castPred h] using h')]
+          (by simpa [Fin.castSuccEmb_castPred h] using h')]
       erw [Fin.succAbove_below i]; swap
-      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
+      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb]
         exact
           lt_of_le_of_lt (Fin.coe_castPred_le_self _)
             (fin.lt_iff_coe_lt_coe.mp ((Ne.le_iff_lt (hi x)).mp h'))
-      rw [Fin.castSucc_castPred]
+      rw [Fin.castSuccEmb_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h' 
       simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.to_order_hom x)
-          (by simpa only [Fin.castSucc_castPred h] using h')]
+          (by simpa only [Fin.castSuccEmb_castPred h] using h')]
       erw [Fin.succAbove_above i _, Fin.succ_pred]
-      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
+      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSuccEmb, Fin.coe_pred] using
         Nat.le_pred_of_lt (fin.lt_iff_coe_lt_coe.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
@@ -876,7 +876,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
       small_category_comp, σ, δ, mk_hom, OrderHom.coe_fun_mk, OrderEmbedding.toOrderHom_coe,
       Fin.predAbove_last, Fin.succAbove_last,
-      Fin.castSucc_castPred ((Ne.le_iff_lt (hi x)).mp (Fin.le_last _))]
+      Fin.castSuccEmb_castPred ((Ne.le_iff_lt (hi x)).mp (Fin.le_last _))]
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 -/
 

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

@@ -43,7 +43,7 @@ universe v
 
 open CategoryTheory CategoryTheory.Limits
 
-/- ./././Mathport/Syntax/Translate/Command.lean:324:31: unsupported: @[derive, irreducible] def -/
+/- ./././Mathport/Syntax/Translate/Command.lean:323:31: unsupported: @[derive, irreducible] def -/
 #print SimplexCategory /-
 /-- The simplex category:
 * objects are natural numbers `n : ℕ`
@@ -68,7 +68,6 @@ def mk (n : ℕ) : SimplexCategory :=
 #align simplex_category.mk SimplexCategory.mk
 -/
 
--- mathport name: simplex_category.mk
 scoped[Simplicial] notation "[" n "]" => SimplexCategory.mk n
 
 #print SimplexCategory.len /-
@@ -119,22 +118,28 @@ namespace Hom
 
 attribute [local semireducible] SimplexCategory.Hom
 
+#print SimplexCategory.Hom.mk /-
 /-- Make a moprhism in `simplex_category` from a monotone map of fin's. -/
 def mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) : SimplexCategory.Hom a b :=
   f
 #align simplex_category.hom.mk SimplexCategory.Hom.mk
+-/
 
+#print SimplexCategory.Hom.toOrderHom /-
 /-- Recover the monotone map from a morphism in the simplex category. -/
 def toOrderHom {a b : SimplexCategory} (f : SimplexCategory.Hom a b) :
     Fin (a.len + 1) →o Fin (b.len + 1) :=
   f
 #align simplex_category.hom.to_order_hom SimplexCategory.Hom.toOrderHom
+-/
 
+#print SimplexCategory.Hom.ext' /-
 @[ext]
 theorem ext' {a b : SimplexCategory} (f g : SimplexCategory.Hom a b) :
     f.toOrderHom = g.toOrderHom → f = g :=
   id
 #align simplex_category.hom.ext SimplexCategory.Hom.ext'
+-/
 
 #print SimplexCategory.Hom.mk_toOrderHom /-
 @[simp]
@@ -143,16 +148,20 @@ theorem mk_toOrderHom {a b : SimplexCategory} (f : SimplexCategory.Hom a b) : mk
 #align simplex_category.hom.mk_to_order_hom SimplexCategory.Hom.mk_toOrderHom
 -/
 
+#print SimplexCategory.Hom.toOrderHom_mk /-
 @[simp]
 theorem toOrderHom_mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) :
     (mk f).toOrderHom = f :=
   rfl
 #align simplex_category.hom.to_order_hom_mk SimplexCategory.Hom.toOrderHom_mk
+-/
 
+#print SimplexCategory.Hom.mk_toOrderHom_apply /-
 theorem mk_toOrderHom_apply {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1))
     (i : Fin (a.len + 1)) : (mk f).toOrderHom i = f i :=
   rfl
 #align simplex_category.hom.mk_to_order_hom_apply SimplexCategory.Hom.mk_toOrderHom_apply
+-/
 
 #print SimplexCategory.Hom.id /-
 /-- Identity morphisms of `simplex_category`. -/
@@ -198,6 +207,7 @@ theorem const_comp (x y : SimplexCategory) (i : Fin (x.len + 1)) (f : x ⟶ y) :
 #align simplex_category.const_comp SimplexCategory.const_comp
 -/
 
+#print SimplexCategory.mkHom /-
 /-- Make a morphism `[n] ⟶ [m]` from a monotone map between fin's.
 This is useful for constructing morphisms beetween `[n]` directly
 without identifying `n` with `[n].len`.
@@ -206,6 +216,7 @@ without identifying `n` with `[n].len`.
 def mkHom {n m : ℕ} (f : Fin (n + 1) →o Fin (m + 1)) : [n] ⟶ [m] :=
   SimplexCategory.Hom.mk f
 #align simplex_category.mk_hom SimplexCategory.mkHom
+-/
 
 #print SimplexCategory.hom_zero_zero /-
 theorem hom_zero_zero (f : [0] ⟶ [0]) : f = 𝟙 _ := by ext : 2; dsimp; apply Subsingleton.elim
@@ -242,6 +253,7 @@ def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
 #align simplex_category.σ SimplexCategory.σ
 -/
 
+#print SimplexCategory.δ_comp_δ /-
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
   by
@@ -254,7 +266,9 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ =
   rcases k with ⟨k, _⟩
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
+-/
 
+#print SimplexCategory.δ_comp_δ' /-
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     δ i ≫ δ j = δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ δ i.cast_succ :=
   by
@@ -264,7 +278,9 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
     simpa only [Fin.le_iff_val_le_val, ← Nat.lt_succ_iff, Nat.succ_eq_add_one, ← Fin.val_succ,
       j.succ_pred, Fin.lt_iff_val_lt_val] using H
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
+-/
 
+#print SimplexCategory.δ_comp_δ'' /-
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
       δ j ≫ δ i :=
@@ -273,18 +289,24 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   · rfl
   · exact H
 #align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''
+-/
 
+#print SimplexCategory.δ_comp_δ_self /-
 /-- The special case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i ≫ δ i.succ :=
   (δ_comp_δ (le_refl i)).symm
 #align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_self
+-/
 
+#print SimplexCategory.δ_comp_δ_self' /-
 @[reassoc]
 theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast_succ) :
     δ i ≫ δ j = δ i ≫ δ i.succ := by subst H; rw [δ_comp_δ_self]
 #align simplex_category.δ_comp_δ_self' SimplexCategory.δ_comp_δ_self'
+-/
 
+#print SimplexCategory.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) :
@@ -322,7 +344,9 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
         | simp at * <;>
       linarith
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
+-/
 
+#print SimplexCategory.δ_comp_σ_self /-
 /-- The first part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [n] :=
@@ -338,11 +362,14 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
   dsimp
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_self
+-/
 
+#print SimplexCategory.δ_comp_σ_self' /-
 @[reassoc]
 theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast_succ) :
     δ j ≫ σ i = 𝟙 [n] := by subst H; rw [δ_comp_σ_self]
 #align simplex_category.δ_comp_σ_self' SimplexCategory.δ_comp_σ_self'
+-/
 
 #print SimplexCategory.δ_comp_σ_succ /-
 /-- The second part of the third simplicial identity -/
@@ -365,6 +392,7 @@ theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ
 #align simplex_category.δ_comp_σ_succ' SimplexCategory.δ_comp_σ_succ'
 -/
 
+#print SimplexCategory.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) :
@@ -403,6 +431,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   -- Hope for the best from `linarith`:
   all_goals simp at h_1 h_2 ⊢ <;> linarith
 #align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gt
+-/
 
 #print SimplexCategory.δ_comp_σ_of_gt' /-
 @[reassoc]
@@ -425,6 +454,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 
 attribute [local simp] Fin.pred_mk
 
+#print SimplexCategory.σ_comp_σ /-
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ j = σ j.succ ≫ σ i :=
@@ -459,6 +489,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ
   -- Deal with the rest automatically.
   all_goals simp at * <;> linarith
 #align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σ
+-/
 
 end Generators
 
@@ -477,10 +508,12 @@ def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v}
 #align simplex_category.skeletal_functor SimplexCategory.skeletalFunctor
 -/
 
+#print SimplexCategory.skeletalFunctor.coe_map /-
 theorem skeletalFunctor.coe_map {Δ₁ Δ₂ : SimplexCategory} (f : Δ₁ ⟶ Δ₂) :
     coeFn (skeletalFunctor.{v}.map f) = ULift.up ∘ f.toOrderHom ∘ ULift.down :=
   rfl
 #align simplex_category.skeletal_functor.coe_map SimplexCategory.skeletalFunctor.coe_map
+-/
 
 #print SimplexCategory.skeletal /-
 theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ =>
@@ -533,11 +566,13 @@ noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
 
 end SkeletalFunctor
 
+#print SimplexCategory.skeletalEquivalence /-
 /-- The equivalence that exhibits `simplex_category` as skeleton
 of `NonemptyFinLinOrd` -/
 noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrdCat.{v} :=
   Functor.asEquivalence skeletalFunctor
 #align simplex_category.skeletal_equivalence SimplexCategory.skeletalEquivalence
+-/
 
 end Skeleton
 
@@ -700,6 +735,7 @@ theorem isIso_of_bijective {x y : SimplexCategory} {f : x ⟶ y}
 #align simplex_category.is_iso_of_bijective SimplexCategory.isIso_of_bijective
 -/
 
+#print SimplexCategory.orderIsoOfIso /-
 /-- An isomorphism in `simplex_category` induces an `order_iso`. -/
 @[simp]
 def orderIsoOfIso {x y : SimplexCategory} (e : x ≅ y) : Fin (x.len + 1) ≃o Fin (y.len + 1) :=
@@ -712,6 +748,7 @@ def orderIsoOfIso {x y : SimplexCategory} (e : x ≅ y) : Fin (x.len + 1) ≃o F
         simpa only using congr_arg (fun φ => (hom.to_order_hom φ) i) e.inv_hom_id' }
     e.Hom.toOrderHom.Monotone e.inv.toOrderHom.Monotone
 #align simplex_category.order_iso_of_iso SimplexCategory.orderIsoOfIso
+-/
 
 #print SimplexCategory.iso_eq_iso_refl /-
 theorem iso_eq_iso_refl {x : SimplexCategory} (e : x ≅ x) : e = Iso.refl x :=
@@ -733,6 +770,7 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [hf : IsIso f] : f =
 #align simplex_category.eq_id_of_is_iso SimplexCategory.eq_id_of_isIso
 -/
 
+#print SimplexCategory.eq_σ_comp_of_not_injective' /-
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (i : Fin (n + 1)) (hi : θ.toOrderHom i.cast_succ = θ.toOrderHom i.succ) :
     ∃ θ' : mk n ⟶ Δ', θ = σ i ≫ θ' := by
@@ -772,6 +810,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       · rw [← hc]
         simp only [add_le_add_iff_left, Nat.succ_eq_add_one, le_add_iff_nonneg_left, zero_le]
 #align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'
+-/
 
 #print SimplexCategory.eq_σ_comp_of_not_injective /-
 theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')

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

@@ -43,7 +43,7 @@ universe v
 
 open CategoryTheory CategoryTheory.Limits
 
-/- ./././Mathport/Syntax/Translate/Command.lean:323:31: unsupported: @[derive, irreducible] def -/
+/- ./././Mathport/Syntax/Translate/Command.lean:324:31: unsupported: @[derive, irreducible] def -/
 #print SimplexCategory /-
 /-- The simplex category:
 * objects are natural numbers `n : ℕ`

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

@@ -305,7 +305,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_le_mk, Fin.castSucc_mk] at H
+  simp only [Fin.mk_le_mk, Fin.castSucc_mk] at H 
   dsimp
   split_ifs
   -- Most of the goals can now be handled by `linarith`,
@@ -315,7 +315,12 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   pick_goal 7
   · have : k ≤ i := Nat.le_of_pred_lt ‹_›; linarith
   -- Hope for the best from `linarith`:
-  all_goals try first |rfl|simp at * <;> linarith
+  all_goals
+    try
+        first
+        | rfl
+        | simp at * <;>
+      linarith
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
 
 /-- The first part of the third simplicial identity -/
@@ -369,7 +374,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_lt_mk, Fin.castSucc_mk] at H
+  simp only [Fin.mk_lt_mk, Fin.castSucc_mk] at H 
   suffices
     ite (_ < ite (k < i + 1) _ _) _ _ = ite _ (ite (j < k) (k - 1) k) (ite (j < k) (k - 1) k + 1) by
     simpa [apply_dite Fin.castSucc, Fin.predAbove, push_cast]
@@ -377,26 +382,26 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   -- Most of the goals can now be handled by `linarith`,
   -- but we have to deal with three of them by hand.
   swap
-  · simp only [Fin.mk_lt_mk] at h_1
-    simp only [not_lt] at h_2
+  · simp only [Fin.mk_lt_mk] at h_1 
+    simp only [not_lt] at h_2 
     simp only [self_eq_add_right, one_ne_zero]
     exact
       lt_irrefl (k - 1)
         (lt_of_lt_of_le (Nat.pred_lt (ne_of_lt (lt_of_le_of_lt (zero_le _) h_1)).symm)
           (le_trans (Nat.le_of_lt_succ h) h_2))
   pick_goal 4
-  · simp only [Fin.mk_lt_mk] at h_1
-    simp only [not_lt] at h
+  · simp only [Fin.mk_lt_mk] at h_1 
+    simp only [not_lt] at h 
     simp only [Nat.add_succ_sub_one, add_zero]
     exfalso
     exact lt_irrefl _ (lt_of_le_of_lt (Nat.le_pred_of_lt (Nat.lt_of_succ_le h)) h_3)
   pick_goal 4
-  · simp only [Fin.mk_lt_mk] at h_1
-    simp only [not_lt] at h_3
+  · simp only [Fin.mk_lt_mk] at h_1 
+    simp only [not_lt] at h_3 
     simp only [Nat.add_succ_sub_one, add_zero]
     exact (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) h_2)).symm
   -- Hope for the best from `linarith`:
-  all_goals simp at h_1 h_2⊢ <;> linarith
+  all_goals simp at h_1 h_2 ⊢ <;> linarith
 #align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gt
 
 #print SimplexCategory.δ_comp_σ_of_gt' /-
@@ -429,7 +434,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  simp only [Fin.mk_le_mk] at H
+  simp only [Fin.mk_le_mk] at H 
   -- At this point `simp with push_cast` makes good progress, but neither `simp?` nor `squeeze_simp`
   -- return usable sets of lemmas.
   -- To avoid using a non-terminal simp, we make a `suffices` statement indicating the shape
@@ -442,14 +447,14 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ
   -- Most of them are dealt with `by simp at *; linarith`,
   -- but we pull out two harder ones to do by hand.
   pick_goal 3
-  · simp only [not_lt] at h_2
+  · simp only [not_lt] at h_2 
     exact
       False.elim
         (lt_irrefl (k - 1)
           (lt_of_lt_of_le (Nat.pred_lt (id (ne_of_lt (lt_of_le_of_lt (zero_le i) h)).symm))
             (le_trans h_2 (Nat.succ_le_of_lt h_1))))
   pick_goal 3
-  · simp only [Subtype.mk_lt_mk, not_lt] at h_1
+  · simp only [Subtype.mk_lt_mk, not_lt] at h_1 
     exact False.elim (lt_irrefl j (lt_of_lt_of_le (Nat.pred_lt_pred (Nat.succ_ne_zero j) h_2) h_1))
   -- Deal with the rest automatically.
   all_goals simp at * <;> linarith
@@ -550,7 +555,8 @@ noncomputable def isSkeletonOf :
 #print SimplexCategory.Truncated /-
 /-- The truncated simplex category. -/
 def Truncated (n : ℕ) :=
-  FullSubcategory fun a : SimplexCategory => a.len ≤ n deriving SmallCategory
+  FullSubcategory fun a : SimplexCategory => a.len ≤ n
+deriving SmallCategory
 #align simplex_category.truncated SimplexCategory.Truncated
 -/
 
@@ -564,7 +570,8 @@ instance {n} : Inhabited (Truncated n) :=
 simplex category.
 -/
 def inclusion {n : ℕ} : SimplexCategory.Truncated n ⥤ SimplexCategory :=
-  fullSubcategoryInclusion _ deriving Full, Faithful
+  fullSubcategoryInclusion _
+deriving Full, Faithful
 #align simplex_category.truncated.inclusion SimplexCategory.Truncated.inclusion
 -/
 
@@ -659,8 +666,8 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) :=
     simp only [Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
-    rw [not_le] at h
-    rw [Fin.lt_iff_val_lt_val] at h⊢
+    rw [not_le] at h 
+    rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
 instance : ReflectsIsomorphisms (forget SimplexCategory) :=
@@ -678,8 +685,8 @@ instance : ReflectsIsomorphisms (forget SimplexCategory) :=
                   · by_contra h''
                     have eq := fun i => congr_hom (iso.inv_hom_id (as_iso ((forget _).map f))) i
                     have ineq := f.to_order_hom.monotone' (le_of_not_ge h'')
-                    dsimp at ineq
-                    erw [Eq, Eq] at ineq
+                    dsimp at ineq 
+                    erw [Eq, Eq] at ineq 
                     exact not_le.mpr h' ineq
                   · rw [eq_of_le_of_not_lt h h'] }
           hom_inv_id' := by ext1; ext1; exact iso.hom_inv_id (as_iso ((forget _).map f))
@@ -739,14 +746,14 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     erw [Fin.succAbove_below i.succ x.cast_pred _]; swap
     · rwa [Eq, ← Fin.le_castSucc_iff]
     rw [Eq]
-  · simp only [not_le] at h'
+  · simp only [not_le] at h' 
     let y :=
       x.pred
         (by
           intro h
-          rw [h] at h'
+          rw [h] at h' 
           simpa only [Fin.lt_iff_val_lt_val, Nat.not_lt_zero, Fin.val_zero] using h')
-    simp only [show x = y.succ by rw [Fin.succ_pred]] at h'⊢
+    simp only [show x = y.succ by rw [Fin.succ_pred]] at h' ⊢
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
     by_cases h'' : y = i
     · rw [h'']
@@ -755,12 +762,12 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       exact Fin.lt_succ
     · erw [Fin.succAbove_above i.succ _]
       simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
-        Nat.lt_succ_iff, Fin.ext_iff] at h' h''⊢
+        Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
       cases c
       · exfalso
-        rw [add_zero] at hc
-        rw [hc] at h''
+        rw [add_zero] at hc 
+        rw [hc] at h'' 
         exact h'' rfl
       · rw [← hc]
         simp only [add_le_add_iff_left, Nat.succ_eq_add_one, le_add_iff_nonneg_left, zero_le]
@@ -768,9 +775,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
 
 #print SimplexCategory.eq_σ_comp_of_not_injective /-
 theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
-    (hθ : ¬Function.Injective θ.toOrderHom) : ∃ (i : Fin (n + 1))(θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' :=
+    (hθ : ¬Function.Injective θ.toOrderHom) : ∃ (i : Fin (n + 1)) (θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' :=
   by
-  simp only [Function.Injective, exists_prop, not_forall] at hθ
+  simp only [Function.Injective, exists_prop, not_forall] at hθ 
   -- as θ is not injective, there exists `x<y` such that `θ x = θ y`
   -- and then, `θ x = θ (x+1)`
   have hθ₂ : ∃ x y : Fin (n + 2), (hom.to_order_hom θ) x = (hom.to_order_hom θ) y ∧ x < y :=
@@ -787,9 +794,9 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   let z := x.cast_pred
   use z
   simp only [←
-    show z.cast_succ = x from Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
+    show z.cast_succ = x from Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂ 
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSucc_lt_iff_succ_le] at h₂
+  rw [Fin.castSucc_lt_iff_succ_le] at h₂ 
   apply le_antisymm
   · exact θ.to_order_hom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
   · rw [h₁]
@@ -817,7 +824,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
             (fin.lt_iff_coe_lt_coe.mp ((Ne.le_iff_lt (hi x)).mp h'))
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
-    · simp only [not_le] at h'
+    · simp only [not_le] at h' 
       simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.to_order_hom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
@@ -836,7 +843,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
 
 #print SimplexCategory.eq_comp_δ_of_not_surjective /-
 theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
-    (hθ : ¬Function.Surjective θ.toOrderHom) : ∃ (i : Fin (n + 2))(θ' : Δ ⟶ mk n), θ = θ' ≫ δ i :=
+    (hθ : ¬Function.Surjective θ.toOrderHom) : ∃ (i : Fin (n + 2)) (θ' : Δ ⟶ mk n), θ = θ' ≫ δ i :=
   by
   cases' not_forall.mp hθ with i hi
   use i

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

@@ -407,7 +407,7 @@ 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))) ≫
         δ (i.pred fun hi => by simpa only [Fin.not_lt_zero, hi] using H) :=
   by

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

@@ -214,7 +214,7 @@ theorem hom_zero_zero (f : [0] ⟶ [0]) : f = 𝟙 _ := by ext : 2; dsimp; apply
 
 end
 
-open Simplicial
+open scoped Simplicial
 
 section Generators
 

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

@@ -119,35 +119,17 @@ namespace Hom
 
 attribute [local semireducible] SimplexCategory.Hom
 
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-Case conversion may be inaccurate. Consider using '#align simplex_category.hom.mk SimplexCategory.Hom.mkₓ'. -/
 /-- Make a moprhism in `simplex_category` from a monotone map of fin's. -/
 def mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) : SimplexCategory.Hom a b :=
   f
 #align simplex_category.hom.mk SimplexCategory.Hom.mk
 
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-Case conversion may be inaccurate. Consider using '#align simplex_category.hom.to_order_hom SimplexCategory.Hom.toOrderHomₓ'. -/
 /-- Recover the monotone map from a morphism in the simplex category. -/
 def toOrderHom {a b : SimplexCategory} (f : SimplexCategory.Hom a b) :
     Fin (a.len + 1) →o Fin (b.len + 1) :=
   f
 #align simplex_category.hom.to_order_hom SimplexCategory.Hom.toOrderHom
 
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-Case conversion may be inaccurate. Consider using '#align simplex_category.hom.ext SimplexCategory.Hom.ext'ₓ'. -/
 @[ext]
 theorem ext' {a b : SimplexCategory} (f g : SimplexCategory.Hom a b) :
     f.toOrderHom = g.toOrderHom → f = g :=
@@ -161,21 +143,12 @@ theorem mk_toOrderHom {a b : SimplexCategory} (f : SimplexCategory.Hom a b) : mk
 #align simplex_category.hom.mk_to_order_hom SimplexCategory.Hom.mk_toOrderHom
 -/
 
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-Case conversion may be inaccurate. Consider using '#align simplex_category.hom.to_order_hom_mk SimplexCategory.Hom.toOrderHom_mkₓ'. -/
 @[simp]
 theorem toOrderHom_mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) :
     (mk f).toOrderHom = f :=
   rfl
 #align simplex_category.hom.to_order_hom_mk SimplexCategory.Hom.toOrderHom_mk
 
-/- warning: simplex_category.hom.mk_to_order_hom_apply -> SimplexCategory.Hom.mk_toOrderHom_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.hom.mk_to_order_hom_apply SimplexCategory.Hom.mk_toOrderHom_applyₓ'. -/
 theorem mk_toOrderHom_apply {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1))
     (i : Fin (a.len + 1)) : (mk f).toOrderHom i = f i :=
   rfl
@@ -225,12 +198,6 @@ theorem const_comp (x y : SimplexCategory) (i : Fin (x.len + 1)) (f : x ⟶ y) :
 #align simplex_category.const_comp SimplexCategory.const_comp
 -/
 
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-  forall {n : Nat} {m : Nat}, (OrderHom.{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) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{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.partialOrder (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)))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) -> (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk m))
-but is expected to have type
-  forall {n : Nat} {m : Nat}, (OrderHom.{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) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) -> (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk m))
-Case conversion may be inaccurate. Consider using '#align simplex_category.mk_hom SimplexCategory.mkHomₓ'. -/
 /-- Make a morphism `[n] ⟶ [m]` from a monotone map between fin's.
 This is useful for constructing morphisms beetween `[n]` directly
 without identifying `n` with `[n].len`.
@@ -275,9 +242,6 @@ def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
 #align simplex_category.σ SimplexCategory.σ
 -/
 
-/- warning: simplex_category.δ_comp_δ -> SimplexCategory.δ_comp_δ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
   by
@@ -291,9 +255,6 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ =
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
 
-/- warning: simplex_category.δ_comp_δ' -> SimplexCategory.δ_comp_δ' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'ₓ'. -/
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     δ i ≫ δ j = δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ δ i.cast_succ :=
   by
@@ -304,9 +265,6 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
       j.succ_pred, Fin.lt_iff_val_lt_val] using H
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
 
-/- warning: simplex_category.δ_comp_δ'' -> SimplexCategory.δ_comp_δ'' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''ₓ'. -/
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
       δ j ≫ δ i :=
@@ -316,26 +274,17 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   · exact H
 #align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''
 
-/- warning: simplex_category.δ_comp_δ_self -> SimplexCategory.δ_comp_δ_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i ≫ δ i.succ :=
   (δ_comp_δ (le_refl i)).symm
 #align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_self
 
-/- warning: simplex_category.δ_comp_δ_self' -> SimplexCategory.δ_comp_δ_self' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self' SimplexCategory.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) :
     δ i ≫ δ j = δ i ≫ δ i.succ := by subst H; rw [δ_comp_δ_self]
 #align simplex_category.δ_comp_δ_self' SimplexCategory.δ_comp_δ_self'
 
-/- warning: simplex_category.δ_comp_σ_of_le -> SimplexCategory.δ_comp_σ_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_le SimplexCategory.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) :
@@ -369,9 +318,6 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   all_goals try first |rfl|simp at * <;> linarith
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
 
-/- warning: simplex_category.δ_comp_σ_self -> SimplexCategory.δ_comp_σ_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [n] :=
@@ -388,9 +334,6 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_self
 
-/- warning: simplex_category.δ_comp_σ_self' -> SimplexCategory.δ_comp_σ_self' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
     δ j ≫ σ i = 𝟙 [n] := by subst H; rw [δ_comp_σ_self]
@@ -417,9 +360,6 @@ theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ
 #align simplex_category.δ_comp_σ_succ' SimplexCategory.δ_comp_σ_succ'
 -/
 
-/- warning: simplex_category.δ_comp_σ_of_gt -> SimplexCategory.δ_comp_σ_of_gt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gtₓ'. -/
 /-- 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) :
@@ -480,9 +420,6 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 
 attribute [local simp] Fin.pred_mk
 
-/- warning: simplex_category.σ_comp_σ -> SimplexCategory.σ_comp_σ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ j = σ j.succ ≫ σ i :=
@@ -535,9 +472,6 @@ def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v}
 #align simplex_category.skeletal_functor SimplexCategory.skeletalFunctor
 -/
 
-/- warning: simplex_category.skeletal_functor.coe_map -> SimplexCategory.skeletalFunctor.coe_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.skeletal_functor.coe_map SimplexCategory.skeletalFunctor.coe_mapₓ'. -/
 theorem skeletalFunctor.coe_map {Δ₁ Δ₂ : SimplexCategory} (f : Δ₁ ⟶ Δ₂) :
     coeFn (skeletalFunctor.{v}.map f) = ULift.up ∘ f.toOrderHom ∘ ULift.down :=
   rfl
@@ -594,12 +528,6 @@ noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
 
 end SkeletalFunctor
 
-/- warning: simplex_category.skeletal_equivalence -> SimplexCategory.skeletalEquivalence is a dubious translation:
-lean 3 declaration is
-  CategoryTheory.Equivalence.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} NonemptyFinLinOrdCat.largeCategory.{u1}
-but is expected to have type
-  CategoryTheory.Equivalence.{0, u1, 0, succ u1} SimplexCategory NonemptyFinLinOrdCat.{u1} SimplexCategory.smallCategory instNonemptyFinLinOrdCatLargeCategory.{u1}
-Case conversion may be inaccurate. Consider using '#align simplex_category.skeletal_equivalence SimplexCategory.skeletalEquivalenceₓ'. -/
 /-- The equivalence that exhibits `simplex_category` as skeleton
 of `NonemptyFinLinOrd` -/
 noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrdCat.{v} :=
@@ -765,12 +693,6 @@ theorem isIso_of_bijective {x y : SimplexCategory} {f : x ⟶ y}
 #align simplex_category.is_iso_of_bijective SimplexCategory.isIso_of_bijective
 -/
 
-/- warning: simplex_category.order_iso_of_iso -> SimplexCategory.orderIsoOfIso is a dubious translation:
-lean 3 declaration is
-  forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (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) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
-but is expected to have type
-  forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
-Case conversion may be inaccurate. Consider using '#align simplex_category.order_iso_of_iso SimplexCategory.orderIsoOfIsoₓ'. -/
 /-- An isomorphism in `simplex_category` induces an `order_iso`. -/
 @[simp]
 def orderIsoOfIso {x y : SimplexCategory} (e : x ≅ y) : Fin (x.len + 1) ≃o Fin (y.len + 1) :=
@@ -804,9 +726,6 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [hf : IsIso f] : f =
 #align simplex_category.eq_id_of_is_iso SimplexCategory.eq_id_of_isIso
 -/
 
-/- warning: simplex_category.eq_σ_comp_of_not_injective' -> SimplexCategory.eq_σ_comp_of_not_injective' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'ₓ'. -/
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (i : Fin (n + 1)) (hi : θ.toOrderHom i.cast_succ = θ.toOrderHom i.succ) :
     ∃ θ' : mk n ⟶ Δ', θ = σ i ≫ θ' := by

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

@@ -241,11 +241,7 @@ def mkHom {n m : ℕ} (f : Fin (n + 1) →o Fin (m + 1)) : [n] ⟶ [m] :=
 #align simplex_category.mk_hom SimplexCategory.mkHom
 
 #print SimplexCategory.hom_zero_zero /-
-theorem hom_zero_zero (f : [0] ⟶ [0]) : f = 𝟙 _ :=
-  by
-  ext : 2
-  dsimp
-  apply Subsingleton.elim
+theorem hom_zero_zero (f : [0] ⟶ [0]) : f = 𝟙 _ := by ext : 2; dsimp; apply Subsingleton.elim
 #align simplex_category.hom_zero_zero SimplexCategory.hom_zero_zero
 -/
 
@@ -334,9 +330,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i 
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self' SimplexCategory.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) :
-    δ i ≫ δ j = δ i ≫ δ i.succ := by
-  subst H
-  rw [δ_comp_δ_self]
+    δ i ≫ δ j = δ i ≫ δ i.succ := by subst H; rw [δ_comp_δ_self]
 #align simplex_category.δ_comp_δ_self' SimplexCategory.δ_comp_δ_self'
 
 /- warning: simplex_category.δ_comp_σ_of_le -> SimplexCategory.δ_comp_σ_of_le is a dubious translation:
@@ -351,18 +345,8 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
     ite (j.succ.cast_succ < ite (k < i) k.cast_succ k.succ) (ite (k < i) (k : ℕ) (k + 1) - 1)
         (ite (k < i) k (k + 1)) =
       ite
-        ((if h : (j : ℕ) < k then
-              k.pred
-                (by
-                  rintro rfl
-                  exact Nat.not_lt_zero _ h)
-            else
-              k.cast_lt
-                (by
-                  cases j
-                  cases k
-                  simp only [len_mk]
-                  linarith)).cast_succ <
+        ((if h : (j : ℕ) < k then k.pred (by rintro rfl; exact Nat.not_lt_zero _ h)
+            else k.cast_lt (by cases j; cases k; simp only [len_mk]; linarith)).cast_succ <
           i)
         (ite (j.cast_succ < k) (k - 1) k) (ite (j.cast_succ < k) (k - 1) k + 1)
     by
@@ -380,8 +364,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   pick_goal 8
   · exact (Nat.succ_pred_eq_of_pos (lt_of_le_of_lt (zero_le _) ‹_›)).symm
   pick_goal 7
-  · have : k ≤ i := Nat.le_of_pred_lt ‹_›
-    linarith
+  · have : k ≤ i := Nat.le_of_pred_lt ‹_›; linarith
   -- Hope for the best from `linarith`:
   all_goals try first |rfl|simp at * <;> linarith
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
@@ -398,9 +381,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
     ite (Fin.castSucc i < ite (j < i) (Fin.castSucc j) j.succ) (ite (j < i) (j : ℕ) (j + 1) - 1)
         (ite (j < i) j (j + 1)) =
       j
-    by
-    dsimp [δ, σ, Fin.succAbove, Fin.predAbove]
-    simpa [Fin.predAbove, push_cast]
+    by dsimp [δ, σ, Fin.succAbove, Fin.predAbove]; simpa [Fin.predAbove, push_cast]
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   dsimp
@@ -412,9 +393,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
-    δ j ≫ σ i = 𝟙 [n] := by
-  subst H
-  rw [δ_comp_σ_self]
+    δ j ≫ σ i = 𝟙 [n] := by subst H; rw [δ_comp_σ_self]
 #align simplex_category.δ_comp_σ_self' SimplexCategory.δ_comp_σ_self'
 
 #print SimplexCategory.δ_comp_σ_succ /-
@@ -434,9 +413,7 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 [n] :=
 #print SimplexCategory.δ_comp_σ_succ' /-
 @[reassoc]
 theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ) :
-    δ j ≫ σ i = 𝟙 [n] := by
-  subst H
-  rw [δ_comp_σ_succ]
+    δ j ≫ σ i = 𝟙 [n] := by subst H; rw [δ_comp_σ_succ]
 #align simplex_category.δ_comp_σ_succ' SimplexCategory.δ_comp_σ_succ'
 -/
 
@@ -553,12 +530,8 @@ def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v}
     where
   obj a := NonemptyFinLinOrdCat.of <| ULift (Fin (a.len + 1))
   map a b f := ⟨fun i => ULift.up (f.toOrderHom i.down), fun i j h => f.toOrderHom.Monotone h⟩
-  map_id' a := by
-    ext
-    simp
-  map_comp' a b c f g := by
-    ext
-    simp
+  map_id' a := by ext; simp
+  map_comp' a b c f g := by ext; simp
 #align simplex_category.skeletal_functor SimplexCategory.skeletalFunctor
 -/
 
@@ -573,10 +546,7 @@ theorem skeletalFunctor.coe_map {Δ₁ Δ₂ : SimplexCategory} (f : Δ₁ ⟶ 
 #print SimplexCategory.skeletal /-
 theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ =>
   by
-  suffices Fintype.card (Fin (X.len + 1)) = Fintype.card (Fin (Y.len + 1))
-    by
-    ext
-    simpa
+  suffices Fintype.card (Fin (X.len + 1)) = Fintype.card (Fin (Y.len + 1)) by ext; simpa
   · apply Fintype.card_congr
     refine' equiv.ulift.symm.trans (((skeletal_functor ⋙ forget _).mapIso I).toEquiv.trans _)
     apply Equiv.ulift
@@ -589,14 +559,7 @@ instance : Full skeletalFunctor.{v}
     where
   Preimage a b f :=
     SimplexCategory.Hom.mk ⟨fun i => (f (ULift.up i)).down, fun i j h => f.Monotone h⟩
-  witness' := by
-    intro m n f
-    dsimp at *
-    ext1 ⟨i⟩
-    ext1
-    ext1
-    cases x
-    simp
+  witness' := by intro m n f; dsimp at *; ext1 ⟨i⟩; ext1; ext1; cases x; simp
 
 instance : Faithful skeletalFunctor.{v}
     where map_injective' m n f g h := by
@@ -617,21 +580,11 @@ instance : EssSurj skeletalFunctor.{v}
             inv := ⟨fun i => ⟨f.symm i⟩, _⟩
             hom_inv_id' := _
             inv_hom_id' := _ }
-        · rintro ⟨i⟩ ⟨j⟩ h
-          show f i ≤ f j
-          exact hf.monotone h
-        · intro i j h
-          show f.symm i ≤ f.symm j
-          rw [← hf.le_iff_le]
-          show f (f.symm i) ≤ f (f.symm j)
-          simpa only [OrderIso.apply_symm_apply]
-        · ext1
-          ext1 ⟨i⟩
-          ext1
-          exact f.symm_apply_apply i
-        · ext1
-          ext1 i
-          exact f.apply_symm_apply i⟩⟩
+        · rintro ⟨i⟩ ⟨j⟩ h; show f i ≤ f j; exact hf.monotone h
+        · intro i j h; show f.symm i ≤ f.symm j; rw [← hf.le_iff_le]
+          show f (f.symm i) ≤ f (f.symm j); simpa only [OrderIso.apply_symm_apply]
+        · ext1; ext1 ⟨i⟩; ext1; exact f.symm_apply_apply i
+        · ext1; ext1 i; exact f.apply_symm_apply i⟩⟩
 
 #print SimplexCategory.SkeletalFunctor.isEquivalence /-
 noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
@@ -801,14 +754,8 @@ instance : ReflectsIsomorphisms (forget SimplexCategory) :=
                     erw [Eq, Eq] at ineq
                     exact not_le.mpr h' ineq
                   · rw [eq_of_le_of_not_lt h h'] }
-          hom_inv_id' := by
-            ext1
-            ext1
-            exact iso.hom_inv_id (as_iso ((forget _).map f))
-          inv_hom_id' := by
-            ext1
-            ext1
-            exact iso.inv_hom_id (as_iso ((forget _).map f)) }⟩
+          hom_inv_id' := by ext1; ext1; exact iso.hom_inv_id (as_iso ((forget _).map f))
+          inv_hom_id' := by ext1; ext1; exact iso.inv_hom_id (as_iso ((forget _).map f)) }⟩
 
 #print SimplexCategory.isIso_of_bijective /-
 theorem isIso_of_bijective {x y : SimplexCategory} {f : x ⟶ y}
@@ -870,8 +817,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   by_cases h' : x ≤ i.cast_succ
   · rw [Fin.predAbove_below i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
-    erw [Fin.succAbove_below i.succ x.cast_pred _]
-    swap
+    erw [Fin.succAbove_below i.succ x.cast_pred _]; swap
     · rwa [Eq, ← Fin.le_castSucc_iff]
     rw [Eq]
   · simp only [not_le] at h'
@@ -938,17 +884,14 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
   by
   by_cases i < Fin.last (n + 1)
   · use θ ≫ σ (Fin.castPred i)
-    ext1
-    ext1
-    ext1 x
+    ext1; ext1; ext1 x
     simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
       small_category_comp]
     by_cases h' : θ.to_order_hom x ≤ i
     · simp only [σ, mk_hom, hom.to_order_hom_mk, OrderHom.coe_fun_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.to_order_hom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
-      erw [Fin.succAbove_below i]
-      swap
+      erw [Fin.succAbove_below i]; swap
       · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
         exact
           lt_of_le_of_lt (Fin.coe_castPred_le_self _)
@@ -964,9 +907,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
         Nat.le_pred_of_lt (fin.lt_iff_coe_lt_coe.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
-    ext1
-    ext1
-    ext1 x
+    ext1; ext1; ext1 x
     simp only [hom.to_order_hom_mk, Function.comp_apply, OrderHom.comp_coe, hom.comp,
       small_category_comp, σ, δ, mk_hom, OrderHom.coe_fun_mk, OrderEmbedding.toOrderHom_coe,
       Fin.predAbove_last, Fin.succAbove_last,
@@ -987,9 +928,7 @@ theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ 
 #print SimplexCategory.eq_id_of_mono /-
 theorem eq_id_of_mono {x : SimplexCategory} (i : x ⟶ x) [Mono i] : i = 𝟙 _ :=
   by
-  suffices is_iso i by
-    haveI := this
-    apply eq_id_of_is_iso
+  suffices is_iso i by haveI := this; apply eq_id_of_is_iso
   apply is_iso_of_bijective
   dsimp
   rw [Fintype.bijective_iff_injective_and_card i.to_order_hom, ← mono_iff_injective,
@@ -1001,9 +940,7 @@ theorem eq_id_of_mono {x : SimplexCategory} (i : x ⟶ x) [Mono i] : i = 𝟙 _
 #print SimplexCategory.eq_id_of_epi /-
 theorem eq_id_of_epi {x : SimplexCategory} (i : x ⟶ x) [Epi i] : i = 𝟙 _ :=
   by
-  suffices is_iso i by
-    haveI := this
-    apply eq_id_of_is_iso
+  suffices is_iso i by haveI := this; apply eq_id_of_is_iso
   apply is_iso_of_bijective
   dsimp
   rw [Fintype.bijective_iff_surjective_and_card i.to_order_hom, ← epi_iff_surjective,
@@ -1020,9 +957,7 @@ theorem eq_σ_of_epi {n : ℕ} (θ : mk (n + 1) ⟶ mk n) [Epi θ] : ∃ i : Fin
     simpa only [Nat.one_ne_zero, add_le_iff_nonpos_right, nonpos_iff_eq_zero] using
       le_of_mono (mono_iff_injective.mpr h)
   use i
-  haveI : epi (σ i ≫ θ') := by
-    rw [← h]
-    infer_instance
+  haveI : epi (σ i ≫ θ') := by rw [← h]; infer_instance
   haveI := CategoryTheory.epi_of_epi (σ i) θ'
   rw [h, eq_id_of_epi θ', category.comp_id]
 #align simplex_category.eq_σ_of_epi SimplexCategory.eq_σ_of_epi
@@ -1036,9 +971,7 @@ theorem eq_δ_of_mono {n : ℕ} (θ : mk n ⟶ mk (n + 1)) [Mono θ] : ∃ i : F
     simpa only [add_le_iff_nonpos_right, nonpos_iff_eq_zero] using
       le_of_epi (epi_iff_surjective.mpr h)
   use i
-  haveI : mono (θ' ≫ δ i) := by
-    rw [← h]
-    infer_instance
+  haveI : mono (θ' ≫ δ i) := by rw [← h]; infer_instance
   haveI := CategoryTheory.mono_of_mono θ' (δ i)
   rw [h, eq_id_of_mono θ', category.id_comp]
 #align simplex_category.eq_δ_of_mono SimplexCategory.eq_δ_of_mono
@@ -1050,11 +983,7 @@ theorem len_lt_of_mono {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [hi : Mono i]
   cases lt_or_eq_of_le (len_le_of_mono hi)
   · exact h
   · exfalso
-    exact
-      hi'
-        (by
-          ext
-          exact h.symm)
+    exact hi' (by ext; exact h.symm)
 #align simplex_category.len_lt_of_mono SimplexCategory.len_lt_of_mono
 -/
 

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

@@ -174,10 +174,7 @@ theorem toOrderHom_mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.l
 #align simplex_category.hom.to_order_hom_mk SimplexCategory.Hom.toOrderHom_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.hom.mk_to_order_hom_apply SimplexCategory.Hom.mk_toOrderHom_applyₓ'. -/
 theorem mk_toOrderHom_apply {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1))
     (i : Fin (a.len + 1)) : (mk f).toOrderHom i = f i :=
@@ -283,10 +280,7 @@ def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
@@ -302,10 +296,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ =
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'ₓ'. -/
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     δ i ≫ δ j = δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ δ i.cast_succ :=
@@ -318,10 +309,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''ₓ'. -/
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
@@ -333,10 +321,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 #align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc]
@@ -345,10 +330,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i 
 #align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_self
 
 /- warning: simplex_category.δ_comp_δ_self' -> SimplexCategory.δ_comp_δ_self' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self' SimplexCategory.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) :
@@ -358,10 +340,7 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast
 #align simplex_category.δ_comp_δ_self' SimplexCategory.δ_comp_δ_self'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc]
@@ -408,10 +387,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
 
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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc]
@@ -432,10 +408,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
 #align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_self
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
@@ -468,10 +441,7 @@ theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc]
@@ -534,10 +504,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 attribute [local simp] Fin.pred_mk
 
 /- warning: simplex_category.σ_comp_σ -> SimplexCategory.σ_comp_σ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc]
@@ -596,10 +563,7 @@ def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v}
 -/
 
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(CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (NonemptyFinLinOrd.toLinearOrder.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁)) (NonemptyFinLinOrdCat.instNonemptyFinLinOrdα.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁))) (DistribLattice.toLattice.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (instDistribLattice.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} 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SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (NonemptyFinLinOrdCat.instNonemptyFinLinOrdα.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂))))) (NonemptyFinLinOrdCat.instOrderHomClassHomNonemptyFinLinOrdCatToQuiverToCategoryStructInstNonemptyFinLinOrdCatLargeCategoryαNonemptyFinLinOrdToLEToPreorderToPartialOrderToSemilatticeInfToLatticeInstDistribLatticeToLinearOrderInstNonemptyFinLinOrdα.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁) (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂))))) (Prefunctor.map.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁ Δ₂ f)) (Function.comp.{succ u1, 1, succ u1} (ULift.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (ULift.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (ULift.up.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Function.comp.{succ u1, 1, 1} (ULift.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHom.toFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (SimplexCategory.Hom.toOrderHom Δ₁ Δ₂ f)) (ULift.down.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.skeletal_functor.coe_map SimplexCategory.skeletalFunctor.coe_mapₓ'. -/
 theorem skeletalFunctor.coe_map {Δ₁ Δ₂ : SimplexCategory} (f : Δ₁ ⟶ Δ₂) :
     coeFn (skeletalFunctor.{v}.map f) = ULift.up ∘ f.toOrderHom ∘ ULift.down :=
@@ -894,10 +858,7 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [hf : IsIso f] : f =
 -/
 
 /- warning: simplex_category.eq_σ_comp_of_not_injective' -> SimplexCategory.eq_σ_comp_of_not_injective' is a dubious translation:
-lean 3 declaration is
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SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ') θ (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) Δ' (SimplexCategory.σ n i) θ')))
+<too large>
 Case conversion may be inaccurate. Consider using '#align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'ₓ'. -/
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (i : Fin (n + 1)) (hi : θ.toOrderHom i.cast_succ = θ.toOrderHom i.succ) :

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

@@ -339,7 +339,7 @@ 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)))) => 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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (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 simplex_category.δ_comp_δ_self SimplexCategory.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)} : δ i ≫ δ i.cast_succ = δ i ≫ δ i.succ :=
   (δ_comp_δ (le_refl i)).symm
 #align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_self
@@ -350,7 +350,7 @@ lean 3 declaration is
 but is expected to have type
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(Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (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 simplex_category.δ_comp_δ_self' SimplexCategory.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) :
     δ i ≫ δ j = δ i ≫ δ i.succ := by
   subst H
@@ -364,7 +364,7 @@ but is expected to have type
   forall {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)))) 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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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(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)) (SimplexCategory.σ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.σ n j) (SimplexCategory.δ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_le SimplexCategory.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) :
     δ i.cast_succ ≫ σ j.succ = σ j ≫ δ i := by
   ext k
@@ -414,7 +414,7 @@ but is expected to have type
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ 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 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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)) (SimplexCategory.σ n i)) (CategoryTheory.CategoryStruct.id.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self SimplexCategory.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)} : δ i.cast_succ ≫ σ i = 𝟙 [n] :=
   by
   ext j
@@ -437,7 +437,7 @@ lean 3 declaration is
 but is expected to have type
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ n j) (SimplexCategory.σ n i)) (CategoryTheory.CategoryStruct.id.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
     δ j ≫ σ i = 𝟙 [n] := by
   subst H
@@ -446,7 +446,7 @@ theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast
 
 #print SimplexCategory.δ_comp_σ_succ /-
 /-- The second part of the third simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 [n] :=
   by
   ext j
@@ -459,7 +459,7 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 [n] :=
 -/
 
 #print SimplexCategory.δ_comp_σ_succ' /-
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ) :
     δ j ≫ σ i = 𝟙 [n] := by
   subst H
@@ -474,7 +474,7 @@ but is expected to have type
   forall {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)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(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.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.σ n j) (SimplexCategory.δ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_gt SimplexCategory.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) :
     δ i.succ ≫ σ j.cast_succ = σ j ≫ δ i := by
   ext k
@@ -513,7 +513,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
 #align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gt
 
 #print SimplexCategory.δ_comp_σ_of_gt' /-
-@[reassoc.1]
+@[reassoc]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     δ i ≫ σ j =
       σ
@@ -540,7 +540,7 @@ but is expected to have type
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (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)))) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (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)))) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.σ (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 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} 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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 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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)) (SimplexCategory.σ n j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (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)))) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.σ (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)) (SimplexCategory.σ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
-@[reassoc.1]
+@[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ j = σ j.succ ≫ σ i :=
   by
   ext k

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

@@ -286,7 +286,7 @@ def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
 lean 3 declaration is
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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i))))
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(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 simplex_category.δ_comp_δ SimplexCategory.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
@@ -305,7 +305,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ =
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'ₓ'. -/
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     δ i ≫ δ j = δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ δ i.cast_succ :=
@@ -321,7 +321,7 @@ 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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(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)))) (SimplexCategory.δ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n j) (SimplexCategory.δ (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 simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''ₓ'. -/
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
@@ -336,7 +336,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 lean 3 declaration is
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n 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(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.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (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))))) (SimplexCategory.δ n i) (SimplexCategory.δ (HAdd.hAdd.{0, 0, 0} 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 but is expected to have type
-  forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (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 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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc.1]
@@ -348,7 +348,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i 
 lean 3 declaration is
   forall {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 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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (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))))) (SimplexCategory.δ n i) (SimplexCategory.δ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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 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 but is expected to have type
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(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)) -> (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (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))))
+  forall {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 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(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 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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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (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 simplex_category.δ_comp_δ_self' SimplexCategory.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) :
@@ -361,7 +361,7 @@ 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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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)) (SimplexCategory.σ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.σ n j) (SimplexCategory.δ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc.1]
@@ -411,7 +411,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 lean 3 declaration is
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (SimplexCategory.mk n) (SimplexCategory.δ 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 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 but is expected to have type
-  forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ 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) 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+  forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ 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 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(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, 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(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)) (SimplexCategory.σ n i)) (CategoryTheory.CategoryStruct.id.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc.1]
@@ -435,7 +435,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
 lean 3 declaration is
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 but is expected to have type
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(Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ n j) (SimplexCategory.σ n i)) (CategoryTheory.CategoryStruct.id.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
@@ -471,7 +471,7 @@ 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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(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)))) j))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.σ n j) (SimplexCategory.δ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc.1]
@@ -537,7 +537,7 @@ attribute [local simp] Fin.pred_mk
 lean 3 declaration is
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(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)) (SimplexCategory.σ n j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (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)))) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.σ (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 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(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 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(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)) (SimplexCategory.σ n j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (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)))) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.σ (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 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 Case conversion may be inaccurate. Consider using '#align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc.1]
@@ -897,7 +897,7 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [hf : IsIso f] : f =
 lean 3 declaration is
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 but is expected to have type
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instAddNat) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (SimplexCategory.Hom.toOrderHom (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ' θ) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))) -> (Exists.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ') (fun (θ' : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ') => Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ') θ (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) Δ' (SimplexCategory.σ n i) θ')))
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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)) (OrderHom.toFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len (SimplexCategory.mk (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) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len (SimplexCategory.mk (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.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len (SimplexCategory.mk (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))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (SimplexCategory.Hom.toOrderHom (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ' θ) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))) -> (Exists.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ') (fun (θ' : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ') => Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ') θ (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) Δ' (SimplexCategory.σ n i) θ')))
 Case conversion may be inaccurate. Consider using '#align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'ₓ'. -/
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (i : Fin (n + 1)) (hi : θ.toOrderHom i.cast_succ = θ.toOrderHom i.succ) :

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

@@ -856,7 +856,7 @@ theorem isIso_of_bijective {x y : SimplexCategory} {f : x ⟶ y}
 
 /- warning: simplex_category.order_iso_of_iso -> SimplexCategory.orderIsoOfIso is a dubious translation:
 lean 3 declaration is
-  forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (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) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+  forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (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) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
   forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align simplex_category.order_iso_of_iso SimplexCategory.orderIsoOfIsoₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -43,7 +43,7 @@ universe v
 
 open CategoryTheory CategoryTheory.Limits
 
-/- ./././Mathport/Syntax/Translate/Command.lean:318:31: unsupported: @[derive, irreducible] def -/
+/- ./././Mathport/Syntax/Translate/Command.lean:323:31: unsupported: @[derive, irreducible] def -/
 #print SimplexCategory /-
 /-- The simplex category:
 * objects are natural numbers `n : ℕ`

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

@@ -286,7 +286,7 @@ def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
@@ -305,7 +305,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ =
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'ₓ'. -/
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     δ i ≫ δ j = δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ δ i.cast_succ :=
@@ -321,7 +321,7 @@ 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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(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.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)))) 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)))) (SimplexCategory.δ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n j) (SimplexCategory.δ (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 simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''ₓ'. -/
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
@@ -336,7 +336,7 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
 lean 3 declaration is
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n 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(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.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (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))))) (SimplexCategory.δ n i) (SimplexCategory.δ (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
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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc.1]
@@ -348,7 +348,7 @@ theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i 
 lean 3 declaration is
   forall {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 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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (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))))) (SimplexCategory.δ n i) (SimplexCategory.δ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (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))))) (SimplexCategory.δ n i) (SimplexCategory.δ (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
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(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 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) (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 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)))) (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)))) (Function.instEmbeddingLikeEmbedding.{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)))))) (RelEmbedding.toEmbedding.{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 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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 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)) -> (Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n i) (SimplexCategory.δ (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))))
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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self' SimplexCategory.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) :
@@ -361,7 +361,7 @@ 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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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)) (SimplexCategory.σ (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.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.σ n j) (SimplexCategory.δ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_leₓ'. -/
 /-- The second simplicial identity -/
 @[reassoc.1]
@@ -411,7 +411,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
 lean 3 declaration is
   forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (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))))) (SimplexCategory.mk n) (SimplexCategory.δ 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 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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))))) 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 but is expected to have type
-  forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ 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 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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 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 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc.1]
@@ -435,7 +435,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
 lean 3 declaration is
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(Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk n)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.δ n j) (SimplexCategory.σ n i)) (CategoryTheory.CategoryStruct.id.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk n)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
@@ -471,7 +471,7 @@ 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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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 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(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)))) j))) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.σ n j) (SimplexCategory.δ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gtₓ'. -/
 /-- The fourth simplicial identity -/
 @[reassoc.1]
@@ -537,7 +537,7 @@ attribute [local simp] Fin.pred_mk
 lean 3 declaration is
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 but is expected to have type
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(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)) (SimplexCategory.σ n j)) (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (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)))) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) (SimplexCategory.σ (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)) (SimplexCategory.σ n i)))
 Case conversion may be inaccurate. Consider using '#align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc.1]
@@ -897,7 +897,7 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [hf : IsIso f] : f =
 lean 3 declaration is
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SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ') θ (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) Δ' (SimplexCategory.σ n i) θ')))
 Case conversion may be inaccurate. Consider using '#align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'ₓ'. -/
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (i : Fin (n + 1)) (hi : θ.toOrderHom i.cast_succ = θ.toOrderHom i.succ) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

@@ -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.simplex_category
-! leanprover-community/mathlib commit e8ac6315bcfcbaf2d19a046719c3b553206dac75
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! 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.Functor.ReflectsIsomorphisms
 
 /-! # The simplex category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We construct a skeletal model of the simplex category, with objects `ℕ` and the
 morphism `n ⟶ m` being the monotone maps from `fin (n+1)` to `fin (m+1)`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -316,9 +316,9 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
 
 /- warning: simplex_category.δ_comp_δ'' -> SimplexCategory.δ_comp_δ'' is a dubious translation:
 lean 3 declaration is
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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (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)))) (SimplexCategory.δ n j) (SimplexCategory.δ (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 simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''ₓ'. -/
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
@@ -523,7 +523,7 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   by
   rw [← δ_comp_σ_of_gt]
   · simpa only [Fin.succ_pred]
-  · rw [Fin.castSucc_cast_lt, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
+  · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -41,6 +41,7 @@ universe v
 open CategoryTheory CategoryTheory.Limits
 
 /- ./././Mathport/Syntax/Translate/Command.lean:318:31: unsupported: @[derive, irreducible] def -/
+#print SimplexCategory /-
 /-- The simplex category:
 * objects are natural numbers `n : ℕ`
 * morphisms from `n` to `m` are monotone functions `fin (n+1) → fin (m+1)`
@@ -48,6 +49,7 @@ open CategoryTheory CategoryTheory.Limits
 irreducible_def SimplexCategory :=
   ℕ
 #align simplex_category SimplexCategory
+-/
 
 namespace SimplexCategory
 
@@ -55,99 +57,150 @@ section
 
 attribute [local semireducible] SimplexCategory
 
+#print SimplexCategory.mk /-
 -- TODO: Make `mk` irreducible.
 /-- Interpet a natural number as an object of the simplex category. -/
 def mk (n : ℕ) : SimplexCategory :=
   n
 #align simplex_category.mk SimplexCategory.mk
+-/
 
 -- mathport name: simplex_category.mk
 scoped[Simplicial] notation "[" n "]" => SimplexCategory.mk n
 
+#print SimplexCategory.len /-
 -- TODO: Make `len` irreducible.
 /-- The length of an object of `simplex_category`. -/
 def len (n : SimplexCategory) : ℕ :=
   n
 #align simplex_category.len SimplexCategory.len
+-/
 
+#print SimplexCategory.ext /-
 @[ext]
 theorem ext (a b : SimplexCategory) : a.len = b.len → a = b :=
   id
 #align simplex_category.ext SimplexCategory.ext
+-/
 
+#print SimplexCategory.len_mk /-
 @[simp]
 theorem len_mk (n : ℕ) : [n].len = n :=
   rfl
 #align simplex_category.len_mk SimplexCategory.len_mk
+-/
 
+#print SimplexCategory.mk_len /-
 @[simp]
 theorem mk_len (n : SimplexCategory) : [n.len] = n :=
   rfl
 #align simplex_category.mk_len SimplexCategory.mk_len
+-/
 
+#print SimplexCategory.rec /-
 /-- A recursor for `simplex_category`. Use it as `induction Δ using simplex_category.rec`. -/
 protected def rec {F : ∀ Δ : SimplexCategory, Sort _} (h : ∀ n : ℕ, F [n]) : ∀ X, F X := fun n =>
   h n.len
 #align simplex_category.rec SimplexCategory.rec
+-/
 
+#print SimplexCategory.Hom /-
 /-- Morphisms in the simplex_category. -/
 @[nolint has_nonempty_instance]
 protected irreducible_def Hom (a b : SimplexCategory) :=
   Fin (a.len + 1) →o Fin (b.len + 1)
 #align simplex_category.hom SimplexCategory.Hom
+-/
 
 namespace Hom
 
 attribute [local semireducible] SimplexCategory.Hom
 
+/- warning: simplex_category.hom.mk -> SimplexCategory.Hom.mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align simplex_category.hom.mk SimplexCategory.Hom.mkₓ'. -/
 /-- Make a moprhism in `simplex_category` from a monotone map of fin's. -/
 def mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) : SimplexCategory.Hom a b :=
   f
 #align simplex_category.hom.mk SimplexCategory.Hom.mk
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.hom.to_order_hom SimplexCategory.Hom.toOrderHomₓ'. -/
 /-- Recover the monotone map from a morphism in the simplex category. -/
 def toOrderHom {a b : SimplexCategory} (f : SimplexCategory.Hom a b) :
     Fin (a.len + 1) →o Fin (b.len + 1) :=
   f
 #align simplex_category.hom.to_order_hom SimplexCategory.Hom.toOrderHom
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.hom.ext SimplexCategory.Hom.ext'ₓ'. -/
 @[ext]
-theorem ext {a b : SimplexCategory} (f g : SimplexCategory.Hom a b) :
+theorem ext' {a b : SimplexCategory} (f g : SimplexCategory.Hom a b) :
     f.toOrderHom = g.toOrderHom → f = g :=
   id
-#align simplex_category.hom.ext SimplexCategory.Hom.ext
+#align simplex_category.hom.ext SimplexCategory.Hom.ext'
 
+#print SimplexCategory.Hom.mk_toOrderHom /-
 @[simp]
 theorem mk_toOrderHom {a b : SimplexCategory} (f : SimplexCategory.Hom a b) : mk f.toOrderHom = f :=
   rfl
 #align simplex_category.hom.mk_to_order_hom SimplexCategory.Hom.mk_toOrderHom
+-/
 
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 @[simp]
 theorem toOrderHom_mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) :
     (mk f).toOrderHom = f :=
   rfl
 #align simplex_category.hom.to_order_hom_mk SimplexCategory.Hom.toOrderHom_mk
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align simplex_category.hom.mk_to_order_hom_apply SimplexCategory.Hom.mk_toOrderHom_applyₓ'. -/
 theorem mk_toOrderHom_apply {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1))
     (i : Fin (a.len + 1)) : (mk f).toOrderHom i = f i :=
   rfl
 #align simplex_category.hom.mk_to_order_hom_apply SimplexCategory.Hom.mk_toOrderHom_apply
 
+#print SimplexCategory.Hom.id /-
 /-- Identity morphisms of `simplex_category`. -/
 @[simp]
 def id (a : SimplexCategory) : SimplexCategory.Hom a a :=
   mk OrderHom.id
 #align simplex_category.hom.id SimplexCategory.Hom.id
+-/
 
+#print SimplexCategory.Hom.comp /-
 /-- Composition of morphisms of `simplex_category`. -/
 @[simp]
 def comp {a b c : SimplexCategory} (f : SimplexCategory.Hom b c) (g : SimplexCategory.Hom a b) :
     SimplexCategory.Hom a c :=
   mk <| f.toOrderHom.comp g.toOrderHom
 #align simplex_category.hom.comp SimplexCategory.Hom.comp
+-/
 
 end Hom
 
+#print SimplexCategory.smallCategory /-
 @[simps]
 instance smallCategory : SmallCategory.{0} SimplexCategory
     where
@@ -155,18 +208,29 @@ instance smallCategory : SmallCategory.{0} SimplexCategory
   id m := SimplexCategory.Hom.id _
   comp _ _ _ f g := SimplexCategory.Hom.comp g f
 #align simplex_category.small_category SimplexCategory.smallCategory
+-/
 
+#print SimplexCategory.const /-
 /-- The constant morphism from [0]. -/
 def const (x : SimplexCategory) (i : Fin (x.len + 1)) : [0] ⟶ x :=
   Hom.mk <| ⟨fun _ => i, by tauto⟩
 #align simplex_category.const SimplexCategory.const
+-/
 
+#print SimplexCategory.const_comp /-
 @[simp]
 theorem const_comp (x y : SimplexCategory) (i : Fin (x.len + 1)) (f : x ⟶ y) :
     const x i ≫ f = const y (f.toOrderHom i) :=
   rfl
 #align simplex_category.const_comp SimplexCategory.const_comp
+-/
 
+/- warning: simplex_category.mk_hom -> SimplexCategory.mkHom is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat} {m : Nat}, (OrderHom.{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) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{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.partialOrder (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)))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) -> (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk m))
+but is expected to have type
+  forall {n : Nat} {m : Nat}, (OrderHom.{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) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) -> (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (SimplexCategory.mk m))
+Case conversion may be inaccurate. Consider using '#align simplex_category.mk_hom SimplexCategory.mkHomₓ'. -/
 /-- Make a morphism `[n] ⟶ [m]` from a monotone map between fin's.
 This is useful for constructing morphisms beetween `[n]` directly
 without identifying `n` with `[n].len`.
@@ -176,12 +240,14 @@ def mkHom {n m : ℕ} (f : Fin (n + 1) →o Fin (m + 1)) : [n] ⟶ [m] :=
   SimplexCategory.Hom.mk f
 #align simplex_category.mk_hom SimplexCategory.mkHom
 
+#print SimplexCategory.hom_zero_zero /-
 theorem hom_zero_zero (f : [0] ⟶ [0]) : f = 𝟙 _ :=
   by
   ext : 2
   dsimp
   apply Subsingleton.elim
 #align simplex_category.hom_zero_zero SimplexCategory.hom_zero_zero
+-/
 
 end
 
@@ -197,18 +263,28 @@ one given by the following generators and relations.
 -/
 
 
+#print SimplexCategory.δ /-
 /-- The `i`-th face map from `[n]` to `[n+1]` -/
 def δ {n} (i : Fin (n + 2)) : [n] ⟶ [n + 1] :=
   mkHom (Fin.succAbove i).toOrderHom
 #align simplex_category.δ SimplexCategory.δ
+-/
 
+#print SimplexCategory.σ /-
 /-- The `i`-th degeneracy map from `[n+1]` to `[n]` -/
 def σ {n} (i : Fin (n + 1)) : [n + 1] ⟶ [n] :=
   mkHom
     { toFun := Fin.predAbove i
       monotone' := Fin.predAbove_right_monotone i }
 #align simplex_category.σ SimplexCategory.σ
+-/
 
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+but is expected to have type
+  forall {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.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) (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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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δₓ'. -/
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ = δ j ≫ δ i.cast_succ :=
   by
@@ -222,6 +298,12 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) : δ i ≫ δ j.succ =
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
 
+/- warning: simplex_category.δ_comp_δ' -> SimplexCategory.δ_comp_δ' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'ₓ'. -/
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j) :
     δ i ≫ δ j = δ (j.pred fun hj => by simpa only [hj, Fin.not_lt_zero] using H) ≫ δ i.cast_succ :=
   by
@@ -232,6 +314,12 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : i.cast_succ < j
       j.succ_pred, Fin.lt_iff_val_lt_val] using H
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
 
+/- warning: simplex_category.δ_comp_δ'' -> SimplexCategory.δ_comp_δ'' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''ₓ'. -/
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_succ) :
     δ (i.cast_lt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
       δ j ≫ δ i :=
@@ -241,12 +329,24 @@ theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ j.cast_s
   · exact H
 #align simplex_category.δ_comp_δ'' SimplexCategory.δ_comp_δ''
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_selfₓ'. -/
 /-- The special case of the first simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ i.cast_succ = δ i ≫ δ i.succ :=
   (δ_comp_δ (le_refl i)).symm
 #align simplex_category.δ_comp_δ_self SimplexCategory.δ_comp_δ_self
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_δ_self' SimplexCategory.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) :
     δ i ≫ δ j = δ i ≫ δ i.succ := by
@@ -254,6 +354,12 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = i.cast
   rw [δ_comp_δ_self]
 #align simplex_category.δ_comp_δ_self' SimplexCategory.δ_comp_δ_self'
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_le SimplexCategory.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) :
@@ -298,6 +404,12 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ j.ca
   all_goals try first |rfl|simp at * <;> linarith
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_selfₓ'. -/
 /-- The first part of the third simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [n] :=
@@ -316,6 +428,12 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} : δ i.cast_succ ≫ σ i = 𝟙 [
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_self
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_self' SimplexCategory.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) :
     δ j ≫ σ i = 𝟙 [n] := by
@@ -323,6 +441,7 @@ theorem δ_comp_σ_self' {n} {j : Fin (n + 2)} {i : Fin (n + 1)} (H : j = i.cast
   rw [δ_comp_σ_self]
 #align simplex_category.δ_comp_σ_self' SimplexCategory.δ_comp_σ_self'
 
+#print SimplexCategory.δ_comp_σ_succ /-
 /-- The second part of the third simplicial identity -/
 @[reassoc.1]
 theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 [n] :=
@@ -334,14 +453,23 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 [n] :=
   simp [Fin.predAbove, push_cast]
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_σ_succ SimplexCategory.δ_comp_σ_succ
+-/
 
+#print SimplexCategory.δ_comp_σ_succ' /-
 @[reassoc.1]
 theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ) :
     δ j ≫ σ i = 𝟙 [n] := by
   subst H
   rw [δ_comp_σ_succ]
 #align simplex_category.δ_comp_σ_succ' SimplexCategory.δ_comp_σ_succ'
+-/
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.δ_comp_σ_of_gt SimplexCategory.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) :
@@ -381,6 +509,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : j.cast_suc
   all_goals simp at h_1 h_2⊢ <;> linarith
 #align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gt
 
+#print SimplexCategory.δ_comp_σ_of_gt' /-
 @[reassoc.1]
 theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ < i) :
     δ i ≫ σ j =
@@ -397,9 +526,16 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
   · rw [Fin.castSucc_cast_lt, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'
+-/
 
 attribute [local simp] Fin.pred_mk
 
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+Case conversion may be inaccurate. Consider using '#align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σₓ'. -/
 /-- The fifth simplicial identity -/
 @[reassoc.1]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) : σ i.cast_succ ≫ σ j = σ j.succ ≫ σ i :=
@@ -439,6 +575,7 @@ end Generators
 
 section Skeleton
 
+#print SimplexCategory.skeletalFunctor /-
 /-- The functor that exhibits `simplex_category` as skeleton
 of `NonemptyFinLinOrd` -/
 @[simps obj map]
@@ -453,12 +590,20 @@ def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v}
     ext
     simp
 #align simplex_category.skeletal_functor SimplexCategory.skeletalFunctor
+-/
 
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+but is expected to have type
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instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁) (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁)) (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (NonemptyFinLinOrd.toLinearOrder.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁)) (NonemptyFinLinOrdCat.instNonemptyFinLinOrdα.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁))) (DistribLattice.toLattice.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (instDistribLattice.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (NonemptyFinLinOrd.toLinearOrder.{u1} (CategoryTheory.Bundled.α.{u1, u1} NonemptyFinLinOrd.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂)) (NonemptyFinLinOrdCat.instNonemptyFinLinOrdα.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂))))) (NonemptyFinLinOrdCat.instOrderHomClassHomNonemptyFinLinOrdCatToQuiverToCategoryStructInstNonemptyFinLinOrdCatLargeCategoryαNonemptyFinLinOrdToLEToPreorderToPartialOrderToSemilatticeInfToLatticeInstDistribLatticeToLinearOrderInstNonemptyFinLinOrdα.{u1} (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁) (Prefunctor.obj.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₂))))) (Prefunctor.map.{1, succ u1, 0, succ u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) NonemptyFinLinOrdCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} NonemptyFinLinOrdCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} instNonemptyFinLinOrdCatLargeCategory.{u1} SimplexCategory.skeletalFunctor.{u1}) Δ₁ Δ₂ f)) (Function.comp.{succ u1, 1, succ u1} (ULift.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (ULift.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (ULift.up.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Function.comp.{succ u1, 1, 1} (ULift.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderHom.toFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₂) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (SimplexCategory.Hom.toOrderHom Δ₁ Δ₂ f)) (ULift.down.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ₁) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align simplex_category.skeletal_functor.coe_map SimplexCategory.skeletalFunctor.coe_mapₓ'. -/
 theorem skeletalFunctor.coe_map {Δ₁ Δ₂ : SimplexCategory} (f : Δ₁ ⟶ Δ₂) :
     coeFn (skeletalFunctor.{v}.map f) = ULift.up ∘ f.toOrderHom ∘ ULift.down :=
   rfl
 #align simplex_category.skeletal_functor.coe_map SimplexCategory.skeletalFunctor.coe_map
 
+#print SimplexCategory.skeletal /-
 theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ =>
   by
   suffices Fintype.card (Fin (X.len + 1)) = Fintype.card (Fin (Y.len + 1))
@@ -469,6 +614,7 @@ theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ =>
     refine' equiv.ulift.symm.trans (((skeletal_functor ⋙ forget _).mapIso I).toEquiv.trans _)
     apply Equiv.ulift
 #align simplex_category.skeletal SimplexCategory.skeletal
+-/
 
 namespace SkeletalFunctor
 
@@ -520,12 +666,20 @@ instance : EssSurj skeletalFunctor.{v}
           ext1 i
           exact f.apply_symm_apply i⟩⟩
 
+#print SimplexCategory.SkeletalFunctor.isEquivalence /-
 noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
   Equivalence.ofFullyFaithfullyEssSurj skeletalFunctor
-#align simplex_category.skeletal_functor.is_equivalence SimplexCategory.skeletalFunctor.isEquivalence
+#align simplex_category.skeletal_functor.is_equivalence SimplexCategory.SkeletalFunctor.isEquivalence
+-/
 
 end SkeletalFunctor
 
+/- warning: simplex_category.skeletal_equivalence -> SimplexCategory.skeletalEquivalence is a dubious translation:
+lean 3 declaration is
+  CategoryTheory.Equivalence.{0, u1, 0, succ u1} SimplexCategory SimplexCategory.smallCategory NonemptyFinLinOrdCat.{u1} NonemptyFinLinOrdCat.largeCategory.{u1}
+but is expected to have type
+  CategoryTheory.Equivalence.{0, u1, 0, succ u1} SimplexCategory NonemptyFinLinOrdCat.{u1} SimplexCategory.smallCategory instNonemptyFinLinOrdCatLargeCategory.{u1}
+Case conversion may be inaccurate. Consider using '#align simplex_category.skeletal_equivalence SimplexCategory.skeletalEquivalenceₓ'. -/
 /-- The equivalence that exhibits `simplex_category` as skeleton
 of `NonemptyFinLinOrd` -/
 noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrdCat.{v} :=
@@ -534,31 +688,37 @@ noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrdCat
 
 end Skeleton
 
+#print SimplexCategory.isSkeletonOf /-
 /-- `simplex_category` is a skeleton of `NonemptyFinLinOrd`.
 -/
 noncomputable def isSkeletonOf :
     IsSkeletonOf NonemptyFinLinOrdCat SimplexCategory skeletalFunctor.{v}
     where
   skel := skeletal
-  eqv := skeletalFunctor.isEquivalence
+  eqv := SkeletalFunctor.isEquivalence
 #align simplex_category.is_skeleton_of SimplexCategory.isSkeletonOf
+-/
 
+#print SimplexCategory.Truncated /-
 /-- The truncated simplex category. -/
 def Truncated (n : ℕ) :=
   FullSubcategory fun a : SimplexCategory => a.len ≤ n deriving SmallCategory
 #align simplex_category.truncated SimplexCategory.Truncated
+-/
 
 namespace Truncated
 
 instance {n} : Inhabited (Truncated n) :=
   ⟨⟨[0], by simp⟩⟩
 
+#print SimplexCategory.Truncated.inclusion /-
 /-- The fully faithful inclusion of the truncated simplex category into the usual
 simplex category.
 -/
 def inclusion {n : ℕ} : SimplexCategory.Truncated n ⥤ SimplexCategory :=
   fullSubcategoryInclusion _ deriving Full, Faithful
 #align simplex_category.truncated.inclusion SimplexCategory.Truncated.inclusion
+-/
 
 end Truncated
 
@@ -575,6 +735,7 @@ end Concrete
 
 section EpiMono
 
+#print SimplexCategory.mono_iff_injective /-
 /-- A morphism in `simplex_category` is a monomorphism precisely when it is an injective function
 -/
 theorem mono_iff_injective {n m : SimplexCategory} {f : n ⟶ m} :
@@ -586,7 +747,9 @@ theorem mono_iff_injective {n m : SimplexCategory} {f : n ⟶ m} :
     Function.Injective.of_comp_iff ULift.up_injective,
     Function.Injective.of_comp_iff' _ ULift.down_bijective]
 #align simplex_category.mono_iff_injective SimplexCategory.mono_iff_injective
+-/
 
+#print SimplexCategory.epi_iff_surjective /-
 /-- A morphism in `simplex_category` is an epimorphism if and only if it is a surjective function
 -/
 theorem epi_iff_surjective {n m : SimplexCategory} {f : n ⟶ m} :
@@ -598,7 +761,9 @@ theorem epi_iff_surjective {n m : SimplexCategory} {f : n ⟶ m} :
     Function.Surjective.of_comp_iff' ULift.up_bijective,
     Function.Surjective.of_comp_iff _ ULift.down_surjective]
 #align simplex_category.epi_iff_surjective SimplexCategory.epi_iff_surjective
+-/
 
+#print SimplexCategory.len_le_of_mono /-
 /-- A monomorphism in `simplex_category` must increase lengths-/
 theorem len_le_of_mono {x y : SimplexCategory} {f : x ⟶ y} : Mono f → x.len ≤ y.len :=
   by
@@ -606,11 +771,15 @@ theorem len_le_of_mono {x y : SimplexCategory} {f : x ⟶ y} : Mono f → x.len
   have f_inj : Function.Injective f.to_order_hom.to_fun := mono_iff_injective.elim_left hyp_f_mono
   simpa using Fintype.card_le_of_injective f.to_order_hom.to_fun f_inj
 #align simplex_category.len_le_of_mono SimplexCategory.len_le_of_mono
+-/
 
+#print SimplexCategory.le_of_mono /-
 theorem le_of_mono {n m : ℕ} {f : [n] ⟶ [m]} : CategoryTheory.Mono f → n ≤ m :=
   len_le_of_mono
 #align simplex_category.le_of_mono SimplexCategory.le_of_mono
+-/
 
+#print SimplexCategory.len_le_of_epi /-
 /-- An epimorphism in `simplex_category` must decrease lengths-/
 theorem len_le_of_epi {x y : SimplexCategory} {f : x ⟶ y} : Epi f → y.len ≤ x.len :=
   by
@@ -618,10 +787,13 @@ theorem len_le_of_epi {x y : SimplexCategory} {f : x ⟶ y} : Epi f → y.len 
   have f_surj : Function.Surjective f.to_order_hom.to_fun := epi_iff_surjective.elim_left hyp_f_epi
   simpa using Fintype.card_le_of_surjective f.to_order_hom.to_fun f_surj
 #align simplex_category.len_le_of_epi SimplexCategory.len_le_of_epi
+-/
 
+#print SimplexCategory.le_of_epi /-
 theorem le_of_epi {n m : ℕ} {f : [n] ⟶ [m]} : Epi f → m ≤ n :=
   len_le_of_epi
 #align simplex_category.le_of_epi SimplexCategory.le_of_epi
+-/
 
 instance {n : ℕ} {i : Fin (n + 2)} : Mono (δ i) :=
   by
@@ -671,12 +843,20 @@ instance : ReflectsIsomorphisms (forget SimplexCategory) :=
             ext1
             exact iso.inv_hom_id (as_iso ((forget _).map f)) }⟩
 
+#print SimplexCategory.isIso_of_bijective /-
 theorem isIso_of_bijective {x y : SimplexCategory} {f : x ⟶ y}
     (hf : Function.Bijective f.toOrderHom.toFun) : IsIso f :=
   haveI : is_iso ((forget SimplexCategory).map f) := (is_iso_iff_bijective _).mpr hf
   is_iso_of_reflects_iso f (forget SimplexCategory)
 #align simplex_category.is_iso_of_bijective SimplexCategory.isIso_of_bijective
+-/
 
+/- warning: simplex_category.order_iso_of_iso -> SimplexCategory.orderIsoOfIso is a dubious translation:
+lean 3 declaration is
+  forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (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) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {x : SimplexCategory} {y : SimplexCategory}, (CategoryTheory.Iso.{0, 0} SimplexCategory SimplexCategory.smallCategory x y) -> (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len x) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+Case conversion may be inaccurate. Consider using '#align simplex_category.order_iso_of_iso SimplexCategory.orderIsoOfIsoₓ'. -/
 /-- An isomorphism in `simplex_category` induces an `order_iso`. -/
 @[simp]
 def orderIsoOfIso {x y : SimplexCategory} (e : x ≅ y) : Fin (x.len + 1) ≃o Fin (y.len + 1) :=
@@ -690,6 +870,7 @@ def orderIsoOfIso {x y : SimplexCategory} (e : x ≅ y) : Fin (x.len + 1) ≃o F
     e.Hom.toOrderHom.Monotone e.inv.toOrderHom.Monotone
 #align simplex_category.order_iso_of_iso SimplexCategory.orderIsoOfIso
 
+#print SimplexCategory.iso_eq_iso_refl /-
 theorem iso_eq_iso_refl {x : SimplexCategory} (e : x ≅ x) : e = Iso.refl x :=
   by
   have h : (Finset.univ : Finset (Fin (x.len + 1))).card = x.len + 1 := Finset.card_fin (x.len + 1)
@@ -701,11 +882,20 @@ theorem iso_eq_iso_refl {x : SimplexCategory} (e : x ≅ x) : e = Iso.refl x :=
   ext1; ext1 i
   rfl
 #align simplex_category.iso_eq_iso_refl SimplexCategory.iso_eq_iso_refl
+-/
 
+#print SimplexCategory.eq_id_of_isIso /-
 theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [hf : IsIso f] : f = 𝟙 _ :=
   congr_arg (fun φ : _ ≅ _ => φ.Hom) (iso_eq_iso_refl (asIso f))
 #align simplex_category.eq_id_of_is_iso SimplexCategory.eq_id_of_isIso
+-/
 
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(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)) (OrderHom.toFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len (SimplexCategory.mk (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) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len (SimplexCategory.mk (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.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len (SimplexCategory.mk (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))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (SimplexCategory.len Δ') (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (SimplexCategory.Hom.toOrderHom (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ' θ) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))) -> (Exists.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ') (fun (θ' : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ') => Eq.{1} (Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Δ') θ (CategoryTheory.CategoryStruct.comp.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk n) Δ' (SimplexCategory.σ n i) θ')))
+Case conversion may be inaccurate. Consider using '#align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'ₓ'. -/
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (i : Fin (n + 1)) (hi : θ.toOrderHom i.cast_succ = θ.toOrderHom i.succ) :
     ∃ θ' : mk n ⟶ Δ', θ = σ i ≫ θ' := by
@@ -747,6 +937,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
         simp only [add_le_add_iff_left, Nat.succ_eq_add_one, le_add_iff_nonneg_left, zero_le]
 #align simplex_category.eq_σ_comp_of_not_injective' SimplexCategory.eq_σ_comp_of_not_injective'
 
+#print SimplexCategory.eq_σ_comp_of_not_injective /-
 theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (hθ : ¬Function.Injective θ.toOrderHom) : ∃ (i : Fin (n + 1))(θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' :=
   by
@@ -775,7 +966,9 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   · rw [h₁]
     exact θ.to_order_hom.monotone h₂
 #align simplex_category.eq_σ_comp_of_not_injective SimplexCategory.eq_σ_comp_of_not_injective
+-/
 
+#print SimplexCategory.eq_comp_δ_of_not_surjective' /-
 theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
     (i : Fin (n + 2)) (hi : ∀ x, θ.toOrderHom x ≠ i) : ∃ θ' : Δ ⟶ mk n, θ = θ' ≫ δ i :=
   by
@@ -815,7 +1008,9 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       Fin.predAbove_last, Fin.succAbove_last,
       Fin.castSucc_castPred ((Ne.le_iff_lt (hi x)).mp (Fin.le_last _))]
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
+-/
 
+#print SimplexCategory.eq_comp_δ_of_not_surjective /-
 theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
     (hθ : ¬Function.Surjective θ.toOrderHom) : ∃ (i : Fin (n + 2))(θ' : Δ ⟶ mk n), θ = θ' ≫ δ i :=
   by
@@ -823,7 +1018,9 @@ theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ 
   use i
   exact eq_comp_δ_of_not_surjective' θ i (not_exists.mp hi)
 #align simplex_category.eq_comp_δ_of_not_surjective SimplexCategory.eq_comp_δ_of_not_surjective
+-/
 
+#print SimplexCategory.eq_id_of_mono /-
 theorem eq_id_of_mono {x : SimplexCategory} (i : x ⟶ x) [Mono i] : i = 𝟙 _ :=
   by
   suffices is_iso i by
@@ -835,7 +1032,9 @@ theorem eq_id_of_mono {x : SimplexCategory} (i : x ⟶ x) [Mono i] : i = 𝟙 _
     eq_self_iff_true, and_true_iff]
   infer_instance
 #align simplex_category.eq_id_of_mono SimplexCategory.eq_id_of_mono
+-/
 
+#print SimplexCategory.eq_id_of_epi /-
 theorem eq_id_of_epi {x : SimplexCategory} (i : x ⟶ x) [Epi i] : i = 𝟙 _ :=
   by
   suffices is_iso i by
@@ -847,7 +1046,9 @@ theorem eq_id_of_epi {x : SimplexCategory} (i : x ⟶ x) [Epi i] : i = 𝟙 _ :=
     eq_self_iff_true, and_true_iff]
   infer_instance
 #align simplex_category.eq_id_of_epi SimplexCategory.eq_id_of_epi
+-/
 
+#print SimplexCategory.eq_σ_of_epi /-
 theorem eq_σ_of_epi {n : ℕ} (θ : mk (n + 1) ⟶ mk n) [Epi θ] : ∃ i : Fin (n + 1), θ = σ i :=
   by
   rcases eq_σ_comp_of_not_injective θ _ with ⟨i, θ', h⟩; swap
@@ -861,7 +1062,9 @@ theorem eq_σ_of_epi {n : ℕ} (θ : mk (n + 1) ⟶ mk n) [Epi θ] : ∃ i : Fin
   haveI := CategoryTheory.epi_of_epi (σ i) θ'
   rw [h, eq_id_of_epi θ', category.comp_id]
 #align simplex_category.eq_σ_of_epi SimplexCategory.eq_σ_of_epi
+-/
 
+#print SimplexCategory.eq_δ_of_mono /-
 theorem eq_δ_of_mono {n : ℕ} (θ : mk n ⟶ mk (n + 1)) [Mono θ] : ∃ i : Fin (n + 2), θ = δ i :=
   by
   rcases eq_comp_δ_of_not_surjective θ _ with ⟨i, θ', h⟩; swap
@@ -875,7 +1078,9 @@ theorem eq_δ_of_mono {n : ℕ} (θ : mk n ⟶ mk (n + 1)) [Mono θ] : ∃ i : F
   haveI := CategoryTheory.mono_of_mono θ' (δ i)
   rw [h, eq_id_of_mono θ', category.id_comp]
 #align simplex_category.eq_δ_of_mono SimplexCategory.eq_δ_of_mono
+-/
 
+#print SimplexCategory.len_lt_of_mono /-
 theorem len_lt_of_mono {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [hi : Mono i] (hi' : Δ ≠ Δ') :
     Δ'.len < Δ.len := by
   cases lt_or_eq_of_le (len_le_of_mono hi)
@@ -887,6 +1092,7 @@ theorem len_lt_of_mono {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [hi : Mono i]
           ext
           exact h.symm)
 #align simplex_category.len_lt_of_mono SimplexCategory.len_lt_of_mono
+-/
 
 noncomputable instance : SplitEpiCategory SimplexCategory :=
   skeletalEquivalence.{0}.inverse.splitEpiCategoryImpOfIsEquivalence
@@ -901,6 +1107,7 @@ instance : HasStrongEpiImages SimplexCategory :=
 instance (Δ Δ' : SimplexCategory) (θ : Δ ⟶ Δ') : Epi (factorThruImage θ) :=
   StrongEpi.epi
 
+#print SimplexCategory.image_eq /-
 theorem image_eq {Δ Δ' Δ'' : SimplexCategory} {φ : Δ ⟶ Δ''} {e : Δ ⟶ Δ'} [Epi e] {i : Δ' ⟶ Δ''}
     [Mono i] (fac : e ≫ i = φ) : image φ = Δ' :=
   by
@@ -911,7 +1118,9 @@ theorem image_eq {Δ Δ' Δ'' : SimplexCategory} {φ : Δ ⟶ Δ''} {e : Δ ⟶
     le_antisymm (len_le_of_epi (inferInstance : epi e.hom))
       (len_le_of_mono (inferInstance : mono e.hom))
 #align simplex_category.image_eq SimplexCategory.image_eq
+-/
 
+#print SimplexCategory.image_ι_eq /-
 theorem image_ι_eq {Δ Δ'' : SimplexCategory} {φ : Δ ⟶ Δ''} {e : Δ ⟶ image φ} [Epi e]
     {i : image φ ⟶ Δ''} [Mono i] (fac : e ≫ i = φ) : image.ι φ = i :=
   by
@@ -919,14 +1128,18 @@ theorem image_ι_eq {Δ Δ'' : SimplexCategory} {φ : Δ ⟶ Δ''} {e : Δ ⟶ i
   rw [← image.iso_strong_epi_mono_hom_comp_ι e i fac,
     SimplexCategory.eq_id_of_isIso (image.iso_strong_epi_mono e i fac).Hom, category.id_comp]
 #align simplex_category.image_ι_eq SimplexCategory.image_ι_eq
+-/
 
+#print SimplexCategory.factorThruImage_eq /-
 theorem factorThruImage_eq {Δ Δ'' : SimplexCategory} {φ : Δ ⟶ Δ''} {e : Δ ⟶ image φ} [Epi e]
     {i : image φ ⟶ Δ''} [Mono i] (fac : e ≫ i = φ) : factorThruImage φ = e := by
   rw [← cancel_mono i, fac, ← image_ι_eq fac, image.fac]
 #align simplex_category.factor_thru_image_eq SimplexCategory.factorThruImage_eq
+-/
 
 end EpiMono
 
+#print SimplexCategory.toCat /-
 /-- This functor `simplex_category ⥤ Cat` sends `[n]` (for `n : ℕ`)
 to the category attached to the ordered set `{0, 1, ..., n}` -/
 @[simps obj map]
@@ -936,6 +1149,7 @@ def toCat : SimplexCategory ⥤ Cat.{0} :=
       forget₂ LinOrdCat LatCat ⋙
         forget₂ LatCat PartOrdCat ⋙ forget₂ PartOrdCat PreordCat ⋙ preordCatToCat
 #align simplex_category.to_Cat SimplexCategory.toCat
+-/
 
 end SimplexCategory
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -932,8 +932,9 @@ to the category attached to the ordered set `{0, 1, ..., n}` -/
 @[simps obj map]
 def toCat : SimplexCategory ⥤ Cat.{0} :=
   SimplexCategory.skeletalFunctor ⋙
-    forget₂ NonemptyFinLinOrdCat LinOrd ⋙
-      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrdCat ⋙ forget₂ PartOrdCat PreordCat ⋙ preordCatToCat
+    forget₂ NonemptyFinLinOrdCat LinOrdCat ⋙
+      forget₂ LinOrdCat LatCat ⋙
+        forget₂ LatCat PartOrdCat ⋙ forget₂ PartOrdCat PreordCat ⋙ preordCatToCat
 #align simplex_category.to_Cat SimplexCategory.toCat
 
 end SimplexCategory

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -933,7 +933,7 @@ to the category attached to the ordered set `{0, 1, ..., n}` -/
 def toCat : SimplexCategory ⥤ Cat.{0} :=
   SimplexCategory.skeletalFunctor ⋙
     forget₂ NonemptyFinLinOrdCat LinOrd ⋙
-      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrd ⋙ forget₂ PartOrd PreordCat ⋙ preordCatToCat
+      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrdCat ⋙ forget₂ PartOrdCat PreordCat ⋙ preordCatToCat
 #align simplex_category.to_Cat SimplexCategory.toCat
 
 end SimplexCategory

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -933,7 +933,7 @@ to the category attached to the ordered set `{0, 1, ..., n}` -/
 def toCat : SimplexCategory ⥤ Cat.{0} :=
   SimplexCategory.skeletalFunctor ⋙
     forget₂ NonemptyFinLinOrdCat LinOrd ⋙
-      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrd ⋙ forget₂ PartOrd Preord ⋙ preordToCat
+      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrd ⋙ forget₂ PartOrd PreordCat ⋙ preordCatToCat
 #align simplex_category.to_Cat SimplexCategory.toCat
 
 end SimplexCategory

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -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.simplex_category
-! leanprover-community/mathlib commit dd1f8496baa505636a82748e6b652165ea888733
+! leanprover-community/mathlib commit e8ac6315bcfcbaf2d19a046719c3b553206dac75
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -932,9 +932,8 @@ to the category attached to the ordered set `{0, 1, ..., n}` -/
 @[simps obj map]
 def toCat : SimplexCategory ⥤ Cat.{0} :=
   SimplexCategory.skeletalFunctor ⋙
-    forget₂ NonemptyFinLinOrdCat LinearOrderCat ⋙
-      forget₂ LinearOrderCat LatticeCat ⋙
-        forget₂ LatticeCat PartialOrderCat ⋙ forget₂ PartialOrderCat PreorderCat ⋙ preorderToCat
+    forget₂ NonemptyFinLinOrdCat LinOrd ⋙
+      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrd ⋙ forget₂ PartOrd Preord ⋙ preordToCat
 #align simplex_category.to_Cat SimplexCategory.toCat
 
 end SimplexCategory

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

A PR accompanying #12339.

Zulip discussion

@@ -761,8 +761,8 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       dsimp [σ, δ]
       erw [Fin.predAbove_of_castSucc_lt _ _ (by rwa [Fin.castSucc_castPred])]
       rw [Fin.succAbove_of_le_castSucc i _]
-      erw [Fin.succ_pred]
-      exact Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')
+      · erw [Fin.succ_pred]
+      · exact Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
     ext x : 3

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

@@ -464,7 +464,7 @@ theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ => by
 namespace SkeletalFunctor
 
 instance : skeletalFunctor.Full where
-  preimage f := SimplexCategory.Hom.mk f
+  map_surjective f := ⟨SimplexCategory.Hom.mk f, rfl⟩
 
 instance : skeletalFunctor.Faithful where
   map_injective {_ _ f g} h := by

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.

@@ -89,7 +89,7 @@ protected def rec {F : SimplexCategory → Sort*} (h : ∀ n : ℕ, F [n]) : ∀
   h n.len
 #align simplex_category.rec SimplexCategory.rec
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- Morphisms in the `SimplexCategory`. -/
 protected def Hom (a b : SimplexCategory) :=
   Fin (a.len + 1) →o Fin (b.len + 1)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

@@ -463,15 +463,15 @@ theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ => by
 
 namespace SkeletalFunctor
 
-instance : Full skeletalFunctor where
+instance : skeletalFunctor.Full where
   preimage f := SimplexCategory.Hom.mk f
 
-instance : Faithful skeletalFunctor where
+instance : skeletalFunctor.Faithful where
   map_injective {_ _ f g} h := by
     ext1
     exact h
 
-instance : EssSurj skeletalFunctor where
+instance : skeletalFunctor.EssSurj where
   mem_essImage X :=
     ⟨mk (Fintype.card X - 1 : ℕ),
       ⟨by
@@ -490,8 +490,8 @@ instance : EssSurj skeletalFunctor where
         show f (f.symm i) ≤ f (f.symm j)
         simpa only [OrderIso.apply_symm_apply]⟩⟩
 
-noncomputable instance isEquivalence : IsEquivalence skeletalFunctor :=
-  Equivalence.ofFullyFaithfullyEssSurj skeletalFunctor
+noncomputable instance isEquivalence : skeletalFunctor.IsEquivalence :=
+  Functor.IsEquivalence.ofFullyFaithfullyEssSurj skeletalFunctor
 #align simplex_category.skeletal_functor.is_equivalence SimplexCategory.SkeletalFunctor.isEquivalence
 
 end SkeletalFunctor
@@ -532,8 +532,8 @@ def inclusion {n : ℕ} : SimplexCategory.Truncated n ⥤ SimplexCategory :=
   fullSubcategoryInclusion _
 #align simplex_category.truncated.inclusion SimplexCategory.Truncated.inclusion
 
-instance (n : ℕ) : Full (inclusion : Truncated n ⥤ _) := FullSubcategory.full _
-instance (n : ℕ) : Faithful (inclusion : Truncated n ⥤ _) := FullSubcategory.faithful _
+instance (n : ℕ) : (inclusion : Truncated n ⥤ _).Full := FullSubcategory.full _
+instance (n : ℕ) : (inclusion : Truncated n ⥤ _).Faithful := FullSubcategory.faithful _
 
 end Truncated
 
@@ -613,7 +613,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
     rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
-instance : ReflectsIsomorphisms (forget SimplexCategory) :=
+instance : (forget SimplexCategory).ReflectsIsomorphisms :=
   ⟨fun f hf =>
     IsIso.of_iso
       { hom := f

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.

@@ -146,13 +146,20 @@ def comp {a b c : SimplexCategory} (f : SimplexCategory.Hom b c) (g : SimplexCat
 
 end Hom
 
-@[simps]
 instance smallCategory : SmallCategory.{0} SimplexCategory where
   Hom n m := SimplexCategory.Hom n m
   id m := SimplexCategory.Hom.id _
   comp f g := SimplexCategory.Hom.comp g f
 #align simplex_category.small_category SimplexCategory.smallCategory
 
+@[simp]
+lemma id_toOrderHom (a : SimplexCategory) :
+    Hom.toOrderHom (𝟙 a) = OrderHom.id := rfl
+
+@[simp]
+lemma comp_toOrderHom {a b c: SimplexCategory} (f : a ⟶ b) (g : b ⟶ c) :
+    (f ≫ g).toOrderHom = g.toOrderHom.comp f.toOrderHom := rfl
+
 -- Porting note: added because `Hom.ext'` is not triggered automatically
 @[ext]
 theorem Hom.ext {a b : SimplexCategory} (f g : a ⟶ b) :
@@ -160,13 +167,21 @@ theorem Hom.ext {a b : SimplexCategory} (f g : a ⟶ b) :
   Hom.ext' _ _
 
 /-- The constant morphism from [0]. -/
-def const (x : SimplexCategory) (i : Fin (x.len + 1)) : ([0] : SimplexCategory) ⟶ x :=
+def const (x y : SimplexCategory) (i : Fin (y.len + 1)) : x ⟶ y :=
   Hom.mk <| ⟨fun _ => i, by tauto⟩
 #align simplex_category.const SimplexCategory.const
 
--- Porting note: removed @[simp] as the linter complains
-theorem const_comp (x y : SimplexCategory) (i : Fin (x.len + 1)) (f : x ⟶ y) :
-    const x i ≫ f = const y (f.toOrderHom i) :=
+@[simp]
+lemma const_eq_id : const [0] [0] 0 = 𝟙 _ := by aesop
+
+@[simp]
+lemma const_apply (x y : SimplexCategory) (i : Fin (y.len + 1)) (a : Fin (x.len + 1)) :
+    (const x y i).toOrderHom a = i := rfl
+
+@[simp]
+theorem const_comp (x : SimplexCategory) {y z : SimplexCategory}
+    (f : y ⟶ z) (i : Fin (y.len + 1)) :
+    const x y i ≫ f = const x z (f.toOrderHom i) :=
   rfl
 #align simplex_category.const_comp SimplexCategory.const_comp
 
@@ -663,8 +678,8 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     ∃ θ' : mk n ⟶ Δ', θ = σ i ≫ θ' := by
   use δ i.succ ≫ θ
   ext1; ext1; ext1 x
-  simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
-    smallCategory_comp, σ, mkHom, OrderHom.coe_mk]
+  simp only [len_mk, σ, mkHom, comp_toOrderHom, Hom.toOrderHom_mk, OrderHom.comp_coe,
+    OrderHom.coe_mk, Function.comp_apply]
   by_cases h' : x ≤ Fin.castSucc i
   · -- This was not needed before leanprover/lean4#2644
     dsimp
@@ -732,12 +747,9 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     ext1
     ext1
     ext1 x
-    simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
-      smallCategory_comp]
+    simp only [len_mk, Category.assoc, comp_toOrderHom, OrderHom.comp_coe, Function.comp_apply]
     by_cases h' : θ.toOrderHom x ≤ i
     · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
-      -- This was not needed before leanprover/lean4#2644
-      dsimp
       -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
       erw [Fin.predAbove_of_le_castSucc _ _ (by rwa [Fin.castSucc_castPred])]
       dsimp [δ]
@@ -746,15 +758,11 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       · rw [(hi x).le_iff_lt] at h'
         exact h'
     · simp only [not_le] at h'
-      -- The next three tactics used to be a simp only call before leanprover/lean4#2644
-      rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
-      erw [OrderHom.coe_mk]
+      dsimp [σ, δ]
       erw [Fin.predAbove_of_castSucc_lt _ _ (by rwa [Fin.castSucc_castPred])]
-      dsimp [δ]
       rw [Fin.succAbove_of_le_castSucc i _]
       erw [Fin.succ_pred]
-      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
-        Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')
+      exact Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
     ext x : 3

The removal of some pointless tactics flagged by #11308.

@@ -752,8 +752,6 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       erw [Fin.predAbove_of_castSucc_lt _ _ (by rwa [Fin.castSucc_castPred])]
       dsimp [δ]
       rw [Fin.succAbove_of_le_castSucc i _]
-      -- This was not needed before leanprover/lean4#2644
-      conv_rhs => dsimp
       erw [Fin.succ_pred]
       simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')

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".

@@ -50,7 +50,7 @@ namespace SimplexCategory
 section
 
 
--- porting note: the definition of `SimplexCategory` is made irreducible below
+-- Porting note: the definition of `SimplexCategory` is made irreducible below
 /-- Interpret a natural number as an object of the simplex category. -/
 def mk (n : ℕ) : SimplexCategory :=
   n
@@ -153,7 +153,7 @@ instance smallCategory : SmallCategory.{0} SimplexCategory where
   comp f g := SimplexCategory.Hom.comp g f
 #align simplex_category.small_category SimplexCategory.smallCategory
 
--- porting note: added because `Hom.ext'` is not triggered automatically
+-- Porting note: added because `Hom.ext'` is not triggered automatically
 @[ext]
 theorem Hom.ext {a b : SimplexCategory} (f g : a ⟶ b) :
     f.toOrderHom = g.toOrderHom → f = g :=
@@ -164,7 +164,7 @@ def const (x : SimplexCategory) (i : Fin (x.len + 1)) : ([0] : SimplexCategory)
   Hom.mk <| ⟨fun _ => i, by tauto⟩
 #align simplex_category.const SimplexCategory.const
 
--- porting note: removed @[simp] as the linter complains
+-- Porting note: removed @[simp] as the linter complains
 theorem const_comp (x y : SimplexCategory) (i : Fin (x.len + 1)) (f : x ⟶ y) :
     const x i ≫ f = const y (f.toOrderHom i) :=
   rfl

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -218,7 +218,7 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
-  split_ifs <;> · simp at * <;> linarith
+  split_ifs <;> · simp at * <;> omega
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
 
 theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
@@ -286,7 +286,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
     Fin.coe_castLT, dite_eq_ite]
   split_ifs
   any_goals simp
-  all_goals linarith
+  all_goals omega
 #align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_self
 
 @[reassoc]
@@ -303,7 +303,7 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 ([n] :
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   dsimp [δ, σ, Fin.succAbove, Fin.predAbove]
-  split_ifs <;> simp <;> simp at * <;> linarith
+  split_ifs <;> simp <;> simp at * <;> omega
 #align simplex_category.δ_comp_σ_succ SimplexCategory.δ_comp_σ_succ
 
 @[reassoc]

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

@@ -89,7 +89,7 @@ protected def rec {F : SimplexCategory → Sort*} (h : ∀ n : ℕ, F [n]) : ∀
   h n.len
 #align simplex_category.rec SimplexCategory.rec
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- Morphisms in the `SimplexCategory`. -/
 protected def Hom (a b : SimplexCategory) :=
   Fin (a.len + 1) →o Fin (b.len + 1)

@@ -589,8 +589,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
     -- This was not needed before leanprover/lean4#2644
     dsimp
     rw [Fin.predAbove_of_le_castSucc i b (by simpa only [Fin.coe_eq_castSucc] using h)]
-    simp only [len_mk, Fin.coe_eq_castSucc]
-    rfl
+    simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
     -- This was not needed before leanprover/lean4#2644
     dsimp
@@ -672,9 +671,8 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     rw [Fin.predAbove_of_le_castSucc i x h']
     dsimp [δ]
     erw [Fin.succAbove_of_castSucc_lt _ _ _]
-    swap
+    · rw [Fin.castSucc_castPred]
     · exact (Fin.castSucc_lt_succ_iff.mpr h')
-    rfl
   · simp only [not_le] at h'
     let y := x.pred <| by rintro (rfl : x = 0); simp at h'
     have hy : x = y.succ := (Fin.succ_pred x _).symm
@@ -741,18 +739,17 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       -- This was not needed before leanprover/lean4#2644
       dsimp
       -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-      erw [Fin.predAbove_of_le_castSucc _ _ (by exact h')]
+      erw [Fin.predAbove_of_le_castSucc _ _ (by rwa [Fin.castSucc_castPred])]
       dsimp [δ]
       erw [Fin.succAbove_of_castSucc_lt i]
-      swap
+      · rw [Fin.castSucc_castPred]
       · rw [(hi x).le_iff_lt] at h'
         exact h'
-      rfl
     · simp only [not_le] at h'
       -- The next three tactics used to be a simp only call before leanprover/lean4#2644
       rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
       erw [OrderHom.coe_mk]
-      erw [Fin.predAbove_of_castSucc_lt _ _ (by exact h')]
+      erw [Fin.predAbove_of_castSucc_lt _ _ (by rwa [Fin.castSucc_castPred])]
       dsimp [δ]
       rw [Fin.succAbove_of_le_castSucc i _]
       -- This was not needed before leanprover/lean4#2644
@@ -765,9 +762,8 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     ext x : 3
     dsimp [δ, σ]
     simp_rw [Fin.succAbove_last, Fin.predAbove_last_apply]
-    split_ifs with h
-    · exact ((hi x) h).elim
-    · rfl
+    erw [dif_neg (hi x)]
+    rw [Fin.castSucc_castPred]
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 
 theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))

Rename succAbove_below, succAbove_above, predAbove_below and predAbove_Above to more appropriate things, and vary and extend these results to allow for faster proofs elsewhere.

Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -259,17 +259,17 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.
   ext k : 3
   dsimp [σ, δ]
   rcases le_or_lt i k with (hik | hik)
-  · rw [Fin.succAbove_above _ _ (Fin.castSucc_le_castSucc_iff.mpr hik),
-    Fin.succ_predAbove_succ, Fin.succAbove_above]
+  · rw [Fin.succAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr hik),
+    Fin.succ_predAbove_succ, Fin.succAbove_of_le_castSucc]
     rcases le_or_lt k (j.castSucc) with (hjk | hjk)
-    · rwa [Fin.predAbove_below _ _ hjk, Fin.castSucc_castPred]
-    · rw [Fin.le_castSucc_iff, Fin.predAbove_above _ _ hjk, Fin.succ_pred]
+    · rwa [Fin.predAbove_of_le_castSucc _ _ hjk, Fin.castSucc_castPred]
+    · rw [Fin.le_castSucc_iff, Fin.predAbove_of_castSucc_lt _ _ hjk, Fin.succ_pred]
       exact H.trans_lt hjk
-  · rw [Fin.succAbove_below _ _ (Fin.castSucc_lt_castSucc_iff.mpr hik)]
+  · rw [Fin.succAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_castSucc_iff.mpr hik)]
     have hjk := H.trans_lt' hik
-    rw [Fin.predAbove_below _ _ (Fin.castSucc_le_castSucc_iff.mpr
+    rw [Fin.predAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr
       (hjk.trans (Fin.castSucc_lt_succ _)).le),
-      Fin.predAbove_below _ _ hjk.le, Fin.castPred_castSucc, Fin.succAbove_below,
+      Fin.predAbove_of_le_castSucc _ _ hjk.le, Fin.castPred_castSucc, Fin.succAbove_of_castSucc_lt,
       Fin.castSucc_castPred]
     rwa [Fin.castSucc_castPred]
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
@@ -320,19 +320,22 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
   ext k : 3
   dsimp [δ, σ]
   rcases le_or_lt k i with (hik | hik)
-  · rw [Fin.succAbove_below _ _ (Fin.castSucc_lt_succ_iff.mpr hik)]
+  · rw [Fin.succAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_succ_iff.mpr hik)]
     rcases le_or_lt k (j.castSucc) with (hjk | hjk)
-    · rw [Fin.predAbove_below _ _ (Fin.castSucc_le_castSucc_iff.mpr hjk), Fin.castPred_castSucc,
-      Fin.predAbove_below _ _ hjk, Fin.succAbove_below, Fin.castSucc_castPred]
+    · rw [Fin.predAbove_of_le_castSucc _ _
+      (Fin.castSucc_le_castSucc_iff.mpr hjk), Fin.castPred_castSucc,
+      Fin.predAbove_of_le_castSucc _ _ hjk, Fin.succAbove_of_castSucc_lt, Fin.castSucc_castPred]
       rw [Fin.castSucc_castPred]
       exact hjk.trans_lt H
-    · rw [Fin.predAbove_above _ _ (Fin.castSucc_lt_castSucc_iff.mpr hjk),
-      Fin.predAbove_above _ _ hjk, Fin.succAbove_below, Fin.castSucc_pred_eq_pred_castSucc]
+    · rw [Fin.predAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_castSucc_iff.mpr hjk),
+      Fin.predAbove_of_castSucc_lt _ _ hjk, Fin.succAbove_of_castSucc_lt,
+      Fin.castSucc_pred_eq_pred_castSucc]
       rwa [Fin.castSucc_lt_iff_succ_le, Fin.succ_pred]
-  · rw [Fin.succAbove_above _ _ (Fin.succ_le_castSucc_iff.mpr hik)]
+  · rw [Fin.succAbove_of_le_castSucc _ _ (Fin.succ_le_castSucc_iff.mpr hik)]
     have hjk := H.trans hik
-    rw [Fin.predAbove_above _ _ hjk, Fin.predAbove_above _ _ (Fin.castSucc_lt_succ_iff.mpr hjk.le),
-    Fin.pred_succ, Fin.succAbove_above, Fin.succ_pred]
+    rw [Fin.predAbove_of_castSucc_lt _ _ hjk, Fin.predAbove_of_castSucc_lt _ _
+      (Fin.castSucc_lt_succ_iff.mpr hjk.le),
+    Fin.pred_succ, Fin.succAbove_of_le_castSucc, Fin.succ_pred]
     rwa [Fin.le_castSucc_pred_iff]
 #align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gt
 
@@ -355,26 +358,29 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   cases' k using Fin.lastCases with k
   · simp only [len_mk, Fin.predAbove_right_last]
   · cases' k using Fin.cases with k
-    · rw [Fin.castSucc_zero, Fin.predAbove_below _ 0 (Fin.zero_le _),
-      Fin.predAbove_below _ _ (Fin.zero_le _), Fin.castPred_zero,
-      Fin.predAbove_below _ 0 (Fin.zero_le _), Fin.predAbove_below _ _ (Fin.zero_le _)]
+    · rw [Fin.castSucc_zero, Fin.predAbove_of_le_castSucc _ 0 (Fin.zero_le _),
+      Fin.predAbove_of_le_castSucc _ _ (Fin.zero_le _), Fin.castPred_zero,
+      Fin.predAbove_of_le_castSucc _ 0 (Fin.zero_le _),
+      Fin.predAbove_of_le_castSucc _ _ (Fin.zero_le _)]
     · rcases le_or_lt i k with (h | h)
-      · simp_rw [Fin.predAbove_above i.castSucc _ (Fin.castSucc_lt_castSucc_iff.mpr
+      · simp_rw [Fin.predAbove_of_castSucc_lt i.castSucc _ (Fin.castSucc_lt_castSucc_iff.mpr
         (Fin.castSucc_lt_succ_iff.mpr h)), ← Fin.succ_castSucc, Fin.pred_succ,
         Fin.succ_predAbove_succ]
-        rw [Fin.predAbove_above i _ (Fin.castSucc_lt_succ_iff.mpr _), Fin.pred_succ]
+        rw [Fin.predAbove_of_castSucc_lt i _ (Fin.castSucc_lt_succ_iff.mpr _), Fin.pred_succ]
         rcases le_or_lt k j with (hkj | hkj)
-        · rwa [Fin.predAbove_below _ _ (Fin.castSucc_le_castSucc_iff.mpr hkj),
+        · rwa [Fin.predAbove_of_le_castSucc _ _ (Fin.castSucc_le_castSucc_iff.mpr hkj),
           Fin.castPred_castSucc]
-        · rw [Fin.predAbove_above _ _ (Fin.castSucc_lt_castSucc_iff.mpr hkj), Fin.le_pred_iff,
+        · rw [Fin.predAbove_of_castSucc_lt _ _ (Fin.castSucc_lt_castSucc_iff.mpr hkj),
+          Fin.le_pred_iff,
           Fin.succ_le_castSucc_iff]
           exact H.trans_lt hkj
-      · simp_rw [Fin.predAbove_below i.castSucc _ (Fin.castSucc_le_castSucc_iff.mpr
+      · simp_rw [Fin.predAbove_of_le_castSucc i.castSucc _ (Fin.castSucc_le_castSucc_iff.mpr
         (Fin.succ_le_castSucc_iff.mpr h)), Fin.castPred_castSucc, ← Fin.succ_castSucc,
         Fin.succ_predAbove_succ]
-        rw [Fin.predAbove_below _ k.castSucc (Fin.castSucc_le_castSucc_iff.mpr (h.le.trans H)),
-        Fin.castPred_castSucc, Fin.predAbove_below _ k.succ
-        (Fin.succ_le_castSucc_iff.mpr (H.trans_lt' h)), Fin.predAbove_below _ k.succ
+        rw [Fin.predAbove_of_le_castSucc _ k.castSucc
+        (Fin.castSucc_le_castSucc_iff.mpr (h.le.trans H)),
+        Fin.castPred_castSucc, Fin.predAbove_of_le_castSucc _ k.succ
+        (Fin.succ_le_castSucc_iff.mpr (H.trans_lt' h)), Fin.predAbove_of_le_castSucc _ k.succ
         (Fin.succ_le_castSucc_iff.mpr h)]
 #align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σ
 
@@ -395,22 +401,22 @@ lemma factor_δ_spec {m n : ℕ} (f : ([m] : SimplexCategory) ⟶ [n+1]) (j : Fi
   specialize hj k
   dsimp [factor_δ, δ, σ]
   cases' j using cases with j
-  · rw [predAbove_below _ _ (zero_le _), castPred_zero, predAbove_above 0 _
+  · rw [predAbove_of_le_castSucc _ _ (zero_le _), castPred_zero, predAbove_of_castSucc_lt 0 _
     (castSucc_zero ▸ pos_of_ne_zero hj),
     zero_succAbove, succ_pred]
-  · rw [predAbove_above 0 _ (castSucc_zero ▸ succ_pos _), pred_succ]
+  · rw [predAbove_of_castSucc_lt 0 _ (castSucc_zero ▸ succ_pos _), pred_succ]
     rcases hj.lt_or_lt with (hj | hj)
-    · rw [predAbove_below j _]
+    · rw [predAbove_of_le_castSucc j _]
       swap
       · exact (le_castSucc_iff.mpr hj)
-      · rw [succAbove_below]
+      · rw [succAbove_of_castSucc_lt]
         swap
         · rwa [castSucc_lt_succ_iff, castPred_le_iff, le_castSucc_iff]
         rw [castSucc_castPred]
-    · rw [predAbove_above]
+    · rw [predAbove_of_castSucc_lt]
       swap
       · exact (castSucc_lt_succ _).trans hj
-      rw [succAbove_above]
+      rw [succAbove_of_le_castSucc]
       swap
       · rwa [succ_le_castSucc_iff, lt_pred_iff]
       rw [succ_pred]
@@ -582,13 +588,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   · use b
     -- This was not needed before leanprover/lean4#2644
     dsimp
-    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
+    rw [Fin.predAbove_of_le_castSucc i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [len_mk, Fin.coe_eq_castSucc]
     rfl
   · use b.succ
     -- This was not needed before leanprover/lean4#2644
     dsimp
-    rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
+    rw [Fin.predAbove_of_castSucc_lt i b.succ _, Fin.pred_succ]
     rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
@@ -663,9 +669,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   by_cases h' : x ≤ Fin.castSucc i
   · -- This was not needed before leanprover/lean4#2644
     dsimp
-    rw [Fin.predAbove_below i x h']
+    rw [Fin.predAbove_of_le_castSucc i x h']
     dsimp [δ]
-    erw [Fin.succAbove_below _ _ _]
+    erw [Fin.succAbove_of_castSucc_lt _ _ _]
     swap
     · exact (Fin.castSucc_lt_succ_iff.mpr h')
     rfl
@@ -675,16 +681,16 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     rw [hy] at h' ⊢
     -- This was not needed before leanprover/lean4#2644
     conv_rhs => dsimp
-    rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
+    rw [Fin.predAbove_of_castSucc_lt i y.succ h', Fin.pred_succ]
     by_cases h'' : y = i
     · rw [h'']
       refine hi.symm.trans ?_
       congr 1
       dsimp [δ]
-      erw [Fin.succAbove_below i.succ]
+      erw [Fin.succAbove_of_castSucc_lt i.succ]
       exact Fin.lt_succ
     · dsimp [δ]
-      erw [Fin.succAbove_above i.succ _]
+      erw [Fin.succAbove_of_le_castSucc i.succ _]
       simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
         Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
@@ -735,9 +741,9 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       -- This was not needed before leanprover/lean4#2644
       dsimp
       -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-      erw [Fin.predAbove_below _ _ (by exact h')]
+      erw [Fin.predAbove_of_le_castSucc _ _ (by exact h')]
       dsimp [δ]
-      erw [Fin.succAbove_below i]
+      erw [Fin.succAbove_of_castSucc_lt i]
       swap
       · rw [(hi x).le_iff_lt] at h'
         exact h'
@@ -746,9 +752,9 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       -- The next three tactics used to be a simp only call before leanprover/lean4#2644
       rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
       erw [OrderHom.coe_mk]
-      erw [Fin.predAbove_above _ _ (by exact h')]
+      erw [Fin.predAbove_of_castSucc_lt _ _ (by exact h')]
       dsimp [δ]
-      rw [Fin.succAbove_above i _]
+      rw [Fin.succAbove_of_le_castSucc i _]
       -- This was not needed before leanprover/lean4#2644
       conv_rhs => dsimp
       erw [Fin.succ_pred]

Fix minor typos in the following files:

• Mathlib/GroupTheory/GroupAction/Opposite.lean
• Mathlib/Init/Control/Lawful.lean
• Mathlib/ModelTheory/ElementarySubstructures.lean
• Mathlib/Algebra/Group/Defs.lean
• Mathlib/Algebra/Group/WithOne/Basic.lean
• Mathlib/Data/Int/Cast/Defs.lean
• Mathlib/LinearAlgebra/Dimension/Basic.lean
• Mathlib/NumberTheory/NumberField/CanonicalEmbedding.lean
• Mathlib/Algebra/Star/StarAlgHom.lean
• Mathlib/AlgebraicTopology/SimplexCategory.lean
• Mathlib/CategoryTheory/Abelian/Homology.lean
• Mathlib/CategoryTheory/Sites/Grothendieck.lean
• Mathlib/RingTheory/IsTensorProduct.lean
• Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean
• Mathlib/AlgebraicTopology/ExtraDegeneracy.lean
• Mathlib/AlgebraicTopology/Nerve.lean
• Mathlib/AlgebraicTopology/SplitSimplicialObject.lean
• Mathlib/Analysis/ConstantSpeed.lean
• Mathlib/Analysis/Convolution.lean

@@ -97,7 +97,7 @@ protected def Hom (a b : SimplexCategory) :=
 
 namespace Hom
 
-/-- Make a moprhism in `SimplexCategory` from a monotone map of `Fin`'s. -/
+/-- Make a morphism in `SimplexCategory` from a monotone map of `Fin`'s. -/
 def mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) : SimplexCategory.Hom a b :=
   f
 #align simplex_category.hom.mk SimplexCategory.Hom.mk

predAbove and castPred are no longer directly related. This patch makes it so that they are, removing castLT from the definition of predAbove and thus making it more directly analogous to succAbove.

@@ -256,16 +256,22 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : j = Fin.ca
 @[reassoc]
 theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSucc j) :
     δ (Fin.castSucc i) ≫ σ j.succ = σ j ≫ δ i := by
-  rcases i with ⟨i, hi⟩
-  rcases j with ⟨j, hj⟩
-  ext ⟨k, hk⟩
-  simp? at H hk says simp only [Fin.castSucc_mk, Fin.mk_le_mk, len_mk] at H hk
-  dsimp [σ, δ, Fin.predAbove, Fin.succAbove]
-  simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
-    Fin.coe_castLT, dite_eq_ite, Fin.coe_castSucc, Fin.val_succ]
-  split_ifs
-  all_goals try simp <;> linarith
-  all_goals cases k <;> simp at * <;> linarith
+  ext k : 3
+  dsimp [σ, δ]
+  rcases le_or_lt i k with (hik | hik)
+  · rw [Fin.succAbove_above _ _ (Fin.castSucc_le_castSucc_iff.mpr hik),
+    Fin.succ_predAbove_succ, Fin.succAbove_above]
+    rcases le_or_lt k (j.castSucc) with (hjk | hjk)
+    · rwa [Fin.predAbove_below _ _ hjk, Fin.castSucc_castPred]
+    · rw [Fin.le_castSucc_iff, Fin.predAbove_above _ _ hjk, Fin.succ_pred]
+      exact H.trans_lt hjk
+  · rw [Fin.succAbove_below _ _ (Fin.castSucc_lt_castSucc_iff.mpr hik)]
+    have hjk := H.trans_lt' hik
+    rw [Fin.predAbove_below _ _ (Fin.castSucc_le_castSucc_iff.mpr
+      (hjk.trans (Fin.castSucc_lt_succ _)).le),
+      Fin.predAbove_below _ _ hjk.le, Fin.castPred_castSucc, Fin.succAbove_below,
+      Fin.castSucc_castPred]
+    rwa [Fin.castSucc_castPred]
 #align simplex_category.δ_comp_σ_of_le SimplexCategory.δ_comp_σ_of_le
 
 /-- The first part of the third simplicial identity -/
@@ -311,16 +317,23 @@ theorem δ_comp_σ_succ' {n} (j : Fin (n + 2)) (i : Fin (n + 1)) (H : j = i.succ
 @[reassoc]
 theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSucc j < i) :
     δ i.succ ≫ σ (Fin.castSucc j) = σ j ≫ δ i := by
-  ext ⟨k, hk⟩
-  rcases i with ⟨i, hi⟩
-  rcases j with ⟨j, hj⟩
-  simp? at H hk says simp only [Fin.castSucc_mk, Fin.mk_lt_mk, len_mk] at H hk
-  dsimp [δ, σ, Fin.predAbove, Fin.succAbove]
-  simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
-    Fin.coe_castLT, dite_eq_ite, Fin.coe_castSucc, Fin.val_succ]
-  split_ifs
-  all_goals try simp <;> linarith
-  all_goals cases k <;> simp at * <;> linarith
+  ext k : 3
+  dsimp [δ, σ]
+  rcases le_or_lt k i with (hik | hik)
+  · rw [Fin.succAbove_below _ _ (Fin.castSucc_lt_succ_iff.mpr hik)]
+    rcases le_or_lt k (j.castSucc) with (hjk | hjk)
+    · rw [Fin.predAbove_below _ _ (Fin.castSucc_le_castSucc_iff.mpr hjk), Fin.castPred_castSucc,
+      Fin.predAbove_below _ _ hjk, Fin.succAbove_below, Fin.castSucc_castPred]
+      rw [Fin.castSucc_castPred]
+      exact hjk.trans_lt H
+    · rw [Fin.predAbove_above _ _ (Fin.castSucc_lt_castSucc_iff.mpr hjk),
+      Fin.predAbove_above _ _ hjk, Fin.succAbove_below, Fin.castSucc_pred_eq_pred_castSucc]
+      rwa [Fin.castSucc_lt_iff_succ_le, Fin.succ_pred]
+  · rw [Fin.succAbove_above _ _ (Fin.succ_le_castSucc_iff.mpr hik)]
+    have hjk := H.trans hik
+    rw [Fin.predAbove_above _ _ hjk, Fin.predAbove_above _ _ (Fin.castSucc_lt_succ_iff.mpr hjk.le),
+    Fin.pred_succ, Fin.succAbove_above, Fin.succ_pred]
+    rwa [Fin.le_castSucc_pred_iff]
 #align simplex_category.δ_comp_σ_of_gt SimplexCategory.δ_comp_σ_of_gt
 
 @[reassoc]
@@ -337,16 +350,32 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
     σ (Fin.castSucc i) ≫ σ j = σ j.succ ≫ σ i := by
-  ext ⟨k, hk⟩
-  rcases i with ⟨i, hi⟩
-  rcases j with ⟨j, hj⟩
-  simp? at H hk says simp only [Fin.mk_le_mk, len_mk] at H hk
-  dsimp [σ, Fin.predAbove]
-  simp only [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.coe_pred, ge_iff_le, dite_eq_ite,
-    Fin.coe_castLT]
-  split_ifs
-  all_goals try linarith
-  all_goals cases k <;> simp at *; linarith
+  ext k : 3
+  dsimp [σ]
+  cases' k using Fin.lastCases with k
+  · simp only [len_mk, Fin.predAbove_right_last]
+  · cases' k using Fin.cases with k
+    · rw [Fin.castSucc_zero, Fin.predAbove_below _ 0 (Fin.zero_le _),
+      Fin.predAbove_below _ _ (Fin.zero_le _), Fin.castPred_zero,
+      Fin.predAbove_below _ 0 (Fin.zero_le _), Fin.predAbove_below _ _ (Fin.zero_le _)]
+    · rcases le_or_lt i k with (h | h)
+      · simp_rw [Fin.predAbove_above i.castSucc _ (Fin.castSucc_lt_castSucc_iff.mpr
+        (Fin.castSucc_lt_succ_iff.mpr h)), ← Fin.succ_castSucc, Fin.pred_succ,
+        Fin.succ_predAbove_succ]
+        rw [Fin.predAbove_above i _ (Fin.castSucc_lt_succ_iff.mpr _), Fin.pred_succ]
+        rcases le_or_lt k j with (hkj | hkj)
+        · rwa [Fin.predAbove_below _ _ (Fin.castSucc_le_castSucc_iff.mpr hkj),
+          Fin.castPred_castSucc]
+        · rw [Fin.predAbove_above _ _ (Fin.castSucc_lt_castSucc_iff.mpr hkj), Fin.le_pred_iff,
+          Fin.succ_le_castSucc_iff]
+          exact H.trans_lt hkj
+      · simp_rw [Fin.predAbove_below i.castSucc _ (Fin.castSucc_le_castSucc_iff.mpr
+        (Fin.succ_le_castSucc_iff.mpr h)), Fin.castPred_castSucc, ← Fin.succ_castSucc,
+        Fin.succ_predAbove_succ]
+        rw [Fin.predAbove_below _ k.castSucc (Fin.castSucc_le_castSucc_iff.mpr (h.le.trans H)),
+        Fin.castPred_castSucc, Fin.predAbove_below _ k.succ
+        (Fin.succ_le_castSucc_iff.mpr (H.trans_lt' h)), Fin.predAbove_below _ k.succ
+        (Fin.succ_le_castSucc_iff.mpr h)]
 #align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σ
 
 /--
@@ -362,18 +391,29 @@ open Fin in
 lemma factor_δ_spec {m n : ℕ} (f : ([m] : SimplexCategory) ⟶ [n+1]) (j : Fin (n+2))
     (hj : ∀ (k : Fin (m+1)), f.toOrderHom k ≠ j) :
     factor_δ f j ≫ δ j = f := by
-  apply Hom.ext
-  ext k : 2
+  ext k : 3
   specialize hj k
-  rw [Ne.def, ext_iff] at hj
-  dsimp [factor_δ, δ, σ, succAbove, predAbove]
-  split <;> rename_i h0j
-  all_goals
-  · split <;> rename_i hjk <;>
-    simp only [← val_fin_lt,
-      coe_castSucc, coe_pred, coe_castLT, succ_pred, castSucc_castLT] at h0j hjk ⊢
-    · rw [if_neg]; omega
-    · rw [if_pos]; omega
+  dsimp [factor_δ, δ, σ]
+  cases' j using cases with j
+  · rw [predAbove_below _ _ (zero_le _), castPred_zero, predAbove_above 0 _
+    (castSucc_zero ▸ pos_of_ne_zero hj),
+    zero_succAbove, succ_pred]
+  · rw [predAbove_above 0 _ (castSucc_zero ▸ succ_pos _), pred_succ]
+    rcases hj.lt_or_lt with (hj | hj)
+    · rw [predAbove_below j _]
+      swap
+      · exact (le_castSucc_iff.mpr hj)
+      · rw [succAbove_below]
+        swap
+        · rwa [castSucc_lt_succ_iff, castPred_le_iff, le_castSucc_iff]
+        rw [castSucc_castPred]
+    · rw [predAbove_above]
+      swap
+      · exact (castSucc_lt_succ _).trans hj
+      rw [succAbove_above]
+      swap
+      · rwa [succ_le_castSucc_iff, lt_pred_iff]
+      rw [succ_pred]
 
 end Generators
 

This PR redefines castPred to be more consistent with the definition of both pred and castSucc, so that the relationship between castSucc and castPred and succ and pred becomes exactly analogous.

It also adds some supplementary and analogous lemmas designed to facilitate this.

As castPred is no longer dependent on predAbove, its definition is moved to a more appropriate place.

@@ -543,7 +543,8 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
     -- This was not needed before leanprover/lean4#2644
     dsimp
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
-    simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
+    simp only [len_mk, Fin.coe_eq_castSucc]
+    rfl
   · use b.succ
     -- This was not needed before leanprover/lean4#2644
     dsimp
@@ -623,12 +624,11 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   · -- This was not needed before leanprover/lean4#2644
     dsimp
     rw [Fin.predAbove_below i x h']
-    have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
     dsimp [δ]
-    erw [Fin.succAbove_below i.succ x.castPred _]
+    erw [Fin.succAbove_below _ _ _]
     swap
-    · rwa [eq, ← Fin.le_castSucc_iff]
-    rw [eq]
+    · exact (Fin.castSucc_lt_succ_iff.mpr h')
+    rfl
   · simp only [not_le] at h'
     let y := x.pred <| by rintro (rfl : x = 0); simp at h'
     have hy : x = y.succ := (Fin.succ_pred x _).symm
@@ -673,22 +673,18 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
       · exfalso
         exact h₂ h'.symm
   rcases hθ₂ with ⟨x, y, ⟨h₁, h₂⟩⟩
-  let z := x.castPred
-  use z
-  rw [← show Fin.castSucc z = x from
-    Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
+  use x.castPred ((Fin.le_last _).trans_lt' h₂).ne
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSucc_lt_iff_succ_le] at h₂
   apply le_antisymm
-  · exact θ.toOrderHom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
-  · rw [h₁]
-    exact θ.toOrderHom.monotone h₂
+  · exact θ.toOrderHom.monotone (le_of_lt (Fin.castSucc_lt_succ _))
+  · rw [Fin.castSucc_castPred, h₁]
+    exact θ.toOrderHom.monotone ((Fin.succ_castPred_le_iff _).mpr h₂)
 #align simplex_category.eq_σ_comp_of_not_injective SimplexCategory.eq_σ_comp_of_not_injective
 
 theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
     (i : Fin (n + 2)) (hi : ∀ x, θ.toOrderHom x ≠ i) : ∃ θ' : Δ ⟶ mk n, θ = θ' ≫ δ i := by
   by_cases h : i < Fin.last (n + 1)
-  · use θ ≫ σ (Fin.castPred i)
+  · use θ ≫ σ (Fin.castPred i h.ne)
     ext1
     ext1
     ext1 x
@@ -699,23 +695,18 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       -- This was not needed before leanprover/lean4#2644
       dsimp
       -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-      erw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
-          (by simpa [Fin.castSucc_castPred h] using h')]
+      erw [Fin.predAbove_below _ _ (by exact h')]
       dsimp [δ]
       erw [Fin.succAbove_below i]
       swap
-      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
-        exact
-          lt_of_le_of_lt (Fin.coe_castPred_le_self _)
-            (Fin.lt_iff_val_lt_val.mp ((Ne.le_iff_lt (hi x)).mp h'))
-      rw [Fin.castSucc_castPred]
-      apply lt_of_le_of_lt h' h
+      · rw [(hi x).le_iff_lt] at h'
+        exact h'
+      rfl
     · simp only [not_le] at h'
       -- The next three tactics used to be a simp only call before leanprover/lean4#2644
       rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
       erw [OrderHom.coe_mk]
-      erw [Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
-          (by simpa only [Fin.castSucc_castPred h] using h')]
+      erw [Fin.predAbove_above _ _ (by exact h')]
       dsimp [δ]
       rw [Fin.succAbove_above i _]
       -- This was not needed before leanprover/lean4#2644
@@ -725,11 +716,12 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
         Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
-    ext x : 4
+    ext x : 3
     dsimp [δ, σ]
-    dsimp only [Fin.castPred]
-    rw [Fin.predAbove_last, Fin.succAbove_last, Fin.castSucc_castPred]
-    exact (Ne.le_iff_lt (hi x)).mp (Fin.le_last _)
+    simp_rw [Fin.succAbove_last, Fin.predAbove_last_apply]
+    split_ifs with h
+    · exact ((hi x) h).elim
+    · rfl
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 
 theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))

@@ -349,6 +349,32 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   all_goals cases k <;> simp at *; linarith
 #align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σ
 
+/--
+If `f : [m] ⟶ [n+1]` is a morphism and `j` is not in the range of `f`,
+then `factor_δ f j` is a morphism `[m] ⟶ [n]` such that
+`factor_δ f j ≫ δ j = f` (as witnessed by `factor_δ_spec`).
+-/
+def factor_δ {m n : ℕ} (f : ([m] : SimplexCategory) ⟶ [n+1]) (j : Fin (n+2)) :
+    ([m] : SimplexCategory) ⟶ [n] :=
+  f ≫ σ (Fin.predAbove 0 j)
+
+open Fin in
+lemma factor_δ_spec {m n : ℕ} (f : ([m] : SimplexCategory) ⟶ [n+1]) (j : Fin (n+2))
+    (hj : ∀ (k : Fin (m+1)), f.toOrderHom k ≠ j) :
+    factor_δ f j ≫ δ j = f := by
+  apply Hom.ext
+  ext k : 2
+  specialize hj k
+  rw [Ne.def, ext_iff] at hj
+  dsimp [factor_δ, δ, σ, succAbove, predAbove]
+  split <;> rename_i h0j
+  all_goals
+  · split <;> rename_i hjk <;>
+    simp only [← val_fin_lt,
+      coe_castSucc, coe_pred, coe_castLT, succ_pred, castSucc_castLT] at h0j hjk ⊢
+    · rw [if_neg]; omega
+    · rw [if_pos]; omega
+
 end Generators
 
 section Skeleton

@@ -85,7 +85,7 @@ theorem mk_len (n : SimplexCategory) : ([n.len] : SimplexCategory) = n :=
 #align simplex_category.mk_len SimplexCategory.mk_len
 
 /-- A recursor for `SimplexCategory`. Use it as `induction Δ using SimplexCategory.rec`. -/
-protected def rec {F : ∀ _ : SimplexCategory, Sort*} (h : ∀ n : ℕ, F [n]) : ∀ X, F X := fun n =>
+protected def rec {F : SimplexCategory → Sort*} (h : ∀ n : ℕ, F [n]) : ∀ X, F X := fun n =>
   h n.len
 #align simplex_category.rec SimplexCategory.rec
 

Subset of #9319

@@ -223,7 +223,7 @@ 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) :
     δ i ≫ δ j =
-      δ (j.pred <| fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) ≫
+      δ (j.pred fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) ≫
         δ (Fin.castSucc i) := by
   rw [← δ_comp_δ]
   · rw [Fin.succ_pred]
@@ -326,7 +326,7 @@ 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) :
     δ i ≫ σ j = σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
-      δ (i.pred <| fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
+      δ (i.pred fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
   rw [← δ_comp_σ_of_gt]
   · simp
   · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -642,7 +642,7 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
     by_cases h : x < y
     · exact ⟨x, y, ⟨h₁, h⟩⟩
     · refine' ⟨y, x, ⟨h₁.symm, _⟩⟩
-      cases' lt_or_eq_of_le (not_lt.mp h) with h' h'
+      rcases lt_or_eq_of_le (not_lt.mp h) with h' | h'
       · exact h'
       · exfalso
         exact h₂ h'.symm

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -259,7 +259,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
   ext ⟨k, hk⟩
-  simp at H hk
+  simp? at H hk says simp only [Fin.castSucc_mk, Fin.mk_le_mk, len_mk] at H hk
   dsimp [σ, δ, Fin.predAbove, Fin.succAbove]
   simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
     Fin.coe_castLT, dite_eq_ite, Fin.coe_castSucc, Fin.val_succ]
@@ -274,7 +274,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
     δ (Fin.castSucc i) ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
   rcases i with ⟨i, hi⟩
   ext ⟨j, hj⟩
-  simp at hj
+  simp? at hj says simp only [len_mk] at hj
   dsimp [σ, δ, Fin.predAbove, Fin.succAbove]
   simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
     Fin.coe_castLT, dite_eq_ite]
@@ -314,7 +314,7 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
   ext ⟨k, hk⟩
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
-  simp at H hk
+  simp? at H hk says simp only [Fin.castSucc_mk, Fin.mk_lt_mk, len_mk] at H hk
   dsimp [δ, σ, Fin.predAbove, Fin.succAbove]
   simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
     Fin.coe_castLT, dite_eq_ite, Fin.coe_castSucc, Fin.val_succ]
@@ -340,7 +340,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   ext ⟨k, hk⟩
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
-  simp at H hk
+  simp? at H hk says simp only [Fin.mk_le_mk, len_mk] at H hk
   dsimp [σ, Fin.predAbove]
   simp only [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.coe_pred, ge_iff_le, dite_eq_ite,
     Fin.coe_castLT]

I've also got a change to make this required, but I'd like to land this first.

@@ -512,7 +512,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   rw [epi_iff_surjective]
   intro b
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
-  by_cases b ≤ i
+  by_cases h : b ≤ i
   · use b
     -- This was not needed before leanprover/lean4#2644
     dsimp
@@ -661,7 +661,7 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
 
 theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
     (i : Fin (n + 2)) (hi : ∀ x, θ.toOrderHom x ≠ i) : ∃ θ' : Δ ⟶ mk n, θ = θ' ≫ δ i := by
-  by_cases i < Fin.last (n + 1)
+  by_cases h : i < Fin.last (n + 1)
   · use θ ≫ σ (Fin.castPred i)
     ext1
     ext1

@@ -696,7 +696,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       conv_rhs => dsimp
       erw [Fin.succ_pred]
       simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
-        Nat.le_pred_of_lt (Fin.lt_iff_val_lt_val.mp h')
+        Nat.le_sub_one_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
     ext x : 4

Removes nonterminal simps on lines looking like simp [...]

@@ -261,7 +261,8 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.
   ext ⟨k, hk⟩
   simp at H hk
   dsimp [σ, δ, Fin.predAbove, Fin.succAbove]
-  simp [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.dite_val]
+  simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
+    Fin.coe_castLT, dite_eq_ite, Fin.coe_castSucc, Fin.val_succ]
   split_ifs
   all_goals try simp <;> linarith
   all_goals cases k <;> simp at * <;> linarith
@@ -275,7 +276,8 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
   ext ⟨j, hj⟩
   simp at hj
   dsimp [σ, δ, Fin.predAbove, Fin.succAbove]
-  simp [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.dite_val]
+  simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
+    Fin.coe_castLT, dite_eq_ite]
   split_ifs
   any_goals simp
   all_goals linarith
@@ -314,7 +316,8 @@ theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSu
   rcases j with ⟨j, hj⟩
   simp at H hk
   dsimp [δ, σ, Fin.predAbove, Fin.succAbove]
-  simp [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.dite_val]
+  simp only [Fin.lt_iff_val_lt_val, Fin.dite_val, Fin.ite_val, Fin.coe_pred, ge_iff_le,
+    Fin.coe_castLT, dite_eq_ite, Fin.coe_castSucc, Fin.val_succ]
   split_ifs
   all_goals try simp <;> linarith
   all_goals cases k <;> simp at * <;> linarith
@@ -339,7 +342,8 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   rcases j with ⟨j, hj⟩
   simp at H hk
   dsimp [σ, Fin.predAbove]
-  simp [Fin.lt_iff_val_lt_val, Fin.ite_val]
+  simp only [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.coe_pred, ge_iff_le, dite_eq_ite,
+    Fin.coe_castLT]
   split_ifs
   all_goals try linarith
   all_goals cases k <;> simp at *; linarith

SimplexCategory used to have a universe parameter, but for already some time, it is no longer the case. However, the functor SimplexCategory.skeletalFunctor was still a functor from the simplex category to NonemptyFinLinOrdCat.{v}. This PR changes this to NonemptyFinLinOrdCat.{0}. The main consequence of this is that if C is a category, the n-simplices of the simplicial set nerve C (see AlgebraicTopology.Nerve) are now definitionally equal to Fin (n+1) ⥤ C.

@@ -352,13 +352,13 @@ section Skeleton
 /-- The functor that exhibits `SimplexCategory` as skeleton
 of `NonemptyFinLinOrd` -/
 @[simps obj map]
-def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrd.{v} where
-  obj a := NonemptyFinLinOrd.of <| ULift (Fin (a.len + 1))
-  map f := ⟨fun i => ULift.up (f.toOrderHom i.down), fun i j h => f.toOrderHom.monotone h⟩
+def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrd where
+  obj a := NonemptyFinLinOrd.of (Fin (a.len + 1))
+  map f := f.toOrderHom
 #align simplex_category.skeletal_functor SimplexCategory.skeletalFunctor
 
 theorem skeletalFunctor.coe_map {Δ₁ Δ₂ : SimplexCategory} (f : Δ₁ ⟶ Δ₂) :
-    ↑(skeletalFunctor.{v}.map f) = ULift.up ∘ f.toOrderHom ∘ ULift.down :=
+    ↑(skeletalFunctor.map f) = f.toOrderHom :=
   rfl
 #align simplex_category.skeletal_functor.coe_map SimplexCategory.skeletalFunctor.coe_map
 
@@ -367,24 +367,20 @@ theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ => by
     ext
     simpa
   apply Fintype.card_congr
-  exact Equiv.ulift.symm.trans
-    (((skeletalFunctor.{0} ⋙ forget NonemptyFinLinOrd).mapIso I).toEquiv.trans Equiv.ulift)
+  exact ((skeletalFunctor ⋙ forget NonemptyFinLinOrd).mapIso I).toEquiv
 #align simplex_category.skeletal SimplexCategory.skeletal
 
 namespace SkeletalFunctor
 
-instance : Full skeletalFunctor.{v} where
-  preimage f :=
-    SimplexCategory.Hom.mk ⟨fun i => (f (ULift.up i)).down, fun i j h => f.monotone h⟩
+instance : Full skeletalFunctor where
+  preimage f := SimplexCategory.Hom.mk f
 
-instance : Faithful skeletalFunctor.{v} where
+instance : Faithful skeletalFunctor where
   map_injective {_ _ f g} h := by
-    ext x : 3
-    apply ULift.up_injective.{v}
-    change (skeletalFunctor.{v}.map f) ⟨x⟩ = (skeletalFunctor.map g) ⟨x⟩
-    rw [h]
+    ext1
+    exact h
 
-instance : EssSurj skeletalFunctor.{v} where
+instance : EssSurj skeletalFunctor where
   mem_essImage X :=
     ⟨mk (Fintype.card X - 1 : ℕ),
       ⟨by
@@ -393,24 +389,17 @@ instance : EssSurj skeletalFunctor.{v} where
         let f := monoEquivOfFin X aux
         have hf := (Finset.univ.orderEmbOfFin aux).strictMono
         refine'
-          { hom := ⟨fun i => f i.down, _⟩
-            inv := ⟨fun i => ⟨f.symm i⟩, _⟩
-            hom_inv_id := _
-            inv_hom_id := _ }
-        · rintro ⟨i⟩ ⟨j⟩ h
-          show f i ≤ f j
-          exact hf.monotone h
-        · intro i j h
-          show f.symm i ≤ f.symm j
-          rw [← hf.le_iff_le]
-          show f (f.symm i) ≤ f (f.symm j)
-          simpa only [OrderIso.apply_symm_apply]
-        · ext1 ⟨i⟩
-          exact congr_arg ULift.up (f.symm_apply_apply i)
-        · ext1 i
-          exact f.apply_symm_apply i⟩⟩
-
-noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
+          { hom := ⟨f, hf.monotone⟩
+            inv := ⟨f.symm, _⟩
+            hom_inv_id := by ext1; apply f.symm_apply_apply
+            inv_hom_id := by ext1; apply f.apply_symm_apply }
+        intro i j h
+        show f.symm i ≤ f.symm j
+        rw [← hf.le_iff_le]
+        show f (f.symm i) ≤ f (f.symm j)
+        simpa only [OrderIso.apply_symm_apply]⟩⟩
+
+noncomputable instance isEquivalence : IsEquivalence skeletalFunctor :=
   Equivalence.ofFullyFaithfullyEssSurj skeletalFunctor
 #align simplex_category.skeletal_functor.is_equivalence SimplexCategory.SkeletalFunctor.isEquivalence
 
@@ -418,7 +407,7 @@ end SkeletalFunctor
 
 /-- The equivalence that exhibits `SimplexCategory` as skeleton
 of `NonemptyFinLinOrd` -/
-noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrd.{v} :=
+noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrd :=
   Functor.asEquivalence skeletalFunctor
 #align simplex_category.skeletal_equivalence SimplexCategory.skeletalEquivalence
 
@@ -427,7 +416,7 @@ end Skeleton
 /-- `SimplexCategory` is a skeleton of `NonemptyFinLinOrd`.
 -/
 noncomputable def isSkeletonOf :
-    IsSkeletonOf NonemptyFinLinOrd SimplexCategory skeletalFunctor.{v} where
+    IsSkeletonOf NonemptyFinLinOrd SimplexCategory skeletalFunctor where
   skel := skeletal
   eqv := SkeletalFunctor.isEquivalence
 #align simplex_category.is_skeleton_of SimplexCategory.isSkeletonOf
@@ -473,22 +462,20 @@ section EpiMono
 -/
 theorem mono_iff_injective {n m : SimplexCategory} {f : n ⟶ m} :
     Mono f ↔ Function.Injective f.toOrderHom := by
-  rw [← Functor.mono_map_iff_mono skeletalEquivalence.functor.{0}]
+  rw [← Functor.mono_map_iff_mono skeletalEquivalence.functor]
   dsimp only [skeletalEquivalence, Functor.asEquivalence_functor]
-  rw [NonemptyFinLinOrd.mono_iff_injective, skeletalFunctor.coe_map,
-    Function.Injective.of_comp_iff ULift.up_injective,
-    Function.Injective.of_comp_iff' _ ULift.down_bijective]
+  simp only [skeletalFunctor_obj, skeletalFunctor_map,
+    NonemptyFinLinOrd.mono_iff_injective, NonemptyFinLinOrd.coe_of]
 #align simplex_category.mono_iff_injective SimplexCategory.mono_iff_injective
 
 /-- A morphism in `SimplexCategory` is an epimorphism if and only if it is a surjective function
 -/
 theorem epi_iff_surjective {n m : SimplexCategory} {f : n ⟶ m} :
     Epi f ↔ Function.Surjective f.toOrderHom := by
-  rw [← Functor.epi_map_iff_epi skeletalEquivalence.functor.{0}]
+  rw [← Functor.epi_map_iff_epi skeletalEquivalence.functor]
   dsimp only [skeletalEquivalence, Functor.asEquivalence_functor]
-  rw [NonemptyFinLinOrd.epi_iff_surjective, skeletalFunctor.coe_map,
-    Function.Surjective.of_comp_iff' ULift.up_bijective,
-    Function.Surjective.of_comp_iff _ ULift.down_surjective]
+  simp only [skeletalFunctor_obj, skeletalFunctor_map,
+    NonemptyFinLinOrd.epi_iff_surjective, NonemptyFinLinOrd.coe_of]
 #align simplex_category.epi_iff_surjective SimplexCategory.epi_iff_surjective
 
 /-- A monomorphism in `SimplexCategory` must increase lengths-/
@@ -777,11 +764,11 @@ theorem len_lt_of_mono {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [hi : Mono i]
 #align simplex_category.len_lt_of_mono SimplexCategory.len_lt_of_mono
 
 noncomputable instance : SplitEpiCategory SimplexCategory :=
-  skeletalEquivalence.{0}.inverse.splitEpiCategoryImpOfIsEquivalence
+  skeletalEquivalence.inverse.splitEpiCategoryImpOfIsEquivalence
 
 instance : HasStrongEpiMonoFactorisations SimplexCategory :=
   Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence
-    SimplexCategory.skeletalEquivalence.{0}.inverse
+    SimplexCategory.skeletalEquivalence.inverse
 
 instance : HasStrongEpiImages SimplexCategory :=
   Limits.hasStrongEpiImages_of_hasStrongEpiMonoFactorisations

This reverts commit f3695eb2.

@@ -523,9 +523,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
   by_cases b ≤ i
   · use b
+    -- This was not needed before leanprover/lean4#2644
+    dsimp
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
+    -- This was not needed before leanprover/lean4#2644
+    dsimp
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
@@ -599,7 +603,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
     smallCategory_comp, σ, mkHom, OrderHom.coe_mk]
   by_cases h' : x ≤ Fin.castSucc i
-  · rw [Fin.predAbove_below i x h']
+  · -- This was not needed before leanprover/lean4#2644
+    dsimp
+    rw [Fin.predAbove_below i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
     dsimp [δ]
     erw [Fin.succAbove_below i.succ x.castPred _]
@@ -610,10 +616,12 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     let y := x.pred <| by rintro (rfl : x = 0); simp at h'
     have hy : x = y.succ := (Fin.succ_pred x _).symm
     rw [hy] at h' ⊢
+    -- This was not needed before leanprover/lean4#2644
+    conv_rhs => dsimp
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
     by_cases h'' : y = i
     · rw [h'']
-      refine' hi.symm.trans _
+      refine hi.symm.trans ?_
       congr 1
       dsimp [δ]
       erw [Fin.succAbove_below i.succ]
@@ -671,7 +679,10 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       smallCategory_comp]
     by_cases h' : θ.toOrderHom x ≤ i
     · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
-      rw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
+      -- This was not needed before leanprover/lean4#2644
+      dsimp
+      -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+      erw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_below i]
@@ -683,11 +694,16 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h'
-      simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk,
-        Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
+      -- The next three tactics used to be a simp only call before leanprover/lean4#2644
+      rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
+      erw [OrderHom.coe_mk]
+      erw [Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
-      erw [Fin.succAbove_above i _, Fin.succ_pred]
+      rw [Fin.succAbove_above i _]
+      -- This was not needed before leanprover/lean4#2644
+      conv_rhs => dsimp
+      erw [Fin.succ_pred]
       simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_pred_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)

This reverts commit 26eb2b0a.

@@ -523,13 +523,9 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
   by_cases b ≤ i
   · use b
-    -- This was not needed before leanprover/lean4#2644
-    dsimp
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
-    -- This was not needed before leanprover/lean4#2644
-    dsimp
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
@@ -603,9 +599,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
     smallCategory_comp, σ, mkHom, OrderHom.coe_mk]
   by_cases h' : x ≤ Fin.castSucc i
-  · -- This was not needed before leanprover/lean4#2644
-    dsimp
-    rw [Fin.predAbove_below i x h']
+  · rw [Fin.predAbove_below i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
     dsimp [δ]
     erw [Fin.succAbove_below i.succ x.castPred _]
@@ -616,12 +610,10 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     let y := x.pred <| by rintro (rfl : x = 0); simp at h'
     have hy : x = y.succ := (Fin.succ_pred x _).symm
     rw [hy] at h' ⊢
-    -- This was not needed before leanprover/lean4#2644
-    conv_rhs => dsimp
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
     by_cases h'' : y = i
     · rw [h'']
-      refine hi.symm.trans ?_
+      refine' hi.symm.trans _
       congr 1
       dsimp [δ]
       erw [Fin.succAbove_below i.succ]
@@ -679,10 +671,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       smallCategory_comp]
     by_cases h' : θ.toOrderHom x ≤ i
     · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
-      -- This was not needed before leanprover/lean4#2644
-      dsimp
-      -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-      erw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
+      rw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_below i]
@@ -694,16 +683,11 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h'
-      -- The next three tactics used to be a simp only call before leanprover/lean4#2644
-      rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
-      erw [OrderHom.coe_mk]
-      erw [Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
+      simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk,
+        Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
-      rw [Fin.succAbove_above i _]
-      -- This was not needed before leanprover/lean4#2644
-      conv_rhs => dsimp
-      erw [Fin.succ_pred]
+      erw [Fin.succAbove_above i _, Fin.succ_pred]
       simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_pred_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)

This includes all the changes from #7606.

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

@@ -523,9 +523,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
   by_cases b ≤ i
   · use b
+    -- This was not needed before leanprover/lean4#2644
+    dsimp
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
+    -- This was not needed before leanprover/lean4#2644
+    dsimp
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
@@ -599,7 +603,9 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
     smallCategory_comp, σ, mkHom, OrderHom.coe_mk]
   by_cases h' : x ≤ Fin.castSucc i
-  · rw [Fin.predAbove_below i x h']
+  · -- This was not needed before leanprover/lean4#2644
+    dsimp
+    rw [Fin.predAbove_below i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
     dsimp [δ]
     erw [Fin.succAbove_below i.succ x.castPred _]
@@ -610,10 +616,12 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     let y := x.pred <| by rintro (rfl : x = 0); simp at h'
     have hy : x = y.succ := (Fin.succ_pred x _).symm
     rw [hy] at h' ⊢
+    -- This was not needed before leanprover/lean4#2644
+    conv_rhs => dsimp
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
     by_cases h'' : y = i
     · rw [h'']
-      refine' hi.symm.trans _
+      refine hi.symm.trans ?_
       congr 1
       dsimp [δ]
       erw [Fin.succAbove_below i.succ]
@@ -671,7 +679,10 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       smallCategory_comp]
     by_cases h' : θ.toOrderHom x ≤ i
     · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
-      rw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
+      -- This was not needed before leanprover/lean4#2644
+      dsimp
+      -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+      erw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_below i]
@@ -683,11 +694,16 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h'
-      simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk,
-        Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
+      -- The next three tactics used to be a simp only call before leanprover/lean4#2644
+      rw [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk, OrderHom.coe_mk]
+      erw [OrderHom.coe_mk]
+      erw [Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
-      erw [Fin.succAbove_above i _, Fin.succ_pred]
+      rw [Fin.succAbove_above i _]
+      -- This was not needed before leanprover/lean4#2644
+      conv_rhs => dsimp
+      erw [Fin.succ_pred]
       simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_pred_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)

These names needn't change in the first place.

@@ -6,7 +6,7 @@ Authors: Johan Commelin, Scott Morrison, Adam Topaz
 import Mathlib.Tactic.Linarith
 import Mathlib.CategoryTheory.Skeletal
 import Mathlib.Data.Fintype.Sort
-import Mathlib.Order.Category.NonemptyFinLinOrdCat
+import Mathlib.Order.Category.NonemptyFinLinOrd
 import Mathlib.CategoryTheory.Functor.ReflectsIso
 
 #align_import algebraic_topology.simplex_category from "leanprover-community/mathlib"@"e8ac6315bcfcbaf2d19a046719c3b553206dac75"
@@ -16,7 +16,7 @@ import Mathlib.CategoryTheory.Functor.ReflectsIso
 We construct a skeletal model of the simplex category, with objects `ℕ` and the
 morphism `n ⟶ m` being the monotone maps from `Fin (n+1)` to `Fin (m+1)`.
 
-We show that this category is equivalent to `NonemptyFinLinOrdCat`.
+We show that this category is equivalent to `NonemptyFinLinOrd`.
 
 ## Remarks
 
@@ -350,10 +350,10 @@ end Generators
 section Skeleton
 
 /-- The functor that exhibits `SimplexCategory` as skeleton
-of `NonemptyFinLinOrdCat` -/
+of `NonemptyFinLinOrd` -/
 @[simps obj map]
-def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrdCat.{v} where
-  obj a := NonemptyFinLinOrdCat.of <| ULift (Fin (a.len + 1))
+def skeletalFunctor : SimplexCategory ⥤ NonemptyFinLinOrd.{v} where
+  obj a := NonemptyFinLinOrd.of <| ULift (Fin (a.len + 1))
   map f := ⟨fun i => ULift.up (f.toOrderHom i.down), fun i j h => f.toOrderHom.monotone h⟩
 #align simplex_category.skeletal_functor SimplexCategory.skeletalFunctor
 
@@ -368,7 +368,7 @@ theorem skeletal : Skeletal SimplexCategory := fun X Y ⟨I⟩ => by
     simpa
   apply Fintype.card_congr
   exact Equiv.ulift.symm.trans
-    (((skeletalFunctor.{0} ⋙ forget NonemptyFinLinOrdCat).mapIso I).toEquiv.trans Equiv.ulift)
+    (((skeletalFunctor.{0} ⋙ forget NonemptyFinLinOrd).mapIso I).toEquiv.trans Equiv.ulift)
 #align simplex_category.skeletal SimplexCategory.skeletal
 
 namespace SkeletalFunctor
@@ -417,17 +417,17 @@ noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
 end SkeletalFunctor
 
 /-- The equivalence that exhibits `SimplexCategory` as skeleton
-of `NonemptyFinLinOrdCat` -/
-noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrdCat.{v} :=
+of `NonemptyFinLinOrd` -/
+noncomputable def skeletalEquivalence : SimplexCategory ≌ NonemptyFinLinOrd.{v} :=
   Functor.asEquivalence skeletalFunctor
 #align simplex_category.skeletal_equivalence SimplexCategory.skeletalEquivalence
 
 end Skeleton
 
-/-- `SimplexCategory` is a skeleton of `NonemptyFinLinOrdCat`.
+/-- `SimplexCategory` is a skeleton of `NonemptyFinLinOrd`.
 -/
 noncomputable def isSkeletonOf :
-    IsSkeletonOf NonemptyFinLinOrdCat SimplexCategory skeletalFunctor.{v} where
+    IsSkeletonOf NonemptyFinLinOrd SimplexCategory skeletalFunctor.{v} where
   skel := skeletal
   eqv := SkeletalFunctor.isEquivalence
 #align simplex_category.is_skeleton_of SimplexCategory.isSkeletonOf
@@ -475,7 +475,7 @@ theorem mono_iff_injective {n m : SimplexCategory} {f : n ⟶ m} :
     Mono f ↔ Function.Injective f.toOrderHom := by
   rw [← Functor.mono_map_iff_mono skeletalEquivalence.functor.{0}]
   dsimp only [skeletalEquivalence, Functor.asEquivalence_functor]
-  rw [NonemptyFinLinOrdCat.mono_iff_injective, skeletalFunctor.coe_map,
+  rw [NonemptyFinLinOrd.mono_iff_injective, skeletalFunctor.coe_map,
     Function.Injective.of_comp_iff ULift.up_injective,
     Function.Injective.of_comp_iff' _ ULift.down_bijective]
 #align simplex_category.mono_iff_injective SimplexCategory.mono_iff_injective
@@ -486,7 +486,7 @@ theorem epi_iff_surjective {n m : SimplexCategory} {f : n ⟶ m} :
     Epi f ↔ Function.Surjective f.toOrderHom := by
   rw [← Functor.epi_map_iff_epi skeletalEquivalence.functor.{0}]
   dsimp only [skeletalEquivalence, Functor.asEquivalence_functor]
-  rw [NonemptyFinLinOrdCat.epi_iff_surjective, skeletalFunctor.coe_map,
+  rw [NonemptyFinLinOrd.epi_iff_surjective, skeletalFunctor.coe_map,
     Function.Surjective.of_comp_iff' ULift.up_bijective,
     Function.Surjective.of_comp_iff _ ULift.down_surjective]
 #align simplex_category.epi_iff_surjective SimplexCategory.epi_iff_surjective
@@ -801,9 +801,9 @@ end EpiMono
 to the category attached to the ordered set `{0, 1, ..., n}` -/
 @[simps! obj map]
 def toCat : SimplexCategory ⥤ Cat.{0} :=
-  SimplexCategory.skeletalFunctor ⋙ forget₂ NonemptyFinLinOrdCat LinOrdCat ⋙
-      forget₂ LinOrdCat LatCat ⋙ forget₂ LatCat PartOrdCat ⋙
-      forget₂ PartOrdCat PreordCat ⋙ preordCatToCat
+  SimplexCategory.skeletalFunctor ⋙ forget₂ NonemptyFinLinOrd LinOrd ⋙
+      forget₂ LinOrd Lat ⋙ forget₂ Lat PartOrd ⋙
+      forget₂ PartOrd Preord ⋙ preordToCat
 set_option linter.uppercaseLean3 false in
 #align simplex_category.to_Cat SimplexCategory.toCat
 

The major change here is adapting to simp failing if it makes no progress. The vast majority of the redundant simps found due to this change were extracted to #6632.

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

@@ -215,8 +215,6 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
     δ i ≫ δ j.succ = δ j ≫ δ (Fin.castSucc i) := by
   ext k
   dsimp [δ, Fin.succAbove]
-  simp only [OrderEmbedding.toOrderHom_coe, OrderEmbedding.coe_ofStrictMono, Function.comp_apply,
-    SimplexCategory.Hom.toOrderHom_mk, OrderHom.comp_coe]
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   rcases k with ⟨k, _⟩
@@ -279,7 +277,8 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
   dsimp [σ, δ, Fin.predAbove, Fin.succAbove]
   simp [Fin.lt_iff_val_lt_val, Fin.ite_val, Fin.dite_val]
   split_ifs
-  all_goals try simp <;> linarith
+  any_goals simp
+  all_goals linarith
 #align simplex_category.δ_comp_σ_self SimplexCategory.δ_comp_σ_self
 
 @[reassoc]
@@ -296,7 +295,6 @@ theorem δ_comp_σ_succ {n} {i : Fin (n + 1)} : δ i.succ ≫ σ i = 𝟙 ([n] :
   rcases i with ⟨i, _⟩
   rcases j with ⟨j, _⟩
   dsimp [δ, σ, Fin.succAbove, Fin.predAbove]
-  simp only [Fin.mk_lt_mk]
   split_ifs <;> simp <;> simp at * <;> linarith
 #align simplex_category.δ_comp_σ_succ SimplexCategory.δ_comp_σ_succ
 

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

This has nice performance benefits.

@@ -85,7 +85,7 @@ theorem mk_len (n : SimplexCategory) : ([n.len] : SimplexCategory) = n :=
 #align simplex_category.mk_len SimplexCategory.mk_len
 
 /-- A recursor for `SimplexCategory`. Use it as `induction Δ using SimplexCategory.rec`. -/
-protected def rec {F : ∀ _ : SimplexCategory, Sort _} (h : ∀ n : ℕ, F [n]) : ∀ X, F X := fun n =>
+protected def rec {F : ∀ _ : SimplexCategory, Sort*} (h : ∀ n : ℕ, F [n]) : ∀ X, F X := fun n =>
   h n.len
 #align simplex_category.rec SimplexCategory.rec
 

Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -522,7 +522,7 @@ instance {n : ℕ} {i : Fin (n + 2)} : Mono (δ i) := by
 instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   rw [epi_iff_surjective]
   intro b
-  simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
+  simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
   by_cases b ≤ i
   · use b
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
@@ -599,7 +599,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
   use δ i.succ ≫ θ
   ext1; ext1; ext1 x
   simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
-    smallCategory_comp, σ, mkHom, OrderHom.coe_fun_mk]
+    smallCategory_comp, σ, mkHom, OrderHom.coe_mk]
   by_cases h' : x ≤ Fin.castSucc i
   · rw [Fin.predAbove_below i x h']
     have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
@@ -672,7 +672,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
       smallCategory_comp]
     by_cases h' : θ.toOrderHom x ≤ i
-    · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
+    · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
           (by simpa [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
@@ -685,7 +685,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
       rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h'
-      simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk,
+      simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
           (by simpa only [Fin.castSucc_castPred h] using h')]
       dsimp [δ]

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>

@@ -225,7 +225,7 @@ 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) :
     δ i ≫ δ j =
-      δ (j.pred <| Fin.vne_of_ne fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) ≫
+      δ (j.pred <| fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) ≫
         δ (Fin.castSucc i) := by
   rw [← δ_comp_δ]
   · rw [Fin.succ_pred]
@@ -325,7 +325,7 @@ 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) :
     δ i ≫ σ j = σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
-      δ (i.pred <| Fin.vne_of_ne fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
+      δ (i.pred <| fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
   rw [← δ_comp_σ_of_gt]
   · simp
   · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
@@ -609,7 +609,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     · rwa [eq, ← Fin.le_castSucc_iff]
     rw [eq]
   · simp only [not_le] at h'
-    let y := x.pred <| Fin.vne_of_ne (by rintro (rfl : x = 0); simp at h')
+    let y := x.pred <| by rintro (rfl : x = 0); simp at h'
     have hy : x = y.succ := (Fin.succ_pred x _).symm
     rw [hy] at h' ⊢
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 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.simplex_category
-! leanprover-community/mathlib commit e8ac6315bcfcbaf2d19a046719c3b553206dac75
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Tactic.Linarith
 import Mathlib.CategoryTheory.Skeletal
@@ -14,6 +9,8 @@ import Mathlib.Data.Fintype.Sort
 import Mathlib.Order.Category.NonemptyFinLinOrdCat
 import Mathlib.CategoryTheory.Functor.ReflectsIso
 
+#align_import algebraic_topology.simplex_category from "leanprover-community/mathlib"@"e8ac6315bcfcbaf2d19a046719c3b553206dac75"
+
 /-! # The simplex category
 
 We construct a skeletal model of the simplex category, with objects `ℕ` and the

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -386,7 +386,7 @@ instance : Faithful skeletalFunctor.{v} where
   map_injective {_ _ f g} h := by
     ext x : 3
     apply ULift.up_injective.{v}
-    change (skeletalFunctor.{v}.map f) ⟨x⟩  = (skeletalFunctor.map g) ⟨x⟩
+    change (skeletalFunctor.{v}.map f) ⟨x⟩ = (skeletalFunctor.map g) ⟨x⟩
     rw [h]
 
 instance : EssSurj skeletalFunctor.{v} where

• 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>

@@ -203,7 +203,7 @@ one given by the following generators and relations.
 
 /-- The `i`-th face map from `[n]` to `[n+1]` -/
 def δ {n} (i : Fin (n + 2)) : ([n] : SimplexCategory) ⟶ [n + 1] :=
-  mkHom (Fin.succAbove i).toOrderHom
+  mkHom (Fin.succAboveEmb i).toOrderHom
 #align simplex_category.δ SimplexCategory.δ
 
 /-- The `i`-th degeneracy map from `[n+1]` to `[n]` -/
@@ -215,7 +215,7 @@ def σ {n} (i : Fin (n + 1)) : ([n + 1] : SimplexCategory) ⟶ [n] :=
 
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    δ i ≫ δ j.succ = δ j ≫ δ (Fin.castSuccEmb i) := by
+    δ i ≫ δ j.succ = δ j ≫ δ (Fin.castSucc i) := by
   ext k
   dsimp [δ, Fin.succAbove]
   simp only [OrderEmbedding.toOrderHom_coe, OrderEmbedding.coe_ofStrictMono, Function.comp_apply,
@@ -226,16 +226,17 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
 
-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) :
     δ i ≫ δ j =
-      δ (j.pred fun hj => by simp [hj, Fin.not_lt_zero] at H) ≫ δ (Fin.castSuccEmb i) := by
+      δ (j.pred <| Fin.vne_of_ne fun (hj : j = 0) => by simp [hj, Fin.not_lt_zero] at H) ≫
+        δ (Fin.castSucc i) := by
   rw [← δ_comp_δ]
   · rw [Fin.succ_pred]
   · simpa only [Fin.le_iff_val_le_val, ← Nat.lt_succ_iff, Nat.succ_eq_add_one, ← Fin.val_succ,
       j.succ_pred, Fin.lt_iff_val_lt_val] using H
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
 
-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) :
     δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
       δ j ≫ δ i := by
   rw [δ_comp_δ]
@@ -245,12 +246,12 @@ 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)} : δ i ≫ δ (Fin.castSuccEmb i) = δ i ≫ δ i.succ :=
+theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ (Fin.castSucc i) = δ i ≫ δ i.succ :=
   (δ_comp_δ (le_refl i)).symm
 #align simplex_category.δ_comp_δ_self SimplexCategory.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) :
     δ i ≫ δ j = δ i ≫ δ i.succ := by
   subst H
   rw [δ_comp_δ_self]
@@ -258,8 +259,8 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (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) :
-    δ (Fin.castSuccEmb i) ≫ σ j.succ = σ j ≫ δ i := by
+theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSucc j) :
+    δ (Fin.castSucc i) ≫ σ j.succ = σ j ≫ δ i := by
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
   ext ⟨k, hk⟩
@@ -274,7 +275,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.
 /-- The first part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
-    δ (Fin.castSuccEmb i) ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
+    δ (Fin.castSucc i) ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
   rcases i with ⟨i, hi⟩
   ext ⟨j, hj⟩
   simp at hj
@@ -285,7 +286,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
 #align simplex_category.δ_comp_σ_self SimplexCategory.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) :
     δ j ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
   subst H
   rw [δ_comp_σ_self]
@@ -311,8 +312,8 @@ 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) :
-    δ i.succ ≫ σ (Fin.castSuccEmb j) = σ j ≫ δ i := by
+theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSucc j < i) :
+    δ i.succ ≫ σ (Fin.castSucc j) = σ j ≫ δ i := by
   ext ⟨k, hk⟩
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
@@ -327,17 +328,17 @@ 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) :
     δ i ≫ σ j = σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
-      δ (i.pred fun hi => by simp only [Fin.not_lt_zero, hi] at H) := by
+      δ (i.pred <| Fin.vne_of_ne fun (hi : i = 0) => by simp only [Fin.not_lt_zero, hi] at H) := by
   rw [← δ_comp_σ_of_gt]
   · simp
-  · rw [Fin.castSuccEmb_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
+  · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'
 
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    σ (Fin.castSuccEmb i) ≫ σ j = σ j.succ ≫ σ i := by
+    σ (Fin.castSucc i) ≫ σ j = σ j.succ ≫ σ i := by
   ext ⟨k, hk⟩
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
@@ -527,13 +528,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
   by_cases b ≤ i
   · use b
-    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSuccEmb] using h)]
-    simp only [len_mk, Fin.coe_eq_castSuccEmb, Fin.castPred_castSuccEmb]
+    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
+    simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
-    simpa only [Fin.val_succ, Fin.coe_castSuccEmb] using Nat.lt.step h
+    simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
 instance : ReflectsIsomorphisms (forget SimplexCategory) :=
   ⟨fun f hf =>
@@ -596,22 +597,22 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [IsIso f] : f = 𝟙
 #align simplex_category.eq_id_of_is_iso SimplexCategory.eq_id_of_isIso
 
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
-    (i : Fin (n + 1)) (hi : θ.toOrderHom (Fin.castSuccEmb i) = θ.toOrderHom i.succ) :
+    (i : Fin (n + 1)) (hi : θ.toOrderHom (Fin.castSucc i) = θ.toOrderHom i.succ) :
     ∃ θ' : mk n ⟶ Δ', θ = σ i ≫ θ' := by
   use δ i.succ ≫ θ
   ext1; ext1; ext1 x
   simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
     smallCategory_comp, σ, mkHom, OrderHom.coe_fun_mk]
-  by_cases h' : x ≤ Fin.castSuccEmb i
+  by_cases h' : x ≤ Fin.castSucc i
   · rw [Fin.predAbove_below i x h']
-    have eq := Fin.castSuccEmb_castPred (gt_of_gt_of_ge (Fin.castSuccEmb_lt_last i) h')
+    have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
     dsimp [δ]
     erw [Fin.succAbove_below i.succ x.castPred _]
     swap
-    · rwa [eq, ← Fin.le_castSuccEmb_iff]
+    · rwa [eq, ← Fin.le_castSucc_iff]
     rw [eq]
   · simp only [not_le] at h'
-    let y := x.pred (by rintro rfl; simp at h')
+    let y := x.pred <| Fin.vne_of_ne (by rintro (rfl : x = 0); simp at h')
     have hy : x = y.succ := (Fin.succ_pred x _).symm
     rw [hy] at h' ⊢
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
@@ -624,7 +625,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       exact Fin.lt_succ
     · dsimp [δ]
       erw [Fin.succAbove_above i.succ _]
-      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSuccEmb,
+      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
         Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
       cases c
@@ -654,12 +655,12 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   rcases hθ₂ with ⟨x, y, ⟨h₁, h₂⟩⟩
   let z := x.castPred
   use z
-  rw [← show Fin.castSuccEmb z = x from
-    Fin.castSuccEmb_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
+  rw [← show Fin.castSucc z = x from
+    Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSuccEmb_lt_iff_succ_le] at h₂
+  rw [Fin.castSucc_lt_iff_succ_le] at h₂
   apply le_antisymm
-  · exact θ.toOrderHom.monotone (le_of_lt (Fin.castSuccEmb_lt_succ z))
+  · exact θ.toOrderHom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
   · rw [h₁]
     exact θ.toOrderHom.monotone h₂
 #align simplex_category.eq_σ_comp_of_not_injective SimplexCategory.eq_σ_comp_of_not_injective
@@ -676,30 +677,30 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     by_cases h' : θ.toOrderHom x ≤ i
     · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
-          (by simpa [Fin.castSuccEmb_castPred h] using h')]
+          (by simpa [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_below i]
       swap
-      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb]
+      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
         exact
           lt_of_le_of_lt (Fin.coe_castPred_le_self _)
             (Fin.lt_iff_val_lt_val.mp ((Ne.le_iff_lt (hi x)).mp h'))
-      rw [Fin.castSuccEmb_castPred]
+      rw [Fin.castSucc_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h'
       simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
-          (by simpa only [Fin.castSuccEmb_castPred h] using h')]
+          (by simpa only [Fin.castSucc_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_above i _, Fin.succ_pred]
-      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSuccEmb, Fin.coe_pred] using
+      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
         Nat.le_pred_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
     ext x : 4
     dsimp [δ, σ]
     dsimp only [Fin.castPred]
-    rw [Fin.predAbove_last, Fin.succAbove_last, Fin.castSuccEmb_castPred]
+    rw [Fin.predAbove_last, Fin.succAbove_last, Fin.castSucc_castPred]
     exact (Ne.le_iff_lt (hi x)).mp (Fin.le_last _)
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 

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

@@ -215,7 +215,7 @@ def σ {n} (i : Fin (n + 1)) : ([n + 1] : SimplexCategory) ⟶ [n] :=
 
 /-- The generic case of the first simplicial identity -/
 theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
-    δ i ≫ δ j.succ = δ j ≫ δ (Fin.castSucc i) := by
+    δ i ≫ δ j.succ = δ j ≫ δ (Fin.castSuccEmb i) := by
   ext k
   dsimp [δ, Fin.succAbove]
   simp only [OrderEmbedding.toOrderHom_coe, OrderEmbedding.coe_ofStrictMono, Function.comp_apply,
@@ -226,15 +226,16 @@ theorem δ_comp_δ {n} {i j : Fin (n + 2)} (H : i ≤ j) :
   split_ifs <;> · simp at * <;> linarith
 #align simplex_category.δ_comp_δ SimplexCategory.δ_comp_δ
 
-theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i < j) :
-    δ i ≫ δ j = δ (j.pred fun hj => by simp [hj, Fin.not_lt_zero] at H) ≫ δ (Fin.castSucc i) := by
+theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSuccEmb i < j) :
+    δ i ≫ δ j =
+      δ (j.pred fun hj => by simp [hj, Fin.not_lt_zero] at H) ≫ δ (Fin.castSuccEmb i) := by
   rw [← δ_comp_δ]
   · rw [Fin.succ_pred]
   · simpa only [Fin.le_iff_val_le_val, ← Nat.lt_succ_iff, Nat.succ_eq_add_one, ← Fin.val_succ,
       j.succ_pred, Fin.lt_iff_val_lt_val] using H
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
 
-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) :
     δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
       δ j ≫ δ i := by
   rw [δ_comp_δ]
@@ -244,12 +245,12 @@ 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)} : δ i ≫ δ (Fin.castSucc i) = δ i ≫ δ i.succ :=
+theorem δ_comp_δ_self {n} {i : Fin (n + 2)} : δ i ≫ δ (Fin.castSuccEmb i) = δ i ≫ δ i.succ :=
   (δ_comp_δ (le_refl i)).symm
 #align simplex_category.δ_comp_δ_self SimplexCategory.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) :
     δ i ≫ δ j = δ i ≫ δ i.succ := by
   subst H
   rw [δ_comp_δ_self]
@@ -257,8 +258,8 @@ theorem δ_comp_δ_self' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (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) :
-    δ (Fin.castSucc i) ≫ σ j.succ = σ j ≫ δ i := by
+theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.castSuccEmb j) :
+    δ (Fin.castSuccEmb i) ≫ σ j.succ = σ j ≫ δ i := by
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
   ext ⟨k, hk⟩
@@ -273,7 +274,7 @@ theorem δ_comp_σ_of_le {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : i ≤ Fin.
 /-- The first part of the third simplicial identity -/
 @[reassoc]
 theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
-    δ (Fin.castSucc i) ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
+    δ (Fin.castSuccEmb i) ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
   rcases i with ⟨i, hi⟩
   ext ⟨j, hj⟩
   simp at hj
@@ -284,7 +285,7 @@ theorem δ_comp_σ_self {n} {i : Fin (n + 1)} :
 #align simplex_category.δ_comp_σ_self SimplexCategory.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) :
     δ j ≫ σ i = 𝟙 ([n] : SimplexCategory) := by
   subst H
   rw [δ_comp_σ_self]
@@ -310,8 +311,8 @@ 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) :
-    δ i.succ ≫ σ (Fin.castSucc j) = σ j ≫ δ i := by
+theorem δ_comp_σ_of_gt {n} {i : Fin (n + 2)} {j : Fin (n + 1)} (H : Fin.castSuccEmb j < i) :
+    δ i.succ ≫ σ (Fin.castSuccEmb j) = σ j ≫ δ i := by
   ext ⟨k, hk⟩
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
@@ -329,14 +330,14 @@ theorem δ_comp_σ_of_gt' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : j.succ <
       δ (i.pred fun hi => by simp only [Fin.not_lt_zero, hi] at H) := by
   rw [← δ_comp_σ_of_gt]
   · simp
-  · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
+  · rw [Fin.castSuccEmb_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'
 
 /-- The fifth simplicial identity -/
 @[reassoc]
 theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
-    σ (Fin.castSucc i) ≫ σ j = σ j.succ ≫ σ i := by
+    σ (Fin.castSuccEmb i) ≫ σ j = σ j.succ ≫ σ i := by
   ext ⟨k, hk⟩
   rcases i with ⟨i, hi⟩
   rcases j with ⟨j, hj⟩
@@ -526,13 +527,13 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
   by_cases b ≤ i
   · use b
-    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
-    simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
+    rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSuccEmb] using h)]
+    simp only [len_mk, Fin.coe_eq_castSuccEmb, Fin.castPred_castSuccEmb]
   · use b.succ
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h
     rw [Fin.lt_iff_val_lt_val] at h ⊢
-    simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
+    simpa only [Fin.val_succ, Fin.coe_castSuccEmb] using Nat.lt.step h
 
 instance : ReflectsIsomorphisms (forget SimplexCategory) :=
   ⟨fun f hf =>
@@ -595,19 +596,19 @@ theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [IsIso f] : f = 𝟙
 #align simplex_category.eq_id_of_is_iso SimplexCategory.eq_id_of_isIso
 
 theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
-    (i : Fin (n + 1)) (hi : θ.toOrderHom (Fin.castSucc i) = θ.toOrderHom i.succ) :
+    (i : Fin (n + 1)) (hi : θ.toOrderHom (Fin.castSuccEmb i) = θ.toOrderHom i.succ) :
     ∃ θ' : mk n ⟶ Δ', θ = σ i ≫ θ' := by
   use δ i.succ ≫ θ
   ext1; ext1; ext1 x
   simp only [Hom.toOrderHom_mk, Function.comp_apply, OrderHom.comp_coe, Hom.comp,
     smallCategory_comp, σ, mkHom, OrderHom.coe_fun_mk]
-  by_cases h' : x ≤ Fin.castSucc i
+  by_cases h' : x ≤ Fin.castSuccEmb i
   · rw [Fin.predAbove_below i x h']
-    have eq := Fin.castSucc_castPred (gt_of_gt_of_ge (Fin.castSucc_lt_last i) h')
+    have eq := Fin.castSuccEmb_castPred (gt_of_gt_of_ge (Fin.castSuccEmb_lt_last i) h')
     dsimp [δ]
     erw [Fin.succAbove_below i.succ x.castPred _]
     swap
-    · rwa [eq, ← Fin.le_castSucc_iff]
+    · rwa [eq, ← Fin.le_castSuccEmb_iff]
     rw [eq]
   · simp only [not_le] at h'
     let y := x.pred (by rintro rfl; simp at h')
@@ -623,7 +624,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
       exact Fin.lt_succ
     · dsimp [δ]
       erw [Fin.succAbove_above i.succ _]
-      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
+      simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSuccEmb,
         Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
       cases c
@@ -653,12 +654,12 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   rcases hθ₂ with ⟨x, y, ⟨h₁, h₂⟩⟩
   let z := x.castPred
   use z
-  rw [← show Fin.castSucc z = x from
-    Fin.castSucc_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
+  rw [← show Fin.castSuccEmb z = x from
+    Fin.castSuccEmb_castPred (lt_of_lt_of_le h₂ (Fin.le_last y))] at h₁ h₂
   apply eq_σ_comp_of_not_injective'
-  rw [Fin.castSucc_lt_iff_succ_le] at h₂
+  rw [Fin.castSuccEmb_lt_iff_succ_le] at h₂
   apply le_antisymm
-  · exact θ.toOrderHom.monotone (le_of_lt (Fin.castSucc_lt_succ z))
+  · exact θ.toOrderHom.monotone (le_of_lt (Fin.castSuccEmb_lt_succ z))
   · rw [h₁]
     exact θ.toOrderHom.monotone h₂
 #align simplex_category.eq_σ_comp_of_not_injective SimplexCategory.eq_σ_comp_of_not_injective
@@ -675,30 +676,30 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
     by_cases h' : θ.toOrderHom x ≤ i
     · simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
       rw [Fin.predAbove_below (Fin.castPred i) (θ.toOrderHom x)
-          (by simpa [Fin.castSucc_castPred h] using h')]
+          (by simpa [Fin.castSuccEmb_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_below i]
       swap
-      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc]
+      · simp only [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb]
         exact
           lt_of_le_of_lt (Fin.coe_castPred_le_self _)
             (Fin.lt_iff_val_lt_val.mp ((Ne.le_iff_lt (hi x)).mp h'))
-      rw [Fin.castSucc_castPred]
+      rw [Fin.castSuccEmb_castPred]
       apply lt_of_le_of_lt h' h
     · simp only [not_le] at h'
       simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk,
         Fin.predAbove_above (Fin.castPred i) (θ.toOrderHom x)
-          (by simpa only [Fin.castSucc_castPred h] using h')]
+          (by simpa only [Fin.castSuccEmb_castPred h] using h')]
       dsimp [δ]
       erw [Fin.succAbove_above i _, Fin.succ_pred]
-      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSucc, Fin.coe_pred] using
+      simpa only [Fin.le_iff_val_le_val, Fin.coe_castSuccEmb, Fin.coe_pred] using
         Nat.le_pred_of_lt (Fin.lt_iff_val_lt_val.mp h')
   · obtain rfl := le_antisymm (Fin.le_last i) (not_lt.mp h)
     use θ ≫ σ (Fin.last _)
     ext x : 4
     dsimp [δ, σ]
     dsimp only [Fin.castPred]
-    rw [Fin.predAbove_last, Fin.succAbove_last, Fin.castSucc_castPred]
+    rw [Fin.predAbove_last, Fin.succAbove_last, Fin.castSuccEmb_castPred]
     exact (Ne.le_iff_lt (hi x)).mp (Fin.le_last _)
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -345,7 +345,7 @@ theorem σ_comp_σ {n} {i j : Fin (n + 1)} (H : i ≤ j) :
   simp [Fin.lt_iff_val_lt_val, Fin.ite_val]
   split_ifs
   all_goals try linarith
-  all_goals cases k <;> simp at * ; linarith
+  all_goals cases k <;> simp at *; linarith
 #align simplex_category.σ_comp_σ SimplexCategory.σ_comp_σ
 
 end Generators
@@ -466,7 +466,7 @@ instance : ConcreteCategory.{0} SimplexCategory where
   forget :=
     { obj := fun i => Fin (i.len + 1)
       map := fun f => f.toOrderHom }
-  forget_faithful := ⟨fun h => by ext : 2 ; exact h⟩
+  forget_faithful := ⟨fun h => by ext : 2; exact h⟩
 
 end Concrete
 
@@ -610,7 +610,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     · rwa [eq, ← Fin.le_castSucc_iff]
     rw [eq]
   · simp only [not_le] at h'
-    let y := x.pred (by rintro rfl ; simp at h')
+    let y := x.pred (by rintro rfl; simp at h')
     have hy : x = y.succ := (Fin.succ_pred x _).symm
     rw [hy] at h' ⊢
     rw [Fin.predAbove_above i y.succ h', Fin.pred_succ]
@@ -760,7 +760,7 @@ theorem len_lt_of_mono {Δ' Δ : SimplexCategory} (i : Δ' ⟶ Δ) [hi : Mono i]
   rcases lt_or_eq_of_le (len_le_of_mono hi) with (h | h)
   · exact h
   · exfalso
-    exact hi' (by ext ; exact h.symm)
+    exact hi' (by ext; exact h.symm)
 #align simplex_category.len_lt_of_mono SimplexCategory.len_lt_of_mono
 
 noncomputable instance : SplitEpiCategory SimplexCategory :=

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -408,9 +408,9 @@ instance : EssSurj skeletalFunctor.{v} where
           rw [← hf.le_iff_le]
           show f (f.symm i) ≤ f (f.symm j)
           simpa only [OrderIso.apply_symm_apply]
-        . ext1 ⟨i⟩
+        · ext1 ⟨i⟩
           exact congr_arg ULift.up (f.symm_apply_apply i)
-        . ext1 i
+        · ext1 i
           exact f.apply_symm_apply i⟩⟩
 
 noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
@@ -525,7 +525,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   intro b
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
   by_cases b ≤ i
-  . use b
+  · use b
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -531,7 +531,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   · use b.succ
     rw [Fin.predAbove_above i b.succ _, Fin.pred_succ]
     rw [not_le] at h
-    rw [Fin.lt_iff_val_lt_val] at h⊢
+    rw [Fin.lt_iff_val_lt_val] at h ⊢
     simpa only [Fin.val_succ, Fin.coe_castSucc] using Nat.lt.step h
 
 instance : ReflectsIsomorphisms (forget SimplexCategory) :=
@@ -624,7 +624,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
     · dsimp [δ]
       erw [Fin.succAbove_above i.succ _]
       simp only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc,
-        Nat.lt_succ_iff, Fin.ext_iff] at h' h''⊢
+        Nat.lt_succ_iff, Fin.ext_iff] at h' h'' ⊢
       cases' Nat.le.dest h' with c hc
       cases c
       · exfalso

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -637,7 +637,7 @@ theorem eq_σ_comp_of_not_injective' {n : ℕ} {Δ' : SimplexCategory} (θ : mk
 
 theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (n + 1) ⟶ Δ')
     (hθ : ¬Function.Injective θ.toOrderHom) :
-    ∃ (i : Fin (n + 1))(θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' := by
+    ∃ (i : Fin (n + 1)) (θ' : mk n ⟶ Δ'), θ = σ i ≫ θ' := by
   simp only [Function.Injective, exists_prop, not_forall] at hθ
   -- as θ is not injective, there exists `x<y` such that `θ x = θ y`
   -- and then, `θ x = θ (x+1)`
@@ -704,7 +704,7 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
 
 theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
     (hθ : ¬Function.Surjective θ.toOrderHom) :
-    ∃ (i : Fin (n + 2))(θ' : Δ ⟶ mk n), θ = θ' ≫ δ i := by
+    ∃ (i : Fin (n + 2)) (θ' : Δ ⟶ mk n), θ = θ' ≫ δ i := by
   cases' not_forall.mp hθ with i hi
   use i
   exact eq_comp_δ_of_not_surjective' θ i (not_exists.mp hi)

I ran codespell Mathlib and got tired halfway through the suggestions.

@@ -54,7 +54,7 @@ section
 
 
 -- porting note: the definition of `SimplexCategory` is made irreducible below
-/-- Interpet a natural number as an object of the simplex category. -/
+/-- Interpret a natural number as an object of the simplex category. -/
 def mk (n : ℕ) : SimplexCategory :=
   n
 #align simplex_category.mk SimplexCategory.mk
@@ -174,7 +174,7 @@ theorem const_comp (x y : SimplexCategory) (i : Fin (x.len + 1)) (f : x ⟶ y) :
 #align simplex_category.const_comp SimplexCategory.const_comp
 
 /-- Make a morphism `[n] ⟶ [m]` from a monotone map between fin's.
-This is useful for constructing morphisms beetween `[n]` directly
+This is useful for constructing morphisms between `[n]` directly
 without identifying `n` with `[n].len`.
 -/
 @[simp]

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -29,7 +29,7 @@ We provide the following functions to work with these objects:
 1. `SimplexCategory.mk` creates an object of `SimplexCategory` out of a natural number.
   Use the notation `[n]` in the `Simplicial` locale.
 2. `SimplexCategory.len` gives the "length" of an object of `SimplexCategory`, as a natural.
-3. `SimplexCategory.Hom.mk` makes a morphism out of a monotone map between `fin`'s.
+3. `SimplexCategory.Hom.mk` makes a morphism out of a monotone map between `Fin`'s.
 4. `SimplexCategory.Hom.toOrderHom` gives the underlying monotone map associated to a
   term of `SimplexCategory.Hom`.
 

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

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

@@ -13,7 +13,6 @@ import Mathlib.CategoryTheory.Skeletal
 import Mathlib.Data.Fintype.Sort
 import Mathlib.Order.Category.NonemptyFinLinOrdCat
 import Mathlib.CategoryTheory.Functor.ReflectsIso
-import Mathlib.Tactic.ScopedNS
 
 /-! # The simplex category
 

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

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

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

@@ -583,8 +583,12 @@ theorem iso_eq_iso_refl {x : SimplexCategory} (e : x ≅ x) : e = Iso.refl x :=
   have eq₁ := Finset.orderEmbOfFin_unique' h fun i => Finset.mem_univ ((orderIsoOfIso e) i)
   have eq₂ :=
     Finset.orderEmbOfFin_unique' h fun i => Finset.mem_univ ((orderIsoOfIso (Iso.refl x)) i)
-  ext1; ext1
-  exact congr_arg (fun φ => OrderEmbedding.toOrderHom φ) (eq₁.trans eq₂.symm)
+  -- Porting note: the proof was rewritten from this point in #3414 (reenableeta)
+  -- It could be investigated again to see if the original can be restored.
+  ext x
+  replace eq₁ := congr_arg (· x) eq₁
+  replace eq₂ := congr_arg (· x) eq₂.symm
+  simp_all
 #align simplex_category.iso_eq_iso_refl SimplexCategory.iso_eq_iso_refl
 
 theorem eq_id_of_isIso {x : SimplexCategory} (f : x ⟶ x) [IsIso f] : f = 𝟙 _ :=

I think the ports

• https://github.com/leanprover-community/mathlib4/pull/2902 (MonCat)
• https://github.com/leanprover-community/mathlib4/pull/3036 (GroupCat)
• https://github.com/leanprover-community/mathlib4/pull/3260 (ModuleCat)

didn't quite get things right, and also have some variation between them. This PR tries to straighten things out.

Major changes:

• Have the coercion to type be via X.\a, and put attribute @[coe] on this.
• Make sure the coercion from morphisms to functions means that simp lemmas about the underlying bundled morphisms apply directly.
  • This means we drop lemmas like

  lemma Hom.map_mul {X Y : MonCat} (f : X ⟶ Y) (x y : X) : ((forget MonCat).map f) (x * y) = f x * f y
  

  • But at the expense of adding lemmas like

  lemma coe_comp {X Y Z : MonCat} {f : X ⟶ Y} {g : Y ⟶ Z} : (f ≫ g : X → Z) = g ∘ f := rfl
  

Overall I'm pretty happy, and it allows me to unstick the long stuck https://github.com/leanprover-community/mathlib4/pull/3105.

This is not everything I want to do to refactor these files, but once I was satisfied that I can move forward with RingCat, I want to get this merged so we can unblock porting progress. I'll promise to come back to this soon! :-)

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

@@ -464,7 +464,7 @@ end Truncated
 section Concrete
 
 instance : ConcreteCategory.{0} SimplexCategory where
-  Forget :=
+  forget :=
     { obj := fun i => Fin (i.len + 1)
       map := fun f => f.toOrderHom }
   forget_faithful := ⟨fun h => by ext : 2 ; exact h⟩

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -700,8 +700,8 @@ theorem eq_comp_δ_of_not_surjective' {n : ℕ} {Δ : SimplexCategory} (θ : Δ
 #align simplex_category.eq_comp_δ_of_not_surjective' SimplexCategory.eq_comp_δ_of_not_surjective'
 
 theorem eq_comp_δ_of_not_surjective {n : ℕ} {Δ : SimplexCategory} (θ : Δ ⟶ mk (n + 1))
-    (hθ : ¬Function.Surjective θ.toOrderHom) : ∃ (i : Fin (n + 2))(θ' : Δ ⟶ mk n), θ = θ' ≫ δ i :=
-  by
+    (hθ : ¬Function.Surjective θ.toOrderHom) :
+    ∃ (i : Fin (n + 2))(θ' : Δ ⟶ mk n), θ = θ' ≫ δ i := by
   cases' not_forall.mp hθ with i hi
   use i
   exact eq_comp_δ_of_not_surjective' θ i (not_exists.mp hi)

@@ -94,14 +94,14 @@ protected def rec {F : ∀ _ : SimplexCategory, Sort _} (h : ∀ n : ℕ, F [n])
 #align simplex_category.rec SimplexCategory.rec
 
 -- porting note: removed @[nolint has_nonempty_instance]
-/-- Morphisms in the simplex_category. -/
+/-- Morphisms in the `SimplexCategory`. -/
 protected def Hom (a b : SimplexCategory) :=
   Fin (a.len + 1) →o Fin (b.len + 1)
 #align simplex_category.hom SimplexCategory.Hom
 
 namespace Hom
 
-/-- Make a moprhism in `SimplexCategory` from a monotone map of fin's. -/
+/-- Make a moprhism in `SimplexCategory` from a monotone map of `Fin`'s. -/
 def mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) : SimplexCategory.Hom a b :=
   f
 #align simplex_category.hom.mk SimplexCategory.Hom.mk
@@ -640,7 +640,7 @@ theorem eq_σ_comp_of_not_injective {n : ℕ} {Δ' : SimplexCategory} (θ : mk (
   -- and then, `θ x = θ (x+1)`
   have hθ₂ : ∃ x y : Fin (n + 2), (Hom.toOrderHom θ) x = (Hom.toOrderHom θ) y ∧ x < y := by
     rcases hθ with ⟨x, y, ⟨h₁, h₂⟩⟩
-    by_cases x < y
+    by_cases h : x < y
     · exact ⟨x, y, ⟨h₁, h⟩⟩
     · refine' ⟨y, x, ⟨h₁.symm, _⟩⟩
       cases' lt_or_eq_of_le (not_lt.mp h) with h' h'

From #2450:

castSucc_cast_lt is misnamed, it should be castSucc_castLt. I wonder why mathport can't align it.

This PR goes one step further and renames castLt to castLT everywhere, per https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/!4.233320/near/347567570.

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

@@ -236,7 +236,7 @@ theorem δ_comp_δ' {n} {i : Fin (n + 2)} {j : Fin (n + 3)} (H : Fin.castSucc i
 #align simplex_category.δ_comp_δ' SimplexCategory.δ_comp_δ'
 
 theorem δ_comp_δ'' {n} {i : Fin (n + 3)} {j : Fin (n + 2)} (H : i ≤ Fin.castSucc j) :
-    δ (i.castLt (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
+    δ (i.castLT (Nat.lt_of_le_of_lt (Fin.le_iff_val_le_val.mp H) j.is_lt)) ≫ δ j.succ =
       δ j ≫ δ i := by
   rw [δ_comp_δ]
   · rfl
@@ -326,11 +326,11 @@ 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) :
-    δ i ≫ σ j = σ (j.castLt ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
+    δ i ≫ σ j = σ (j.castLT ((add_lt_add_iff_right 1).mp (lt_of_lt_of_le H i.is_le))) ≫
       δ (i.pred fun hi => by simp only [Fin.not_lt_zero, hi] at H) := by
   rw [← δ_comp_σ_of_gt]
   · simp
-  · rw [Fin.castSucc_cast_lt, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
+  · rw [Fin.castSucc_castLT, ← Fin.succ_lt_succ_iff, Fin.succ_pred]
     exact H
 #align simplex_category.δ_comp_σ_of_gt' SimplexCategory.δ_comp_σ_of_gt'