algebraic_topology.dold_kan.degeneracies ⟷ Mathlib.AlgebraicTopology.DoldKan.Degeneracies

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

@@ -77,7 +77,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         by
         cases' le_iff_exists_add.mp hi with j hj
         rw [← Nat.lt_succ_iff, Nat.succ_eq_add_one, add_assoc, hj, not_lt, add_le_iff_nonpos_right,
-          nonpos_iff_eq_zero] at h 
+          nonpos_iff_eq_zero] at h
         rw [← add_left_inj 1, add_assoc, hj, self_eq_add_right, h]
       cases n
       · fin_cases i
@@ -107,10 +107,10 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         swap
         · ext; simp only [Fin.val_mk, Fin.val_succ]
         · intro j hj
-          simp only [true_and_iff, Finset.mem_univ, Finset.mem_filter] at hj 
-          simp only [Nat.succ_eq_add_one] at hi' 
+          simp only [true_and_iff, Finset.mem_univ, Finset.mem_filter] at hj
+          simp only [Nat.succ_eq_add_one] at hi'
           obtain ⟨k, hk⟩ := Nat.le.dest (nat.lt_succ_iff.mp (Fin.is_lt j))
-          rw [add_comm] at hk 
+          rw [add_comm] at hk
           have hi'' : i = Fin.castSuccEmb ⟨i, by linarith⟩ := by ext;
             simp only [Fin.castSucc_mk, Fin.eta]
           have eq :=
@@ -141,7 +141,7 @@ theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
 theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
     (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=
   by
-  rw [SimplexCategory.mono_iff_injective] at hθ 
+  rw [SimplexCategory.mono_iff_injective] at hθ
   cases n
   · exfalso
     apply hθ

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.AlgebraicTopology.DoldKan.Decomposition
-import Mathbin.Tactic.FinCases
+import AlgebraicTopology.DoldKan.Decomposition
+import Tactic.FinCases
 
 #align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -116,13 +116,12 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           have eq :=
             hq j.rev.succ
               (by
-                simp only [← hk, Fin.revPerm_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk,
-                  Fin.val_mk]
+                simp only [← hk, Fin.rev_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
                 linarith)
           rw [HomologicalComplex.comp_f, assoc, assoc, assoc, hi'',
             simplicial_object.σ_comp_σ_assoc, reassoc_of Eq, zero_comp, comp_zero, comp_zero,
             comp_zero]
-          simp only [Fin.revPerm_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
+          simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
           linarith
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -6,7 +6,7 @@ Authors: Joël Riou
 import Mathbin.AlgebraicTopology.DoldKan.Decomposition
 import Mathbin.Tactic.FinCases
 
-#align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+#align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -26,6 +26,8 @@ if `X : simplicial_object C` with `C` a preadditive category,
 `X.map θ.op ≫ P_infty.f n = 0`. It follows from the more precise
 statement vanishing statement `σ_comp_P_eq_zero` for the `P q`.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 

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

@@ -88,11 +88,11 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           Fin.sum_univ_succ, Fin.sum_univ_two]
         simp only [pow_zero, pow_one, pow_two, Fin.val_zero, Fin.val_one, Fin.val_two, one_zsmul,
           neg_zsmul, Fin.mk_zero, Fin.mk_one, Fin.val_succ, pow_add, one_mul, neg_mul, neg_neg,
-          Fin.succ_zero_eq_one, Fin.succ_one_eq_two, comp_neg, neg_comp, add_comp, comp_add]
+          Fin.succ_zero_eq_one', Fin.succ_one_eq_two', comp_neg, neg_comp, add_comp, comp_add]
         erw [simplicial_object.δ_comp_σ_self, simplicial_object.δ_comp_σ_self_assoc,
           simplicial_object.δ_comp_σ_succ, comp_id,
           simplicial_object.δ_comp_σ_of_le X
-            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSucc_zero]),
+            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSucc_zero']),
           simplicial_object.δ_comp_σ_self_assoc, simplicial_object.δ_comp_σ_succ_assoc]
         abel
       · rw [← id_comp (X.σ i), ← (P_add_Q_f q n.succ : _ = 𝟙 (X.obj _)), add_comp, add_comp]

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.degeneracies
-! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.Decomposition
 import Mathbin.Tactic.FinCases
 
+#align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+
 /-!
 
 # Behaviour of P_infty with respect to degeneracies

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

@@ -95,7 +95,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         erw [simplicial_object.δ_comp_σ_self, simplicial_object.δ_comp_σ_self_assoc,
           simplicial_object.δ_comp_σ_succ, comp_id,
           simplicial_object.δ_comp_σ_of_le X
-            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSuccEmb_zero]),
+            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSucc_zero]),
           simplicial_object.δ_comp_σ_self_assoc, simplicial_object.δ_comp_σ_succ_assoc]
         abel
       · rw [← id_comp (X.σ i), ← (P_add_Q_f q n.succ : _ = 𝟙 (X.obj _)), add_comp, add_comp]
@@ -113,7 +113,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           obtain ⟨k, hk⟩ := Nat.le.dest (nat.lt_succ_iff.mp (Fin.is_lt j))
           rw [add_comm] at hk 
           have hi'' : i = Fin.castSuccEmb ⟨i, by linarith⟩ := by ext;
-            simp only [Fin.castSuccEmb_mk, Fin.eta]
+            simp only [Fin.castSucc_mk, Fin.eta]
           have eq :=
             hq j.rev.succ
               (by

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

@@ -95,7 +95,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         erw [simplicial_object.δ_comp_σ_self, simplicial_object.δ_comp_σ_self_assoc,
           simplicial_object.δ_comp_σ_succ, comp_id,
           simplicial_object.δ_comp_σ_of_le X
-            (show (0 : Fin 2) ≤ Fin.castSucc 0 by rw [Fin.castSucc_zero]),
+            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSuccEmb_zero]),
           simplicial_object.δ_comp_σ_self_assoc, simplicial_object.δ_comp_σ_succ_assoc]
         abel
       · rw [← id_comp (X.σ i), ← (P_add_Q_f q n.succ : _ = 𝟙 (X.obj _)), add_comp, add_comp]
@@ -112,8 +112,8 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           simp only [Nat.succ_eq_add_one] at hi' 
           obtain ⟨k, hk⟩ := Nat.le.dest (nat.lt_succ_iff.mp (Fin.is_lt j))
           rw [add_comm] at hk 
-          have hi'' : i = Fin.castSucc ⟨i, by linarith⟩ := by ext;
-            simp only [Fin.castSucc_mk, Fin.eta]
+          have hi'' : i = Fin.castSuccEmb ⟨i, by linarith⟩ := by ext;
+            simp only [Fin.castSuccEmb_mk, Fin.eta]
           have eq :=
             hq j.rev.succ
               (by

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

@@ -117,12 +117,13 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           have eq :=
             hq j.rev.succ
               (by
-                simp only [← hk, Fin.rev_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
+                simp only [← hk, Fin.revPerm_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk,
+                  Fin.val_mk]
                 linarith)
           rw [HomologicalComplex.comp_f, assoc, assoc, assoc, hi'',
             simplicial_object.σ_comp_σ_assoc, reassoc_of Eq, zero_comp, comp_zero, comp_zero,
             comp_zero]
-          simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
+          simp only [Fin.revPerm_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
           linarith
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
 -/

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

@@ -43,6 +43,7 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C]
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ /-
 theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ} {φ : Y ⟶ X _[n + 1]}
     (v : HigherFacesVanish q φ) (hnbq : n + 1 = b + q) :
     HigherFacesVanish q
@@ -59,7 +60,9 @@ theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ}
       add_le_add_iff_right]
     linarith
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ
+-/
 
+#print AlgebraicTopology.DoldKan.σ_comp_P_eq_zero /-
 theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1)) (hi : n + 1 ≤ i + q) :
     X.σ i ≫ (P q).f (n + 1) = 0 :=
   by
@@ -122,7 +125,9 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
           linarith
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
+-/
 
+#print AlgebraicTopology.DoldKan.σ_comp_PInfty /-
 @[simp, reassoc]
 theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ PInfty.f (n + 1) = 0 :=
@@ -130,7 +135,9 @@ theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
   rw [P_infty_f, σ_comp_P_eq_zero X i]
   simp only [le_add_iff_nonneg_left, zero_le]
 #align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInfty
+-/
 
+#print AlgebraicTopology.DoldKan.degeneracy_comp_PInfty /-
 @[reassoc]
 theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
     (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=
@@ -146,6 +153,7 @@ theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : Simplex
     rw [h, op_comp, X.map_comp, assoc, show X.map (SimplexCategory.σ i).op = X.σ i by rfl,
       σ_comp_P_infty, comp_zero]
 #align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_PInfty
+-/
 
 end DoldKan
 

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

@@ -32,8 +32,8 @@ statement vanishing statement `σ_comp_P_eq_zero` for the `P q`.
 -/
 
 
-open
-  CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Preadditive Opposite
+open CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Preadditive
+  Opposite
 
 open scoped Simplicial DoldKan
 
@@ -75,7 +75,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         by
         cases' le_iff_exists_add.mp hi with j hj
         rw [← Nat.lt_succ_iff, Nat.succ_eq_add_one, add_assoc, hj, not_lt, add_le_iff_nonpos_right,
-          nonpos_iff_eq_zero] at h
+          nonpos_iff_eq_zero] at h 
         rw [← add_left_inj 1, add_assoc, hj, self_eq_add_right, h]
       cases n
       · fin_cases i
@@ -105,10 +105,10 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         swap
         · ext; simp only [Fin.val_mk, Fin.val_succ]
         · intro j hj
-          simp only [true_and_iff, Finset.mem_univ, Finset.mem_filter] at hj
-          simp only [Nat.succ_eq_add_one] at hi'
+          simp only [true_and_iff, Finset.mem_univ, Finset.mem_filter] at hj 
+          simp only [Nat.succ_eq_add_one] at hi' 
           obtain ⟨k, hk⟩ := Nat.le.dest (nat.lt_succ_iff.mp (Fin.is_lt j))
-          rw [add_comm] at hk
+          rw [add_comm] at hk 
           have hi'' : i = Fin.castSucc ⟨i, by linarith⟩ := by ext;
             simp only [Fin.castSucc_mk, Fin.eta]
           have eq :=
@@ -135,7 +135,7 @@ theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
 theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
     (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=
   by
-  rw [SimplexCategory.mono_iff_injective] at hθ
+  rw [SimplexCategory.mono_iff_injective] at hθ 
   cases n
   · exfalso
     apply hθ

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

@@ -35,7 +35,7 @@ statement vanishing statement `σ_comp_P_eq_zero` for the `P q`.
 open
   CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Preadditive Opposite
 
-open Simplicial DoldKan
+open scoped Simplicial DoldKan
 
 namespace AlgebraicTopology
 

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

@@ -43,9 +43,6 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C]
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_σ -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σₓ'. -/
 theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ} {φ : Y ⟶ X _[n + 1]}
     (v : HigherFacesVanish q φ) (hnbq : n + 1 = b + q) :
     HigherFacesVanish q
@@ -63,9 +60,6 @@ theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ}
     linarith
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ
 
-/- warning: algebraic_topology.dold_kan.σ_comp_P_eq_zero -> AlgebraicTopology.DoldKan.σ_comp_P_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zeroₓ'. -/
 theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1)) (hi : n + 1 ≤ i + q) :
     X.σ i ≫ (P q).f (n + 1) = 0 :=
   by
@@ -129,9 +123,6 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           linarith
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
 
-/- warning: algebraic_topology.dold_kan.σ_comp_P_infty -> AlgebraicTopology.DoldKan.σ_comp_PInfty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInftyₓ'. -/
 @[simp, reassoc]
 theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ PInfty.f (n + 1) = 0 :=
@@ -140,9 +131,6 @@ theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
   simp only [le_add_iff_nonneg_left, zero_le]
 #align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInfty
 
-/- warning: algebraic_topology.dold_kan.degeneracy_comp_P_infty -> AlgebraicTopology.DoldKan.degeneracy_comp_PInfty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_PInftyₓ'. -/
 @[reassoc]
 theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
     (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=

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

@@ -109,16 +109,13 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
           comp_id, v.comp_Hσ_eq hi', assoc, simplicial_object.δ_comp_σ_succ'_assoc, Fin.eta,
           decomposition_Q n q, sum_comp, sum_comp, Finset.sum_eq_zero, add_zero, add_neg_eq_zero]
         swap
-        · ext
-          simp only [Fin.val_mk, Fin.val_succ]
+        · ext; simp only [Fin.val_mk, Fin.val_succ]
         · intro j hj
           simp only [true_and_iff, Finset.mem_univ, Finset.mem_filter] at hj
           simp only [Nat.succ_eq_add_one] at hi'
           obtain ⟨k, hk⟩ := Nat.le.dest (nat.lt_succ_iff.mp (Fin.is_lt j))
           rw [add_comm] at hk
-          have hi'' : i = Fin.castSucc ⟨i, by linarith⟩ :=
-            by
-            ext
+          have hi'' : i = Fin.castSucc ⟨i, by linarith⟩ := by ext;
             simp only [Fin.castSucc_mk, Fin.eta]
           have eq :=
             hq j.rev.succ

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

@@ -44,10 +44,7 @@ namespace DoldKan
 variable {C : Type _} [Category C] [Preadditive C]
 
 /- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_σ -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {Y : C} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {b : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))}, (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (forall (hnbq : Eq.{1} Nat (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)))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σₓ'. -/
 theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ} {φ : Y ⟶ X _[n + 1]}
     (v : HigherFacesVanish q φ) (hnbq : n + 1 = b + q) :
@@ -67,10 +64,7 @@ theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ}
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zeroₓ'. -/
 theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1)) (hi : n + 1 ≤ i + q) :
     X.σ i ≫ (P q).f (n + 1) = 0 :=
@@ -139,10 +133,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
 
 /- warning: algebraic_topology.dold_kan.σ_comp_P_infty -> AlgebraicTopology.DoldKan.σ_comp_PInfty is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInftyₓ'. -/
 @[simp, reassoc]
 theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
@@ -153,10 +144,7 @@ theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
 #align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInfty
 
 /- warning: algebraic_topology.dold_kan.degeneracy_comp_P_infty -> AlgebraicTopology.DoldKan.degeneracy_comp_PInfty is a dubious translation:
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(Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.map.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ' θ)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) n)) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (OfNat.mk.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (Zero.zero.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n))))))
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat) {Δ' : SimplexCategory} (θ : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ'), (Not (CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (SimplexCategory.mk n) Δ' θ)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ' θ)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) n)) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (Zero.toOfNat0.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_PInftyₓ'. -/
 @[reassoc]
 theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}

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

@@ -144,7 +144,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n i) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 0 (Zero.toOfNat0.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInftyₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ PInfty.f (n + 1) = 0 :=
   by
@@ -158,7 +158,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat) {Δ' : SimplexCategory} (θ : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ'), (Not (CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (SimplexCategory.mk n) Δ' θ)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ' θ)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) n)) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (Zero.toOfNat0.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_PInftyₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
     (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=
   by

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

@@ -45,7 +45,7 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 /- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_σ -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {Y : C} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {b : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))}, (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (forall (hnbq : Eq.{1} Nat (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)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)), AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y (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)))) q (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) φ (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.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)))) b (Eq.mpr.{0} (LT.lt.{0} Nat Nat.hasLt b (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} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (LT.lt.{0} Nat Nat.hasLt b (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} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q)) (Eq.trans.{1} Prop (LT.lt.{0} Nat Nat.hasLt b (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} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)) (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q) (Eq.trans.{1} Prop (LT.lt.{0} Nat Nat.hasLt b (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))))) (LT.lt.{0} Nat Nat.hasLt b (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) b q) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)) ((fun [self : LT.{0} Nat] (ᾰ : Nat) (ᾰ_1 : Nat) (e_2 : Eq.{1} Nat ᾰ ᾰ_1) (ᾰ_2 : Nat) (ᾰ_3 : Nat) (e_3 : Eq.{1} Nat ᾰ_2 ᾰ_3) => congr.{1, 1} Nat Prop (LT.lt.{0} Nat self ᾰ) (LT.lt.{0} Nat self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{1, 1} Nat (Nat -> Prop) ᾰ ᾰ_1 (LT.lt.{0} Nat self) e_2) e_3) Nat.hasLt b b (rfl.{1} Nat b) (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)))) (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) b q) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) ((fun [self : Add.{0} Nat] (ᾰ : Nat) (ᾰ_1 : Nat) (e_2 : Eq.{1} Nat ᾰ ᾰ_1) (ᾰ_2 : Nat) (ᾰ_3 : Nat) (e_3 : Eq.{1} Nat ᾰ_2 ᾰ_3) => congr.{1, 1} Nat Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat self) ᾰ) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat self) ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{1, 1} Nat (Nat -> Nat) ᾰ ᾰ_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat self)) e_2) e_3) 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)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q) hnbq (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))) (rfl.{1} Nat (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (propext (LT.lt.{0} Nat Nat.hasLt b (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q))) (LE.le.{0} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)) (Nat.lt_succ_iff b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)))) (propext (LE.le.{0} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) b q)) (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q) (le_add_iff_nonneg_right.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) Nat.hasLe (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)) (AddLeftCancelSemigroup.contravariant_add_le_of_contravariant_add_lt.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedCancelAddCommMonoid.to_contravariantClass_left.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) b q)))) (Eq.mp.{0} (LE.le.{0} Nat (Preorder.toLE.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedAddCommMonoid.toPartialOrder.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat (AddCommMonoid.toAddMonoid.{0} Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))))))) q) (LE.le.{0} Nat (Preorder.toLE.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedAddCommMonoid.toPartialOrder.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat (AddCommMonoid.toAddMonoid.{0} Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))))))) q) (rfl.{1} Prop (LE.le.{0} Nat (Preorder.toLE.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedAddCommMonoid.toPartialOrder.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat (AddCommMonoid.toAddMonoid.{0} Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))))))) q)) (zero_le.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) q)))))))
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {Y : C} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {b : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))}, (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (forall (hnbq : Eq.{1} Nat (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)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)), AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y (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)))) q (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) φ (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.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)))) b (Eq.mpr.{0} (LT.lt.{0} Nat Nat.hasLt b (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} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (LT.lt.{0} Nat Nat.hasLt b (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} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q)) (Eq.trans.{1} Prop (LT.lt.{0} Nat Nat.hasLt b (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} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)) (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q) (Eq.trans.{1} Prop (LT.lt.{0} Nat Nat.hasLt b (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))))) (LT.lt.{0} Nat Nat.hasLt b (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) b q) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)) ((fun [self : LT.{0} Nat] (ᾰ : Nat) (ᾰ_1 : Nat) (e_2 : Eq.{1} Nat ᾰ ᾰ_1) (ᾰ_2 : Nat) (ᾰ_3 : Nat) (e_3 : Eq.{1} Nat ᾰ_2 ᾰ_3) => congr.{1, 1} Nat Prop (LT.lt.{0} Nat self ᾰ) (LT.lt.{0} Nat self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{1, 1} Nat (Nat -> Prop) ᾰ ᾰ_1 (LT.lt.{0} Nat self) e_2) e_3) Nat.hasLt b b (rfl.{1} Nat b) (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)))) (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) b q) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) ((fun [self : Add.{0} Nat] (ᾰ : Nat) (ᾰ_1 : Nat) (e_2 : Eq.{1} Nat ᾰ ᾰ_1) (ᾰ_2 : Nat) (ᾰ_3 : Nat) (e_3 : Eq.{1} Nat ᾰ_2 ᾰ_3) => congr.{1, 1} Nat Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat self) ᾰ) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat self) ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{1, 1} Nat (Nat -> Nat) ᾰ ᾰ_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat self)) e_2) e_3) 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)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q) hnbq (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))) (rfl.{1} Nat (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (propext (LT.lt.{0} Nat Nat.hasLt b (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q))) (LE.le.{0} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)) (Nat.lt_succ_iff b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)))) (propext (LE.le.{0} Nat Nat.hasLe b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) b q)) (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) q) (le_add_iff_nonneg_right.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) Nat.hasLe (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)) (AddLeftCancelSemigroup.contravariant_add_le_of_contravariant_add_lt.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedCancelAddCommMonoid.to_contravariantClass_left.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) b q)))) (Eq.mp.{0} (LE.le.{0} Nat (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedAddCommMonoid.toPartialOrder.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat (AddCommMonoid.toAddMonoid.{0} Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))))))) q) (LE.le.{0} Nat (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedAddCommMonoid.toPartialOrder.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat (AddCommMonoid.toAddMonoid.{0} Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))))))) q) (rfl.{1} Prop (LE.le.{0} Nat (Preorder.toHasLe.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedAddCommMonoid.toPartialOrder.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat (AddCommMonoid.toAddMonoid.{0} Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} Nat (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring))))))))) q)) (zero_le.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) q)))))))
 but is expected to have type
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {Y : C} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {b : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))}, (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (forall (hnbq : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q)), AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) q (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) φ (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.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))) b (of_eq_true (LT.lt.{0} Nat instLTNat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.trans.{1} Prop (LT.lt.{0} Nat instLTNat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 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} Nat instLENat (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) q) True (Eq.trans.{1} Prop (LT.lt.{0} Nat instLTNat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 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} Nat instLENat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q)) (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) q) (Eq.trans.{1} Prop (LT.lt.{0} Nat instLTNat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LT.lt.{0} Nat instLTNat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LE.le.{0} Nat instLENat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q)) (congrArg.{1, 1} Nat Prop (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (LT.lt.{0} Nat instLTNat b) (congrFun.{1, 1} Nat (fun (a._@.Init.Prelude._hyg.2296 : Nat) => Nat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q)) (congrArg.{1, 1} Nat (Nat -> Nat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat)) hnbq) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Mathlib.AlgebraicTopology.DoldKan.Degeneracies._auxLemma.1 b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) b q))) (Mathlib.AlgebraicTopology.DoldKan.Degeneracies._auxLemma.2.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) instLENat (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)) (AddLeftCancelSemigroup.contravariant_add_le_of_contravariant_add_lt.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedCancelAddCommMonoid.to_contravariantClass_left.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) b q)) (Mathlib.AlgebraicTopology.DoldKan.Degeneracies._auxLemma.3.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) q)))))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 
 ! This file was ported from Lean 3 source module algebraic_topology.dold_kan.degeneracies
-! leanprover-community/mathlib commit ec1c7d810034d4202b0dd239112d1792be9f6fdc
+! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Tactic.FinCases
 
 # Behaviour of P_infty with respect to degeneracies
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 For any `X : simplicial_object C` where `C` is an abelian category,
 the projector `P_infty : K[X] ⟶ K[X]` is supposed to be the projection
 on the normalized subcomplex, parallel to the degenerate subcomplex, i.e.

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

@@ -40,6 +40,12 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C]
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_σ -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {Y : C} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {b : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))}, (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (forall (hnbq : Eq.{1} Nat (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)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) b q)), AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y (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)))) q (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk 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+but is expected to have type
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instLENat (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)) (AddLeftCancelSemigroup.contravariant_add_le_of_contravariant_add_lt.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedCancelAddCommMonoid.to_contravariantClass_left.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) b q)) (Mathlib.AlgebraicTopology.DoldKan.Degeneracies._auxLemma.3.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring) q)))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σₓ'. -/
 theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ} {φ : Y ⟶ X _[n + 1]}
     (v : HigherFacesVanish q φ) (hnbq : n + 1 = b + q) :
     HigherFacesVanish q
@@ -57,7 +63,13 @@ theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ}
     linarith
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ
 
-theorem σ_comp_p_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1)) (hi : n + 1 ≤ i + q) :
+/- warning: algebraic_topology.dold_kan.σ_comp_P_eq_zero -> AlgebraicTopology.DoldKan.σ_comp_P_eq_zero is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))) 0 (Zero.zero.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) {n : Nat} {q : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), (LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) q)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat 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(SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat 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(CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) 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(CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zeroₓ'. -/
+theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1)) (hi : n + 1 ≤ i + q) :
     X.σ i ≫ (P q).f (n + 1) = 0 :=
   by
   induction' q with q hq generalizing i hi
@@ -121,18 +133,30 @@ theorem σ_comp_p_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
             comp_zero]
           simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
           linarith
-#align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_p_eq_zero
-
+#align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
+
+/- warning: algebraic_topology.dold_kan.σ_comp_P_infty -> AlgebraicTopology.DoldKan.σ_comp_PInfty is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInftyₓ'. -/
 @[simp, reassoc.1]
-theorem σ_comp_pInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
+theorem σ_comp_PInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
     X.σ i ≫ PInfty.f (n + 1) = 0 :=
   by
   rw [P_infty_f, σ_comp_P_eq_zero X i]
   simp only [le_add_iff_nonneg_left, zero_le]
-#align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_pInfty
-
+#align algebraic_topology.dold_kan.σ_comp_P_infty AlgebraicTopology.DoldKan.σ_comp_PInfty
+
+/- warning: algebraic_topology.dold_kan.degeneracy_comp_P_infty -> AlgebraicTopology.DoldKan.degeneracy_comp_PInfty is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat) {Δ' : SimplexCategory} (θ : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ'), (Not (CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (SimplexCategory.mk n) Δ' θ)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.map.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ' θ)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) n)) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (OfNat.mk.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (Zero.zero.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n))))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat) {Δ' : SimplexCategory} (θ : Quiver.Hom.{1, 0} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ'), (Not (CategoryTheory.Mono.{0, 0} SimplexCategory SimplexCategory.smallCategory (SimplexCategory.mk n) Δ' θ)) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (Prefunctor.map.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ') (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)) (Quiver.Hom.op.{0, 1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{0, 0} SimplexCategory SimplexCategory.smallCategory)) (SimplexCategory.mk n) Δ' θ)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} C _inst_1 _inst_2 X) n)) (OfNat.ofNat.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) 0 (Zero.toOfNat0.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory Δ')) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n)))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_PInftyₓ'. -/
 @[reassoc.1]
-theorem degeneracy_comp_pInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
+theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
     (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=
   by
   rw [SimplexCategory.mono_iff_injective] at hθ
@@ -145,7 +169,7 @@ theorem degeneracy_comp_pInfty (X : SimplicialObject C) (n : ℕ) {Δ' : Simplex
   · obtain ⟨i, α, h⟩ := SimplexCategory.eq_σ_comp_of_not_injective θ hθ
     rw [h, op_comp, X.map_comp, assoc, show X.map (SimplexCategory.σ i).op = X.σ i by rfl,
       σ_comp_P_infty, comp_zero]
-#align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_pInfty
+#align algebraic_topology.dold_kan.degeneracy_comp_P_infty AlgebraicTopology.DoldKan.degeneracy_comp_PInfty
 
 end DoldKan
 

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

@@ -125,7 +125,7 @@ theorem σ_comp_p_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
 
 @[simp, reassoc.1]
 theorem σ_comp_pInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
-    X.σ i ≫ pInfty.f (n + 1) = 0 :=
+    X.σ i ≫ PInfty.f (n + 1) = 0 :=
   by
   rw [P_infty_f, σ_comp_P_eq_zero X i]
   simp only [le_add_iff_nonneg_left, zero_le]
@@ -133,7 +133,7 @@ theorem σ_comp_pInfty (X : SimplicialObject C) {n : ℕ} (i : Fin (n + 1)) :
 
 @[reassoc.1]
 theorem degeneracy_comp_pInfty (X : SimplicialObject C) (n : ℕ) {Δ' : SimplexCategory}
-    (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ pInfty.f n = 0 :=
+    (θ : [n] ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 :=
   by
   rw [SimplexCategory.mono_iff_injective] at hθ
   cases n

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

@@ -58,7 +58,7 @@ theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ}
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ
 
 theorem σ_comp_p_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1)) (hi : n + 1 ≤ i + q) :
-    X.σ i ≫ (p q).f (n + 1) = 0 :=
+    X.σ i ≫ (P q).f (n + 1) = 0 :=
   by
   induction' q with q hq generalizing i hi
   · exfalso

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 
 ! This file was ported from Lean 3 source module algebraic_topology.dold_kan.degeneracies
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit ec1c7d810034d4202b0dd239112d1792be9f6fdc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.Decomposition
+import Mathbin.Tactic.FinCases
 
 /-!
 

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

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.

@@ -72,7 +72,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
       rcases n with _|n
       · fin_cases i
         dsimp at h hi
-        rw [show q = 0 by linarith]
+        rw [show q = 0 by omega]
         change X.σ 0 ≫ (P 1).f 1 = 0
         simp only [P_succ, HomologicalComplex.add_f_apply, comp_add,
           HomologicalComplex.id_f, AlternatingFaceMapComplex.obj_d_eq, Hσ,
@@ -102,17 +102,17 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         simp only [Nat.succ_eq_add_one] at hi
         obtain ⟨k, hk⟩ := Nat.le.dest (Nat.lt_succ_iff.mp (Fin.is_lt j))
         rw [add_comm] at hk
-        have hi' : i = Fin.castSucc ⟨i, by linarith⟩ := by
+        have hi' : i = Fin.castSucc ⟨i, by omega⟩ := by
           ext
           simp only [Fin.castSucc_mk, Fin.eta]
         have eq := hq j.rev.succ (by
           simp only [← hk, Fin.rev_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
-          linarith)
+          omega)
         rw [HomologicalComplex.comp_f, assoc, assoc, assoc, hi',
           SimplicialObject.σ_comp_σ_assoc, reassoc_of% eq, zero_comp, comp_zero, comp_zero,
           comp_zero]
         simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
-        linarith
+        omega
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero
 

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

@@ -62,7 +62,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
     exfalso
     linarith [Fin.is_lt i]
   · intro i (hi : n + 1 ≤ i + q + 1)
-    by_cases n + 1 ≤ (i : ℕ) + q
+    by_cases h : n + 1 ≤ (i : ℕ) + q
     · rw [P_succ, HomologicalComplex.comp_f, ← assoc, hq i h, zero_comp]
     · replace hi : n = i + q := by
         obtain ⟨j, hj⟩ := le_iff_exists_add.mp hi

Some theorems in Data.Fin.Basic are copied to Std at the recent commit in Std. These are written using Fin.cast and Fin.rev, so declarations using Fin.castIso and Fin.revPerm in Mathlib should be rewritten.

Co-authored-by: Pol'tta / Miyahara Kō <52843868+Komyyy@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -105,13 +105,13 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         have hi' : i = Fin.castSucc ⟨i, by linarith⟩ := by
           ext
           simp only [Fin.castSucc_mk, Fin.eta]
-        have eq := hq j.revPerm.succ (by
-          simp only [← hk, Fin.revPerm_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
+        have eq := hq j.rev.succ (by
+          simp only [← hk, Fin.rev_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
           linarith)
         rw [HomologicalComplex.comp_f, assoc, assoc, assoc, hi',
           SimplicialObject.σ_comp_σ_assoc, reassoc_of% eq, zero_comp, comp_zero, comp_zero,
           comp_zero]
-        simp only [Fin.revPerm_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
+        simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
         linarith
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero

@@ -6,7 +6,7 @@ Authors: Joël Riou
 import Mathlib.AlgebraicTopology.DoldKan.Decomposition
 import Mathlib.Tactic.FinCases
 
-#align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"ec1c7d810034d4202b0dd239112d1792be9f6fdc"
+#align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 

In this PR (which is a forward port of https://github.com/leanprover-community/mathlib/pull/17926), the Dold-Kan equivalence between simplicial objects and chain complexes in abelian categories is constructed.

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

@@ -23,6 +23,8 @@ if `X : SimplicialObject C` with `C` a preadditive category,
 `X.map θ.op ≫ P_infty.f n = 0`. It follows from the more precise
 statement vanishing statement `σ_comp_P_eq_zero` for the `P q`.
 
+(See `Equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C]
+variable {C : Type*} [Category C] [Preadditive C]
 
 theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ} {φ : Y ⟶ X _[n + 1]}
     (v : HigherFacesVanish q φ) (hnbq : n + 1 = b + q) :

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.degeneracies
-! leanprover-community/mathlib commit ec1c7d810034d4202b0dd239112d1792be9f6fdc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.Decomposition
 import Mathlib.Tactic.FinCases
 
+#align_import algebraic_topology.dold_kan.degeneracies from "leanprover-community/mathlib"@"ec1c7d810034d4202b0dd239112d1792be9f6fdc"
+
 /-!
 
 # Behaviour of P_infty with respect to degeneracies

• 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>

@@ -88,7 +88,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         erw [SimplicialObject.δ_comp_σ_self, SimplicialObject.δ_comp_σ_self_assoc,
           SimplicialObject.δ_comp_σ_succ, comp_id,
           SimplicialObject.δ_comp_σ_of_le X
-            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSuccEmb_zero]),
+            (show (0 : Fin 2) ≤ Fin.castSucc 0 by rw [Fin.castSucc_zero]),
           SimplicialObject.δ_comp_σ_self_assoc, SimplicialObject.δ_comp_σ_succ_assoc]
         simp only [add_right_neg, add_zero, zero_add]
       · rw [← id_comp (X.σ i), ← (P_add_Q_f q n.succ : _ = 𝟙 (X.obj _)), add_comp, add_comp,
@@ -103,9 +103,9 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         simp only [Nat.succ_eq_add_one] at hi
         obtain ⟨k, hk⟩ := Nat.le.dest (Nat.lt_succ_iff.mp (Fin.is_lt j))
         rw [add_comm] at hk
-        have hi' : i = Fin.castSuccEmb ⟨i, by linarith⟩ := by
+        have hi' : i = Fin.castSucc ⟨i, by linarith⟩ := by
           ext
-          simp only [Fin.castSuccEmb_mk, Fin.eta]
+          simp only [Fin.castSucc_mk, Fin.eta]
         have eq := hq j.revPerm.succ (by
           simp only [← hk, Fin.revPerm_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
           linarith)

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

@@ -88,7 +88,7 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         erw [SimplicialObject.δ_comp_σ_self, SimplicialObject.δ_comp_σ_self_assoc,
           SimplicialObject.δ_comp_σ_succ, comp_id,
           SimplicialObject.δ_comp_σ_of_le X
-            (show (0 : Fin 2) ≤ Fin.castSucc 0 by rw [Fin.castSucc_zero]),
+            (show (0 : Fin 2) ≤ Fin.castSuccEmb 0 by rw [Fin.castSuccEmb_zero]),
           SimplicialObject.δ_comp_σ_self_assoc, SimplicialObject.δ_comp_σ_succ_assoc]
         simp only [add_right_neg, add_zero, zero_add]
       · rw [← id_comp (X.σ i), ← (P_add_Q_f q n.succ : _ = 𝟙 (X.obj _)), add_comp, add_comp,
@@ -103,9 +103,9 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         simp only [Nat.succ_eq_add_one] at hi
         obtain ⟨k, hk⟩ := Nat.le.dest (Nat.lt_succ_iff.mp (Fin.is_lt j))
         rw [add_comm] at hk
-        have hi' : i = Fin.castSucc ⟨i, by linarith⟩ := by
+        have hi' : i = Fin.castSuccEmb ⟨i, by linarith⟩ := by
           ext
-          simp only [Fin.castSucc_mk, Fin.eta]
+          simp only [Fin.castSuccEmb_mk, Fin.eta]
         have eq := hq j.revPerm.succ (by
           simp only [← hk, Fin.revPerm_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
           linarith)

@@ -106,13 +106,13 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
         have hi' : i = Fin.castSucc ⟨i, by linarith⟩ := by
           ext
           simp only [Fin.castSucc_mk, Fin.eta]
-        have eq := hq j.rev.succ (by
-          simp only [← hk, Fin.rev_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
+        have eq := hq j.revPerm.succ (by
+          simp only [← hk, Fin.revPerm_eq j hk.symm, Nat.succ_eq_add_one, Fin.succ_mk, Fin.val_mk]
           linarith)
         rw [HomologicalComplex.comp_f, assoc, assoc, assoc, hi',
           SimplicialObject.σ_comp_σ_assoc, reassoc_of% eq, zero_comp, comp_zero, comp_zero,
           comp_zero]
-        simp only [Fin.rev_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
+        simp only [Fin.revPerm_eq j hk.symm, Fin.le_iff_val_le_val, Fin.val_mk]
         linarith
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.σ_comp_P_eq_zero AlgebraicTopology.DoldKan.σ_comp_P_eq_zero

@@ -47,10 +47,10 @@ theorem HigherFacesVanish.comp_σ {Y : C} {X : SimplicialObject C} {n b q : ℕ}
   fun j hj => by
   rw [assoc, SimplicialObject.δ_comp_σ_of_gt', Fin.pred_succ, v.comp_δ_eq_zero_assoc _ _ hj,
     zero_comp]
-  . dsimp
+  · dsimp
     rw [Fin.lt_iff_val_lt_val, Fin.val_succ]
     linarith
-  . intro hj'
+  · intro hj'
     simp only [hnbq, add_comm b, add_assoc, hj', Fin.val_zero, zero_add, add_le_iff_nonpos_right,
       nonpos_iff_eq_zero, add_eq_zero, false_and] at hj
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_σ AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ
@@ -59,19 +59,19 @@ theorem σ_comp_P_eq_zero (X : SimplicialObject C) {n q : ℕ} (i : Fin (n + 1))
     X.σ i ≫ (P q).f (n + 1) = 0 := by
   revert i hi
   induction' q with q hq
-  . intro i (hi : n + 1 ≤ i)
+  · intro i (hi : n + 1 ≤ i)
     exfalso
     linarith [Fin.is_lt i]
   · intro i (hi : n + 1 ≤ i + q + 1)
     by_cases n + 1 ≤ (i : ℕ) + q
-    . rw [P_succ, HomologicalComplex.comp_f, ← assoc, hq i h, zero_comp]
-    . replace hi : n = i + q := by
+    · rw [P_succ, HomologicalComplex.comp_f, ← assoc, hq i h, zero_comp]
+    · replace hi : n = i + q := by
         obtain ⟨j, hj⟩ := le_iff_exists_add.mp hi
         rw [← Nat.lt_succ_iff, Nat.succ_eq_add_one, hj, not_lt, add_le_iff_nonpos_right,
           nonpos_iff_eq_zero] at h
         rw [← add_left_inj 1, hj, self_eq_add_right, h]
       rcases n with _|n
-      . fin_cases i
+      · fin_cases i
         dsimp at h hi
         rw [show q = 0 by linarith]
         change X.σ 0 ≫ (P 1).f 1 = 0
@@ -130,13 +130,13 @@ theorem degeneracy_comp_PInfty (X : SimplicialObject C) (n : ℕ) {Δ' : Simplex
     (θ : ([n] : SimplexCategory) ⟶ Δ') (hθ : ¬Mono θ) : X.map θ.op ≫ PInfty.f n = 0 := by
   rw [SimplexCategory.mono_iff_injective] at hθ
   cases n
-  . exfalso
+  · exfalso
     apply hθ
     intro x y h
     fin_cases x
     fin_cases y
     rfl
-  . obtain ⟨i, α, h⟩ := SimplexCategory.eq_σ_comp_of_not_injective θ hθ
+  · obtain ⟨i, α, h⟩ := SimplexCategory.eq_σ_comp_of_not_injective θ hθ
     rw [h, op_comp, X.map_comp, assoc, show X.map (SimplexCategory.σ i).op = X.σ i by rfl,
       σ_comp_PInfty, comp_zero]
 set_option linter.uppercaseLean3 false in