algebraic_topology.dold_kan.faces | Mathlib porting status

(last sync)

feat(algebraic_topology/dold_kan): The Dold-Kan equivalence for abelian categories (#17926)

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

Diff

@@ -25,6 +25,8 @@ The main lemma in this file is `higher_faces_vanish.induction`. It is based
 on two technical lemmas `higher_faces_vanish.comp_Hσ_eq` and
 `higher_faces_vanish.comp_Hσ_eq_zero`.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 open nat

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -123,8 +123,8 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
     · intro h
-      rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h 
-      dsimp at h 
+      rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
+      dsimp at h
       linarith
     · dsimp
       simp only [Fin.coe_pred, Fin.val_mk, succ_add_sub_one]
@@ -189,8 +189,8 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
     · intro j
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
       · intro h
-        rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h 
-        dsimp at h 
+        rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
+        dsimp at h
         linarith
       · dsimp
         simp only [Fin.cast_natAdd, Fin.coe_pred, Fin.coe_addNat, add_succ_sub_one]
@@ -231,7 +231,7 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
   have hj₃ := j.is_lt
   have ham : a ≤ m := by
     by_contra
-    rw [not_le, ← Nat.succ_le_iff] at h 
+    rw [not_le, ← Nat.succ_le_iff] at h
     linarith
   rw [X.δ_comp_σ_of_gt', j.pred_succ]; swap
   · rw [Fin.lt_iff_val_lt_val]

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -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.Homotopies
-import Mathbin.Tactic.RingExp
+import AlgebraicTopology.DoldKan.Homotopies
+import Tactic.RingExp
 
 #align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-09-17-06

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

a754d78a

Diff

@@ -113,7 +113,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   swap
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
-      simp only [this, Fin.natAdd_mk, Fin.castIso_mk, zero_comp, smul_zero]
+      simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
     convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk]; linarith)
     rw [Nat.succ_eq_add_one]
     linarith
@@ -137,7 +137,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     skip
     rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
   rw [Fin.sum_univ_castSucc]
-  simp only [Fin.last, Fin.castLE_mk, Fin.coe_castIso, Fin.castIso_mk, Fin.coe_castLE, Fin.val_mk,
+  simp only [Fin.last, Fin.castLE_mk, Fin.coe_cast, Fin.cast_mk, Fin.coe_castLE, Fin.val_mk,
     Fin.castSucc_mk, Fin.coe_castSucc]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -162,7 +162,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     have hia :
       (⟨i, by linarith⟩ : Fin (n + 2)) ≤ Fin.castSuccEmb (⟨a, by linarith⟩ : Fin (n + 1)) := by
       simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSucc_mk, ← lt_succ_iff] using hi
-    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.castIso_mk, ←
+    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.cast_mk, ←
       δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr
     ring
@@ -182,7 +182,7 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       alternating_face_map_complex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
     · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.castIso_mk, Fin.castSucc_mk]
+        Fin.cast_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]
@@ -193,7 +193,7 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
         dsimp at h 
         linarith
       · dsimp
-        simp only [Fin.castIso_natAdd, Fin.coe_pred, Fin.coe_addNat, add_succ_sub_one]
+        simp only [Fin.cast_natAdd, Fin.coe_pred, Fin.coe_addNat, add_succ_sub_one]
         linarith
       · rw [Fin.lt_iff_val_lt_val]
         dsimp

bump to nightly-2023-08-06-03

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

b0e28731

Diff

@@ -6,7 +6,7 @@ Authors: Joël Riou
 import Mathbin.AlgebraicTopology.DoldKan.Homotopies
 import Mathbin.Tactic.RingExp
 
-#align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+#align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -26,6 +26,8 @@ The main lemma in this file is `higher_faces_vanish.induction`. It is based
 on two technical lemmas `higher_faces_vanish.comp_Hσ_eq` and
 `higher_faces_vanish.comp_Hσ_eq_zero`.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -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.faces
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.Homotopies
 import Mathbin.Tactic.RingExp
 
+#align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 
 # Study of face maps for the Dold-Kan correspondence

bump to nightly-2023-07-16-17

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

6db63fa6

Diff

@@ -136,10 +136,10 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   conv_lhs =>
     congr
     skip
-    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb]
-  rw [Fin.sum_univ_castSuccEmb]
+    rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
+  rw [Fin.sum_univ_castSucc]
   simp only [Fin.last, Fin.castLE_mk, Fin.coe_castIso, Fin.castIso_mk, Fin.coe_castLE, Fin.val_mk,
-    Fin.castSuccEmb_mk, Fin.coe_castSuccEmb]
+    Fin.castSucc_mk, Fin.coe_castSucc]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
   have simplif :
@@ -153,7 +153,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     use a
     linarith
   · -- d+e = 0
-    rw [assoc, assoc, X.δ_comp_σ_self' (Fin.castSuccEmb_mk _ _ _).symm,
+    rw [assoc, assoc, X.δ_comp_σ_self' (Fin.castSucc_mk _ _ _).symm,
       X.δ_comp_σ_succ' (Fin.succ_mk _ _ _).symm]
     simp only [comp_id, pow_add _ (a + 1) 1, pow_one, mul_neg, mul_one, neg_smul, add_right_neg]
   · -- c+a = 0
@@ -162,8 +162,8 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rintro ⟨i, hi⟩ h₀
     have hia :
       (⟨i, by linarith⟩ : Fin (n + 2)) ≤ Fin.castSuccEmb (⟨a, by linarith⟩ : Fin (n + 1)) := by
-      simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSuccEmb_mk, ← lt_succ_iff] using hi
-    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSuccEmb_mk, Fin.succ_mk, assoc, Fin.castIso_mk, ←
+      simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSucc_mk, ← lt_succ_iff] using hi
+    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.castIso_mk, ←
       δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr
     ring
@@ -182,8 +182,8 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       Fin.mk_zero, one_zsmul, eq_to_hom_refl, comp_id, comp_sum,
       alternating_face_map_complex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
-    · simp only [Fin.sum_univ_castSuccEmb, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.castIso_mk, Fin.castSuccEmb_mk]
+    · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
+        Fin.castIso_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]

bump to nightly-2023-07-06-11

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

a2f50eda

Diff

@@ -136,10 +136,10 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   conv_lhs =>
     congr
     skip
-    rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
-  rw [Fin.sum_univ_castSucc]
+    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb]
+  rw [Fin.sum_univ_castSuccEmb]
   simp only [Fin.last, Fin.castLE_mk, Fin.coe_castIso, Fin.castIso_mk, Fin.coe_castLE, Fin.val_mk,
-    Fin.castSucc_mk, Fin.coe_castSucc]
+    Fin.castSuccEmb_mk, Fin.coe_castSuccEmb]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
   have simplif :
@@ -153,16 +153,17 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     use a
     linarith
   · -- d+e = 0
-    rw [assoc, assoc, X.δ_comp_σ_self' (Fin.castSucc_mk _ _ _).symm,
+    rw [assoc, assoc, X.δ_comp_σ_self' (Fin.castSuccEmb_mk _ _ _).symm,
       X.δ_comp_σ_succ' (Fin.succ_mk _ _ _).symm]
     simp only [comp_id, pow_add _ (a + 1) 1, pow_one, mul_neg, mul_one, neg_smul, add_right_neg]
   · -- c+a = 0
     rw [← Finset.sum_add_distrib]
     apply Finset.sum_eq_zero
     rintro ⟨i, hi⟩ h₀
-    have hia : (⟨i, by linarith⟩ : Fin (n + 2)) ≤ Fin.castSucc (⟨a, by linarith⟩ : Fin (n + 1)) :=
-      by simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSucc_mk, ← lt_succ_iff] using hi
-    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.castIso_mk, ←
+    have hia :
+      (⟨i, by linarith⟩ : Fin (n + 2)) ≤ Fin.castSuccEmb (⟨a, by linarith⟩ : Fin (n + 1)) := by
+      simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSuccEmb_mk, ← lt_succ_iff] using hi
+    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSuccEmb_mk, Fin.succ_mk, assoc, Fin.castIso_mk, ←
       δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr
     ring
@@ -181,8 +182,8 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       Fin.mk_zero, one_zsmul, eq_to_hom_refl, comp_id, comp_sum,
       alternating_face_map_complex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
-    · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.castIso_mk, Fin.castSucc_mk]
+    · simp only [Fin.sum_univ_castSuccEmb, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
+        Fin.castIso_mk, Fin.castSuccEmb_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]

bump to nightly-2023-07-04-19

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

4217d5f4

Diff

@@ -114,7 +114,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   swap
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
-      simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
+      simp only [this, Fin.natAdd_mk, Fin.castIso_mk, zero_comp, smul_zero]
     convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk]; linarith)
     rw [Nat.succ_eq_add_one]
     linarith
@@ -138,7 +138,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     skip
     rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
   rw [Fin.sum_univ_castSucc]
-  simp only [Fin.last, Fin.castLE_mk, Fin.coe_cast, Fin.cast_mk, Fin.coe_castLE, Fin.val_mk,
+  simp only [Fin.last, Fin.castLE_mk, Fin.coe_castIso, Fin.castIso_mk, Fin.coe_castLE, Fin.val_mk,
     Fin.castSucc_mk, Fin.coe_castSucc]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -162,7 +162,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rintro ⟨i, hi⟩ h₀
     have hia : (⟨i, by linarith⟩ : Fin (n + 2)) ≤ Fin.castSucc (⟨a, by linarith⟩ : Fin (n + 1)) :=
       by simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSucc_mk, ← lt_succ_iff] using hi
-    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.cast_mk, ←
+    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.castIso_mk, ←
       δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr
     ring
@@ -182,7 +182,7 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       alternating_face_map_complex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
     · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.cast_mk, Fin.castSucc_mk]
+        Fin.castIso_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]
@@ -193,7 +193,7 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
         dsimp at h 
         linarith
       · dsimp
-        simp only [Fin.cast_natAdd, Fin.coe_pred, Fin.coe_addNat, add_succ_sub_one]
+        simp only [Fin.castIso_natAdd, Fin.coe_pred, Fin.coe_addNat, add_succ_sub_one]
         linarith
       · rw [Fin.lt_iff_val_lt_val]
         dsimp

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -54,6 +54,7 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 variable {X : SimplicialObject C}
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish /-
 /-- A morphism `φ : Y ⟶ X _[n+1]` satisfies `higher_faces_vanish q φ`
 when the compositions `φ ≫ X.δ j` are `0` for `j ≥ max 1 (n+2-q)`. When `q ≤ n+1`,
 it basically means that the composition `φ ≫ X.δ j` are `0` for the `q` highest
@@ -64,9 +65,11 @@ the identity `φ ≫ (P q).f (n+1) = φ`. -/
 def HigherFacesVanish {Y : C} {n : ℕ} (q : ℕ) (φ : Y ⟶ X _[n + 1]) : Prop :=
   ∀ j : Fin (n + 1), n + 1 ≤ (j : ℕ) + q → φ ≫ X.δ j.succ = 0
 #align algebraic_topology.dold_kan.higher_faces_vanish AlgebraicTopology.DoldKan.HigherFacesVanish
+-/
 
 namespace HigherFacesVanish
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero /-
 @[reassoc]
 theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (j : Fin (n + 2)) (hj₁ : j ≠ 0) (hj₂ : n + 2 ≤ (j : ℕ) + q) : φ ≫ X.δ j = 0 :=
@@ -77,15 +80,21 @@ theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v :
   rw [← @Nat.add_le_add_iff_right 1, add_assoc]
   simpa only [Fin.val_succ, add_assoc, add_comm 1] using hj₂
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero
+-/
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ /-
 theorem of_succ {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish (q + 1) φ) :
     HigherFacesVanish q φ := fun j hj => v j (by simpa only [← add_assoc] using le_add_right hj)
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_succ AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ
+-/
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp /-
 theorem of_comp {Y Z : C} {q n : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) (f : Z ⟶ Y) :
     HigherFacesVanish q (f ≫ φ) := fun j hj => by rw [assoc, v j hj, comp_zero]
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_comp AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp
+-/
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq /-
 theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hnaq : n = a + q) :
     φ ≫ (hσ q).f (n + 1) =
@@ -158,7 +167,9 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     congr
     ring
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq
+-/
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero /-
 theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hqn : n < q) : φ ≫ (hσ q).f (n + 1) = 0 :=
   by
@@ -188,7 +199,9 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
         dsimp
         linarith
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero
+-/
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.induction /-
 theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     HigherFacesVanish (q + 1) (φ ≫ (𝟙 _ + hσ q).f (n + 1)) :=
   by
@@ -238,6 +251,7 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
       linarith
     simp only [← assoc, v j (by linarith), zero_comp]
 #align algebraic_topology.dold_kan.higher_faces_vanish.induction AlgebraicTopology.DoldKan.HigherFacesVanish.induction
+-/
 
 end HigherFacesVanish

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -115,8 +115,8 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
     · intro h
-      rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
-      dsimp at h
+      rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h 
+      dsimp at h 
       linarith
     · dsimp
       simp only [Fin.coe_pred, Fin.val_mk, succ_add_sub_one]
@@ -178,8 +178,8 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
     · intro j
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
       · intro h
-        rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
-        dsimp at h
+        rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h 
+        dsimp at h 
         linarith
       · dsimp
         simp only [Fin.cast_natAdd, Fin.coe_pred, Fin.coe_addNat, add_succ_sub_one]
@@ -218,7 +218,7 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
   have hj₃ := j.is_lt
   have ham : a ≤ m := by
     by_contra
-    rw [not_le, ← Nat.succ_le_iff] at h
+    rw [not_le, ← Nat.succ_le_iff] at h 
     linarith
   rw [X.δ_comp_σ_of_gt', j.pred_succ]; swap
   · rw [Fin.lt_iff_val_lt_val]

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -44,7 +44,7 @@ open CategoryTheory.Preadditive
 
 open CategoryTheory.SimplicialObject
 
-open Simplicial DoldKan
+open scoped Simplicial DoldKan
 
 namespace AlgebraicTopology

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -54,12 +54,6 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 variable {X : SimplicialObject C}
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish AlgebraicTopology.DoldKan.HigherFacesVanishₓ'. -/
 /-- A morphism `φ : Y ⟶ X _[n+1]` satisfies `higher_faces_vanish q φ`
 when the compositions `φ ≫ X.δ j` are `0` for `j ≥ max 1 (n+2-q)`. When `q ≤ n+1`,
 it basically means that the composition `φ ≫ X.δ j` are `0` for the `q` highest
@@ -73,9 +67,6 @@ def HigherFacesVanish {Y : C} {n : ℕ} (q : ℕ) (φ : Y ⟶ X _[n + 1]) : Prop
 
 namespace HigherFacesVanish
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zeroₓ'. -/
 @[reassoc]
 theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (j : Fin (n + 2)) (hj₁ : j ≠ 0) (hj₂ : n + 2 ≤ (j : ℕ) + q) : φ ≫ X.δ j = 0 :=
@@ -87,29 +78,14 @@ theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v :
   simpa only [Fin.val_succ, add_assoc, add_comm 1] using hj₂
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.of_succ AlgebraicTopology.DoldKan.HigherFacesVanish.of_succₓ'. -/
 theorem of_succ {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish (q + 1) φ) :
     HigherFacesVanish q φ := fun j hj => v j (by simpa only [← add_assoc] using le_add_right hj)
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_succ AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.of_comp AlgebraicTopology.DoldKan.HigherFacesVanish.of_compₓ'. -/
 theorem of_comp {Y Z : C} {q n : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) (f : Z ⟶ Y) :
     HigherFacesVanish q (f ≫ φ) := fun j hj => by rw [assoc, v j hj, comp_zero]
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_comp AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqₓ'. -/
 theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hnaq : n = a + q) :
     φ ≫ (hσ q).f (n + 1) =
@@ -183,9 +159,6 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     ring
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroₓ'. -/
 theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hqn : n < q) : φ ≫ (hσ q).f (n + 1) = 0 :=
   by
@@ -216,9 +189,6 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
         linarith
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.induction -> AlgebraicTopology.DoldKan.HigherFacesVanish.induction is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.induction AlgebraicTopology.DoldKan.HigherFacesVanish.inductionₓ'. -/
 theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     HigherFacesVanish (q + 1) (φ ≫ (𝟙 _ + hσ q).f (n + 1)) :=
   by

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -117,9 +117,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
           X.δ ⟨a + 1, Nat.succ_lt_succ (Nat.lt_succ_iff.mpr (Nat.le.intro hnaq.symm))⟩ ≫
             X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro hnaq.symm)⟩ :=
   by
-  have hnaq_shift : ∀ d : ℕ, n + d = a + d + q :=
-    by
-    intro d
+  have hnaq_shift : ∀ d : ℕ, n + d = a + d + q := by intro d;
     rw [add_assoc, add_comm d, ← add_assoc, hnaq]
   rw [Hσ, Homotopy.nullHomotopicMap'_f (c_mk (n + 2) (n + 1) rfl) (c_mk (n + 1) n rfl),
     hσ'_eq hnaq (c_mk (n + 1) n rfl), hσ'_eq (hnaq_shift 1) (c_mk (n + 2) (n + 1) rfl)]
@@ -127,19 +125,16 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     comp_add]
   simp only [comp_zsmul, zsmul_comp, ← assoc, ← mul_zsmul]
   -- cleaning up the first sum
-  rw [← Fin.sum_congr' _ (hnaq_shift 2).symm, Fin.sum_trunc]
+  rw [← Fin.sum_congr' _ (hnaq_shift 2).symm, Fin.sum_trunc];
   swap
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
       simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
-    convert v ⟨a + k + 1, by linarith⟩
-        (by
-          rw [Fin.val_mk]
-          linarith)
+    convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk]; linarith)
     rw [Nat.succ_eq_add_one]
     linarith
   -- cleaning up the second sum
-  rw [← Fin.sum_congr' _ (hnaq_shift 3).symm, @Fin.sum_trunc _ _ (a + 3)]
+  rw [← Fin.sum_congr' _ (hnaq_shift 3).symm, @Fin.sum_trunc _ _ (a + 3)];
   swap
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
@@ -255,21 +250,18 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
     by_contra
     rw [not_le, ← Nat.succ_le_iff] at h
     linarith
-  rw [X.δ_comp_σ_of_gt', j.pred_succ]
-  swap
+  rw [X.δ_comp_σ_of_gt', j.pred_succ]; swap
   · rw [Fin.lt_iff_val_lt_val]
     simpa only [Fin.val_mk, Fin.val_succ, add_lt_add_iff_right] using haj
   obtain ham' | ham'' := ham.lt_or_eq
   · -- case where `a<m`
-    rw [← X.δ_comp_δ''_assoc]
-    swap
+    rw [← X.δ_comp_δ''_assoc]; swap
     · rw [Fin.le_iff_val_le_val]
       dsimp
       linarith
     simp only [← assoc, v j (by linarith), zero_comp]
   · -- in the last case, a=m, q=1 and j=a+1
-    rw [X.δ_comp_δ_self'_assoc]
-    swap
+    rw [X.δ_comp_δ_self'_assoc]; swap
     · ext
       dsimp
       have hq : q = 1 := by rw [← add_left_inj a, ha, ham'', add_comm]

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -74,10 +74,7 @@ def HigherFacesVanish {Y : C} {n : ℕ} (q : ℕ) (φ : Y ⟶ X _[n + 1]) : Prop
 namespace HigherFacesVanish
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zeroₓ'. -/
 @[reassoc]
 theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
@@ -111,10 +108,7 @@ theorem of_comp {Y Z : C} {q n : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_comp AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqₓ'. -/
 theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hnaq : n = a + q) :
@@ -195,10 +189,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroₓ'. -/
 theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hqn : n < q) : φ ≫ (hσ q).f (n + 1) = 0 :=
@@ -231,10 +222,7 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero
 
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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) -> (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (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) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) φ (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) (HAdd.hAdd.{u2, u2, u2} (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (instHAdd.{u2} (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (HomologicalComplex.instAddHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u2, u1, 0} Nat 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))) (CategoryTheory.CategoryStruct.id.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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.DoldKan.Hσ.{u1, u2} C _inst_1 _inst_2 X q)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.induction AlgebraicTopology.DoldKan.HigherFacesVanish.inductionₓ'. -/
 theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     HigherFacesVanish (q + 1) (φ ≫ (𝟙 _ + hσ q).f (n + 1)) :=

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -79,7 +79,7 @@ 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} {Y : C} {n : 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 (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))), (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) j (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (NeZero.succ (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 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) j) q)) -> (Eq.{succ u2} (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 n)))) (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 n))) φ (CategoryTheory.SimplicialObject.δ.{u2, u1} C _inst_1 X n j)) (OfNat.ofNat.{u2} (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 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)) 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 n)))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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 n))))))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zeroₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (j : Fin (n + 2)) (hj₁ : j ≠ 0) (hj₂ : n + 2 ≤ (j : ℕ) + q) : φ ≫ X.δ j = 0 :=
   by

bump to nightly-2023-04-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

21a90077

Diff

@@ -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.faces
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! 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.RingExp
 
 # Study of face maps for the Dold-Kan correspondence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 TODO (@joelriou) continue adding the various files referenced below
 
 In this file, we obtain the technical lemmas that are used in the file

bump to nightly-2023-04-20-12

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

ffd433f8

Diff

@@ -51,6 +51,12 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 variable {X : SimplicialObject C}
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish -> AlgebraicTopology.DoldKan.HigherFacesVanish 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} {Y : C} {n : Nat}, Nat -> (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)))))))) -> Prop
+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} {Y : C} {n : Nat}, Nat -> (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))))))) -> Prop
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish AlgebraicTopology.DoldKan.HigherFacesVanishₓ'. -/
 /-- A morphism `φ : Y ⟶ X _[n+1]` satisfies `higher_faces_vanish q φ`
 when the compositions `φ ≫ X.δ j` are `0` for `j ≥ max 1 (n+2-q)`. When `q ≤ n+1`,
 it basically means that the composition `φ ≫ X.δ j` are `0` for the `q` highest
@@ -64,6 +70,12 @@ def HigherFacesVanish {Y : C} {n : ℕ} (q : ℕ) (φ : Y ⟶ X _[n + 1]) : Prop
 
 namespace HigherFacesVanish
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero is a dubious translation:
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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)))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zeroₓ'. -/
 @[reassoc.1]
 theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (j : Fin (n + 2)) (hj₁ : j ≠ 0) (hj₂ : n + 2 ≤ (j : ℕ) + q) : φ ≫ X.δ j = 0 :=
@@ -75,15 +87,33 @@ theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v :
   simpa only [Fin.val_succ, add_assoc, add_comm 1] using hj₂
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.of_succ -> AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.of_succ AlgebraicTopology.DoldKan.HigherFacesVanish.of_succₓ'. -/
 theorem of_succ {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish (q + 1) φ) :
     HigherFacesVanish q φ := fun j hj => v j (by simpa only [← add_assoc] using le_add_right hj)
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_succ AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.of_comp AlgebraicTopology.DoldKan.HigherFacesVanish.of_compₓ'. -/
 theorem of_comp {Y Z : C} {q n : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) (f : Z ⟶ Y) :
     HigherFacesVanish q (f ≫ φ) := fun j hj => by rw [assoc, v j hj, comp_zero]
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_comp AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp
 
-theorem comp_hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
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Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (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))))))) (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} 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(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 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (CategoryTheory.SimplicialObject.δ.{u2, u1} C _inst_1 X n (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Nat.succ_lt_succ a (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Iff.mpr (LT.lt.{0} Nat Nat.hasLt a (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe a n) (Nat.lt_succ_iff a n) (Nat.le.intro a n q (Eq.symm.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a q) hnaq)))))) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n (Fin.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)))) a (Iff.mpr (LT.lt.{0} Nat Nat.hasLt a (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe a n) (Nat.lt_succ_iff a n) (Nat.le.intro a n q (Eq.symm.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a q) hnaq)))))))))
+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} {Y : C} {n : Nat} {a : 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 (hnaq : Eq.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q)), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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) 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)))))) (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)))) φ (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.Hσ.{u1, u2} C _inst_1 _inst_2 X q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Neg.neg.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (Prefunctor.obj.{1, 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(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))))))) (SubNegZeroMonoid.toNegZeroClass.{u2} (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))))))) (SubtractionMonoid.toSubNegZeroMonoid.{u2} (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))))))) (SubtractionCommMonoid.toSubtractionMonoid.{u2} (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) 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqₓ'. -/
+theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hnaq : n = a + q) :
     φ ≫ (hσ q).f (n + 1) =
       -φ ≫
@@ -159,9 +189,15 @@ theorem comp_hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
       δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr
     ring
-#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_hσ_eq
+#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq
 
-theorem comp_hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroₓ'. -/
+theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ)
     (hqn : n < q) : φ ≫ (hσ q).f (n + 1) = 0 :=
   by
   simp only [Hσ, Homotopy.nullHomotopicMap'_f (c_mk (n + 2) (n + 1) rfl) (c_mk (n + 1) n rfl)]
@@ -189,8 +225,14 @@ theorem comp_hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       · rw [Fin.lt_iff_val_lt_val]
         dsimp
         linarith
-#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_hσ_eq_zero
+#align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.induction -> AlgebraicTopology.DoldKan.HigherFacesVanish.induction is a dubious translation:
+lean 3 declaration is
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+  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} {Y : C} {n : 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) -> (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (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) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) φ (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) (HAdd.hAdd.{u2, u2, u2} (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (instHAdd.{u2} (Quiver.Hom.{succ u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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)) (HomologicalComplex.instAddHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u2, u1, 0} Nat 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))) (CategoryTheory.CategoryStruct.id.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) 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)) (HomologicalComplex.instCategoryHomologicalComplex.{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.DoldKan.Hσ.{u1, u2} C _inst_1 _inst_2 X q)) (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.higher_faces_vanish.induction AlgebraicTopology.DoldKan.HigherFacesVanish.inductionₓ'. -/
 theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     HigherFacesVanish (q + 1) (φ ≫ (𝟙 _ + hσ q).f (n + 1)) :=
   by

bump to nightly-2023-04-12-16

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

06c79b19

Diff

@@ -131,7 +131,7 @@ theorem comp_hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     skip
     rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
   rw [Fin.sum_univ_castSucc]
-  simp only [Fin.last, Fin.castLe_mk, Fin.coe_cast, Fin.cast_mk, Fin.coe_castLe, Fin.val_mk,
+  simp only [Fin.last, Fin.castLE_mk, Fin.coe_cast, Fin.cast_mk, Fin.coe_castLE, Fin.val_mk,
     Fin.castSucc_mk, Fin.coe_castSucc]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -155,7 +155,7 @@ theorem comp_hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rintro ⟨i, hi⟩ h₀
     have hia : (⟨i, by linarith⟩ : Fin (n + 2)) ≤ Fin.castSucc (⟨a, by linarith⟩ : Fin (n + 1)) :=
       by simpa only [Fin.le_iff_val_le_val, Fin.val_mk, Fin.castSucc_mk, ← lt_succ_iff] using hi
-    simp only [Fin.val_mk, Fin.castLe_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.cast_mk, ←
+    simp only [Fin.val_mk, Fin.castLE_mk, Fin.castSucc_mk, Fin.succ_mk, assoc, Fin.cast_mk, ←
       δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr
     ring
@@ -172,7 +172,7 @@ theorem comp_hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       Fin.mk_zero, one_zsmul, eq_to_hom_refl, comp_id, comp_sum,
       alternating_face_map_complex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
-    · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLe_mk,
+    · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
         Fin.cast_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -105,8 +105,7 @@ theorem comp_hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
       simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
-    convert
-      v ⟨a + k + 1, by linarith⟩
+    convert v ⟨a + k + 1, by linarith⟩
         (by
           rw [Fin.val_mk]
           linarith)

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -34,7 +34,6 @@ namespace AlgebraicTopology
 namespace DoldKan
 
 variable {C : Type*} [Category C] [Preadditive C]
-
 variable {X : SimplicialObject C}
 
 /-- A morphism `φ : Y ⟶ X _[n+1]` satisfies `HigherFacesVanish q φ`

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -207,13 +207,15 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
     swap
     · rw [Fin.le_iff_val_le_val]
       dsimp
-      omega
+      linarith
     simp only [← assoc, v j (by omega), zero_comp]
   · -- in the last case, a=m, q=1 and j=a+1
     rw [X.δ_comp_δ_self'_assoc]
     swap
     · ext
+      cases j
       dsimp
+      dsimp only [Nat.succ_eq_add_one] at *
       omega
     simp only [← assoc, v j (by omega), zero_comp]
 #align algebraic_topology.dold_kan.higher_faces_vanish.induction AlgebraicTopology.DoldKan.HigherFacesVanish.induction

refactor: optimize proofs with omega (#11093)

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.

37bc4aba

Diff

@@ -56,7 +56,7 @@ theorem comp_δ_eq_zero {Y : C} {n : ℕ} {q : ℕ} {φ : Y ⟶ X _[n + 1]} (v :
   obtain ⟨i, rfl⟩ := Fin.eq_succ_of_ne_zero hj₁
   apply v i
   simp only [Fin.val_succ] at hj₂
-  linarith
+  omega
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_δ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero
 
 theorem of_succ {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish (q + 1) φ) :
@@ -84,11 +84,11 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   rw [← Fin.sum_congr' _ (hnaq_shift 2).symm, Fin.sum_trunc]
   swap
   · rintro ⟨k, hk⟩
-    suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
+    suffices φ ≫ X.δ (⟨a + 2 + k, by omega⟩ : Fin (n + 2)) = 0 by
       simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
-    convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk]; linarith)
+    convert v ⟨a + k + 1, by omega⟩ (by rw [Fin.val_mk]; omega)
     dsimp
-    linarith
+    omega
   -- cleaning up the second sum
   rw [← Fin.sum_congr' _ (hnaq_shift 3).symm, @Fin.sum_trunc _ _ (a + 3)]
   swap
@@ -96,14 +96,14 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
     · simp only [Fin.lt_iff_val_lt_val]
       dsimp [Fin.natAdd, Fin.cast]
-      linarith
+      omega
     · intro h
       rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
       dsimp [Fin.cast] at h
-      linarith
+      omega
     · dsimp [Fin.cast, Fin.pred]
       rw [Nat.add_right_comm, Nat.add_sub_assoc (by norm_num : 1 ≤ 3)]
-      linarith
+      omega
   simp only [assoc]
   conv_lhs =>
     congr
@@ -119,7 +119,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   apply simplif
   · -- b = f
     rw [← pow_add, Odd.neg_one_pow, neg_smul, one_zsmul]
-    exact ⟨a, by linarith⟩
+    exact ⟨a, by omega⟩
   · -- d + e = 0
     rw [X.δ_comp_σ_self' (Fin.castSucc_mk _ _ _).symm,
       X.δ_comp_σ_succ' (Fin.succ_mk _ _ _).symm]
@@ -130,11 +130,11 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     apply Finset.sum_eq_zero
     rintro ⟨i, hi⟩ _
     simp only
-    have hia : (⟨i, by linarith⟩ : Fin (n + 2)) ≤
-        Fin.castSucc (⟨a, by linarith⟩ : Fin (n + 1)) := by
+    have hia : (⟨i, by omega⟩ : Fin (n + 2)) ≤
+        Fin.castSucc (⟨a, by omega⟩ : Fin (n + 1)) := by
       rw [Fin.le_iff_val_le_val]
       dsimp
-      linarith
+      omega
     erw [δ_comp_σ_of_le X hia, add_eq_zero_iff_eq_neg, ← neg_zsmul]
     congr 2
     ring
@@ -147,10 +147,10 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
   rw [hσ'_eq_zero hqn (c_mk (n + 1) n rfl), comp_zero, zero_add]
   by_cases hqn' : n + 1 < q
   · rw [hσ'_eq_zero hqn' (c_mk (n + 2) (n + 1) rfl), zero_comp, comp_zero]
-  · simp only [hσ'_eq (show n + 1 = 0 + q by linarith) (c_mk (n + 2) (n + 1) rfl), pow_zero,
+  · simp only [hσ'_eq (show n + 1 = 0 + q by omega) (c_mk (n + 2) (n + 1) rfl), pow_zero,
       Fin.mk_zero, one_zsmul, eqToHom_refl, comp_id, comp_sum,
       AlternatingFaceMapComplex.obj_d_eq]
-    rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
+    rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by omega), Fin.sum_trunc]
     · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
         Fin.cast_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
@@ -161,12 +161,12 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
       · simp only [Fin.lt_iff_val_lt_val]
         dsimp [Fin.succ]
-        linarith
+        omega
       · intro h
         simp only [Fin.pred, Fin.subNat, Fin.ext_iff, Nat.succ_add_sub_one,
           Fin.val_zero, add_eq_zero, false_and] at h
       · simp only [Fin.pred, Fin.subNat, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
-        linarith
+        omega
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero
 
@@ -177,10 +177,10 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
   simp only [comp_add, add_comp, comp_id]
   -- when n < q, the result follows immediately from the assumption
   by_cases hqn : n < q
-  · rw [v.comp_Hσ_eq_zero hqn, zero_comp, add_zero, v j (by linarith)]
+  · rw [v.comp_Hσ_eq_zero hqn, zero_comp, add_zero, v j (by omega)]
   -- we now assume that n≥q, and write n=a+q
   cases' Nat.le.dest (not_lt.mp hqn) with a ha
-  rw [v.comp_Hσ_eq (show n = a + q by linarith), neg_comp, add_neg_eq_zero, assoc, assoc]
+  rw [v.comp_Hσ_eq (show n = a + q by omega), neg_comp, add_neg_eq_zero, assoc, assoc]
   cases' n with m hm
   -- the boundary case n=0
   · simp only [Nat.eq_zero_of_add_eq_zero_left ha, Fin.eq_zero j, Fin.mk_zero, Fin.mk_one,
@@ -192,12 +192,11 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
   · simp only [hj₂, Fin.eta, δ_comp_σ_succ, comp_id]
     rfl
   -- now, we assume j ≠ a (i.e. a < j)
-  have haj : a < j := (Ne.le_iff_lt hj₂).mp (by linarith)
-  have hj₃ := j.is_lt
+  have haj : a < j := (Ne.le_iff_lt hj₂).mp (by omega)
   have ham : a ≤ m := by
     by_contra h
     rw [not_le, ← Nat.succ_le_iff] at h
-    linarith
+    omega
   rw [X.δ_comp_σ_of_gt', j.pred_succ]
   swap
   · rw [Fin.lt_iff_val_lt_val]
@@ -208,15 +207,15 @@ theorem induction {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVa
     swap
     · rw [Fin.le_iff_val_le_val]
       dsimp
-      linarith
-    simp only [← assoc, v j (by linarith), zero_comp]
+      omega
+    simp only [← assoc, v j (by omega), zero_comp]
   · -- in the last case, a=m, q=1 and j=a+1
     rw [X.δ_comp_δ_self'_assoc]
     swap
     · ext
       dsimp
-      linarith
-    simp only [← assoc, v j (by linarith), zero_comp]
+      omega
+    simp only [← assoc, v j (by omega), zero_comp]
 #align algebraic_topology.dold_kan.higher_faces_vanish.induction AlgebraicTopology.DoldKan.HigherFacesVanish.induction
 
 end HigherFacesVanish

chore: replace Fin.castIso and Fin.revPerm with Fin.cast and Fin.rev for the bump of Std (#5847)

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>

45b31dda

Diff

@@ -85,7 +85,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   swap
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
-      simp only [this, Fin.natAdd_mk, Fin.castIso_mk, zero_comp, smul_zero]
+      simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
     convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk]; linarith)
     dsimp
     linarith
@@ -95,13 +95,13 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
     · simp only [Fin.lt_iff_val_lt_val]
-      dsimp [Fin.natAdd, Fin.castIso]
+      dsimp [Fin.natAdd, Fin.cast]
       linarith
     · intro h
       rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
-      dsimp [Fin.castIso] at h
+      dsimp [Fin.cast] at h
       linarith
-    · dsimp [Fin.castIso, Fin.pred]
+    · dsimp [Fin.cast, Fin.pred]
       rw [Nat.add_right_comm, Nat.add_sub_assoc (by norm_num : 1 ≤ 3)]
       linarith
   simp only [assoc]
@@ -109,7 +109,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     congr
     · rw [Fin.sum_univ_castSucc]
     · rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
-  dsimp [Fin.castIso, Fin.castLE, Fin.castLT]
+  dsimp [Fin.cast, Fin.castLE, Fin.castLT]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
   have simplif :
@@ -152,12 +152,12 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       AlternatingFaceMapComplex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
     · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.castIso_mk, Fin.castSucc_mk]
+        Fin.cast_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]
     · intro j
-      dsimp [Fin.castIso, Fin.castLE, Fin.castLT]
+      dsimp [Fin.cast, Fin.castLE, Fin.castLT]
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
       · simp only [Fin.lt_iff_val_lt_val]
         dsimp [Fin.succ]

chore: linarith only needs ring1 (#7090)

I appreciate that this is "going backwards" in the sense of requiring more explicit imports of tactics (and making it more likely that users writing new files will need to import tactics rather than finding them already available).

However it's useful for me while I'm intensively working on refactoring and upstreaming tactics if I can minimise the dependencies between tactics. I'm very much aware that in the long run we don't want users to have to manage imports of tactics, and I am definitely going to tidy this all up again once I'm finished with this project!

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

37e6e50e

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.DoldKan.Homotopies
+import Mathlib.Tactic.Ring
 
 #align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

chore: fix SHA for Dold-Kan equivalence files (#6834)

cf01bdac

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.DoldKan.Homotopies
 
-#align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+#align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!

feat: forward port of Mathlib.AlgebraicTopology.DoldKan.Equivalence (#6444)

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>

c532d7b8

Diff

@@ -20,6 +20,8 @@ The main lemma in this file is `HigherFacesVanish.induction`. It is based
 on two technical lemmas `HigherFacesVanish.comp_Hσ_eq` and
 `HigherFacesVanish.comp_Hσ_eq_zero`.
 
+(See `Equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -30,7 +30,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C]
+variable {C : Type*} [Category C] [Preadditive C]
 
 variable {X : SimplicialObject C}

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 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.faces
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.Homotopies
 
+#align_import algebraic_topology.dold_kan.faces from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 
 # Study of face maps for the Dold-Kan correspondence

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

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

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

906f7221

Diff

@@ -102,13 +102,13 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
       dsimp [Fin.castIso] at h
       linarith
     · dsimp [Fin.castIso, Fin.pred]
-      rw [Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
+      rw [Nat.add_right_comm, Nat.add_sub_assoc (by norm_num : 1 ≤ 3)]
       linarith
   simp only [assoc]
   conv_lhs =>
     congr
-    · rw [Fin.sum_univ_castSuccEmb]
-    · rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb]
+    · rw [Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
   dsimp [Fin.castIso, Fin.castLE, Fin.castLT]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -121,7 +121,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rw [← pow_add, Odd.neg_one_pow, neg_smul, one_zsmul]
     exact ⟨a, by linarith⟩
   · -- d + e = 0
-    rw [X.δ_comp_σ_self' (Fin.castSuccEmb_mk _ _ _).symm,
+    rw [X.δ_comp_σ_self' (Fin.castSucc_mk _ _ _).symm,
       X.δ_comp_σ_succ' (Fin.succ_mk _ _ _).symm]
     simp only [comp_id, pow_add _ (a + 1) 1, pow_one, mul_neg, mul_one, neg_mul, neg_smul,
       add_right_neg]
@@ -131,7 +131,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rintro ⟨i, hi⟩ _
     simp only
     have hia : (⟨i, by linarith⟩ : Fin (n + 2)) ≤
-        Fin.castSuccEmb (⟨a, by linarith⟩ : Fin (n + 1)) := by
+        Fin.castSucc (⟨a, by linarith⟩ : Fin (n + 1)) := by
       rw [Fin.le_iff_val_le_val]
       dsimp
       linarith
@@ -151,8 +151,8 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       Fin.mk_zero, one_zsmul, eqToHom_refl, comp_id, comp_sum,
       AlternatingFaceMapComplex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
-    · simp only [Fin.sum_univ_castSuccEmb, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.castIso_mk, Fin.castSuccEmb_mk]
+    · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
+        Fin.castIso_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]
@@ -163,9 +163,9 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
         dsimp [Fin.succ]
         linarith
       · intro h
-        simp only [Fin.pred, Fin.ext_iff, Nat.pred_eq_sub_one, Nat.succ_add_sub_one, Fin.val_zero,
-          add_eq_zero, false_and] at h
-      · simp only [Fin.pred, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
+        simp only [Fin.pred, Fin.subNat, Fin.ext_iff, Nat.succ_add_sub_one,
+          Fin.val_zero, add_eq_zero, false_and] at h
+      · simp only [Fin.pred, Fin.subNat, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
         linarith
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero

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

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

f4e42872

Diff

@@ -107,8 +107,8 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   simp only [assoc]
   conv_lhs =>
     congr
-    · rw [Fin.sum_univ_castSucc]
-    · rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSuccEmb]
+    · rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb]
   dsimp [Fin.castIso, Fin.castLE, Fin.castLT]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -121,7 +121,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rw [← pow_add, Odd.neg_one_pow, neg_smul, one_zsmul]
     exact ⟨a, by linarith⟩
   · -- d + e = 0
-    rw [X.δ_comp_σ_self' (Fin.castSucc_mk _ _ _).symm,
+    rw [X.δ_comp_σ_self' (Fin.castSuccEmb_mk _ _ _).symm,
       X.δ_comp_σ_succ' (Fin.succ_mk _ _ _).symm]
     simp only [comp_id, pow_add _ (a + 1) 1, pow_one, mul_neg, mul_one, neg_mul, neg_smul,
       add_right_neg]
@@ -131,7 +131,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     rintro ⟨i, hi⟩ _
     simp only
     have hia : (⟨i, by linarith⟩ : Fin (n + 2)) ≤
-        Fin.castSucc (⟨a, by linarith⟩ : Fin (n + 1)) := by
+        Fin.castSuccEmb (⟨a, by linarith⟩ : Fin (n + 1)) := by
       rw [Fin.le_iff_val_le_val]
       dsimp
       linarith
@@ -151,8 +151,8 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       Fin.mk_zero, one_zsmul, eqToHom_refl, comp_id, comp_sum,
       AlternatingFaceMapComplex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
-    · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.castIso_mk, Fin.castSucc_mk]
+    · simp only [Fin.sum_univ_castSuccEmb, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
+        Fin.castIso_mk, Fin.castSuccEmb_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]

chore: remove occurrences of semicolon after space (#5713)

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

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

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

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

c795bd35

Diff

@@ -86,7 +86,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
       simp only [this, Fin.natAdd_mk, Fin.castIso_mk, zero_comp, smul_zero]
-    convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk] ; linarith)
+    convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk]; linarith)
     dsimp
     linarith
   -- cleaning up the second sum

chore: rename Fin.cast to Fin.castIso (#5584)

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

b0bb2972

Diff

@@ -85,7 +85,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   swap
   · rintro ⟨k, hk⟩
     suffices φ ≫ X.δ (⟨a + 2 + k, by linarith⟩ : Fin (n + 2)) = 0 by
-      simp only [this, Fin.natAdd_mk, Fin.cast_mk, zero_comp, smul_zero]
+      simp only [this, Fin.natAdd_mk, Fin.castIso_mk, zero_comp, smul_zero]
     convert v ⟨a + k + 1, by linarith⟩ (by rw [Fin.val_mk] ; linarith)
     dsimp
     linarith
@@ -95,13 +95,13 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
     · simp only [Fin.lt_iff_val_lt_val]
-      dsimp [Fin.natAdd, Fin.cast]
+      dsimp [Fin.natAdd, Fin.castIso]
       linarith
     · intro h
       rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
-      dsimp [Fin.cast] at h
+      dsimp [Fin.castIso] at h
       linarith
-    · dsimp [Fin.cast, Fin.pred]
+    · dsimp [Fin.castIso, Fin.pred]
       rw [Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
       linarith
   simp only [assoc]
@@ -109,7 +109,7 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
     congr
     · rw [Fin.sum_univ_castSucc]
     · rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
-  dsimp [Fin.cast, Fin.castLE, Fin.castLT]
+  dsimp [Fin.castIso, Fin.castLE, Fin.castLT]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
   have simplif :
@@ -152,12 +152,12 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
       AlternatingFaceMapComplex.obj_d_eq]
     rw [← Fin.sum_congr' _ (show 2 + (n + 1) = n + 1 + 2 by linarith), Fin.sum_trunc]
     · simp only [Fin.sum_univ_castSucc, Fin.sum_univ_zero, zero_add, Fin.last, Fin.castLE_mk,
-        Fin.cast_mk, Fin.castSucc_mk]
+        Fin.castIso_mk, Fin.castSucc_mk]
       simp only [Fin.mk_zero, Fin.val_zero, pow_zero, one_zsmul, Fin.mk_one, Fin.val_one, pow_one,
         neg_smul, comp_neg]
       erw [δ_comp_σ_self, δ_comp_σ_succ, add_right_neg]
     · intro j
-      dsimp [Fin.cast, Fin.castLE, Fin.castLT]
+      dsimp [Fin.castIso, Fin.castLE, Fin.castLT]
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
       · simp only [Fin.lt_iff_val_lt_val]
         dsimp [Fin.succ]

chore: fix focusing dots (#5708)

This PR is the result of running

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

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

cb02d09e

Diff

@@ -94,21 +94,21 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   swap
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
-    . simp only [Fin.lt_iff_val_lt_val]
+    · simp only [Fin.lt_iff_val_lt_val]
       dsimp [Fin.natAdd, Fin.cast]
       linarith
-    . intro h
+    · intro h
       rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
       dsimp [Fin.cast] at h
       linarith
-    . dsimp [Fin.cast, Fin.pred]
+    · dsimp [Fin.cast, Fin.pred]
       rw [Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
       linarith
   simp only [assoc]
   conv_lhs =>
     congr
-    . rw [Fin.sum_univ_castSucc]
-    . rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
   dsimp [Fin.cast, Fin.castLE, Fin.castLT]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -159,13 +159,13 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
     · intro j
       dsimp [Fin.cast, Fin.castLE, Fin.castLT]
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
-      . simp only [Fin.lt_iff_val_lt_val]
+      · simp only [Fin.lt_iff_val_lt_val]
         dsimp [Fin.succ]
         linarith
-      . intro h
+      · intro h
         simp only [Fin.pred, Fin.ext_iff, Nat.pred_eq_sub_one, Nat.succ_add_sub_one, Fin.val_zero,
           add_eq_zero, false_and] at h
-      . simp only [Fin.pred, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
+      · simp only [Fin.pred, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
         linarith
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero