Changes since the initial port

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

Changes in mathlib3

618ea3d5

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

86d1873c

bump to nightly-2023-10-29-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

abdd1870

Diff

@@ -910,16 +910,16 @@ end HomotopyEquiv
 
 variable [HasEqualizers V] [HasCokernels V] [HasImages V] [HasImageMaps V]
 
-#print homology_map_eq_of_homotopy /-
+#print homology'_map_eq_of_homotopy /-
 /-- Homotopic maps induce the same map on homology.
 -/
-theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
-    (homologyFunctor V c i).map f = (homologyFunctor V c i).map g :=
+theorem homology'_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
+    (homology'Functor V c i).map f = (homology'Functor V c i).map g :=
   by
-  dsimp [homologyFunctor]
+  dsimp [homology'Functor]
   apply eq_of_sub_eq_zero
   ext
-  simp only [homology.π_map, comp_zero, preadditive.comp_sub]
+  simp only [homology'.π_map, comp_zero, preadditive.comp_sub]
   dsimp [kernel_subobject_map]
   simp_rw [h.comm i]
   simp only [zero_add, zero_comp, dNext_eq_dFrom_fromNext, kernel_subobject_arrow_comp_assoc,
@@ -930,21 +930,21 @@ theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
   · simp
   · rw [prevD_eq_toPrev_dTo, ← category.assoc]
     apply image_subobject_factors_comp_self
-#align homology_map_eq_of_homotopy homology_map_eq_of_homotopy
+#align homology_map_eq_of_homotopy homology'_map_eq_of_homotopy
 -/
 
 #print homologyObjIsoOfHomotopyEquiv /-
 /-- Homotopy equivalent complexes have isomorphic homologies. -/
 def homologyObjIsoOfHomotopyEquiv (f : HomotopyEquiv C D) (i : ι) :
-    (homologyFunctor V c i).obj C ≅ (homologyFunctor V c i).obj D
+    (homology'Functor V c i).obj C ≅ (homology'Functor V c i).obj D
     where
-  Hom := (homologyFunctor V c i).map f.Hom
-  inv := (homologyFunctor V c i).map f.inv
+  Hom := (homology'Functor V c i).map f.Hom
+  inv := (homology'Functor V c i).map f.inv
   hom_inv_id' := by
-    rw [← functor.map_comp, homology_map_eq_of_homotopy f.homotopy_hom_inv_id,
+    rw [← functor.map_comp, homology'_map_eq_of_homotopy f.homotopy_hom_inv_id,
       CategoryTheory.Functor.map_id]
   inv_hom_id' := by
-    rw [← functor.map_comp, homology_map_eq_of_homotopy f.homotopy_inv_hom_id,
+    rw [← functor.map_comp, homology'_map_eq_of_homotopy f.homotopy_inv_hom_id,
       CategoryTheory.Functor.map_id]
 #align homology_obj_iso_of_homotopy_equiv homologyObjIsoOfHomotopyEquiv
 -/

86d1873c

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Algebra.Homology.Additive
-import Mathbin.Tactic.Abel
+import Algebra.Homology.Additive
+import Tactic.Abel
 
 #align_import algebra.homology.homotopy from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"

86d1873c

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -181,8 +181,6 @@ variable {f g}
 
 namespace Homotopy
 
-restate_axiom Homotopy.zero'
-
 #print Homotopy.equivSubZero /-
 /-- `f` is homotopic to `g` iff `f - g` is homotopic to `0`.
 -/

86d1873c

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.homology.homotopy
-! 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.Algebra.Homology.Additive
 import Mathbin.Tactic.Abel
 
+#align_import algebra.homology.homotopy from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 # Chain homotopies

86d1873c

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -364,7 +364,7 @@ theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)
   ext n
   erw [null_homotopic_map_comp]
   congr
-  ext (i j)
+  ext i j
   split_ifs
   · rfl
   · rw [zero_comp]
@@ -392,7 +392,7 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt
   ext n
   erw [comp_null_homotopic_map]
   congr
-  ext (i j)
+  ext i j
   split_ifs
   · rfl
   · rw [comp_zero]
@@ -422,7 +422,7 @@ theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V 
   ext n
   erw [map_null_homotopic_map]
   congr
-  ext (i j)
+  ext i j
   split_ifs
   · rfl
   · rw [G.map_zero]

86d1873c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -57,27 +57,35 @@ def fromNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.xNext i ⟶ D.pt i)
 #align from_next fromNext
 -/
 
+#print dNext_eq_dFrom_fromNext /-
 @[simp]
 theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
     dNext i f = C.dFrom i ≫ fromNext i f :=
   rfl
 #align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNext
+-/
 
+#print dNext_eq /-
 theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
     dNext i f = C.d i i' ≫ f i' i := by obtain rfl := c.next_eq' w; rfl
 #align d_next_eq dNext_eq
+-/
 
+#print dNext_comp_left /-
 @[simp]
 theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (i : ι) :
     (dNext i fun i j => f.f i ≫ g i j) = f.f i ≫ dNext i g :=
   (f.comm_assoc _ _ _).symm
 #align d_next_comp_left dNext_comp_left
+-/
 
+#print dNext_comp_right /-
 @[simp]
 theorem dNext_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (i : ι) :
     (dNext i fun i j => f i j ≫ g.f j) = dNext i f ≫ g.f i :=
   (Category.assoc _ _ _).symm
 #align d_next_comp_right dNext_comp_right
+-/
 
 #print prevD /-
 /-- The composition of `f j j' ≫ D.d j' j` if there is some `j'` coming before `j`,
@@ -97,28 +105,37 @@ def toPrev (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.xPrev j) :
 #align to_prev toPrev
 -/
 
+#print prevD_eq_toPrev_dTo /-
 @[simp]
 theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
     prevD j f = toPrev j f ≫ D.dTo j :=
   rfl
 #align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dTo
+-/
 
+#print prevD_eq /-
 theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
     prevD j f = f j j' ≫ D.d j' j := by obtain rfl := c.prev_eq' w; rfl
 #align prev_d_eq prevD_eq
+-/
 
+#print prevD_comp_left /-
 @[simp]
 theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι) :
     (prevD j fun i j => f.f i ≫ g i j) = f.f j ≫ prevD j g :=
   Category.assoc _ _ _
 #align prev_d_comp_left prevD_comp_left
+-/
 
+#print prevD_comp_right /-
 @[simp]
 theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι) :
     (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j := by dsimp [prevD];
   simp only [category.assoc, g.comm]
 #align prev_d_comp_right prevD_comp_right
+-/
 
+#print dNext_nat /-
 theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     dNext i f = C.d i (i - 1) ≫ f (i - 1) i :=
   by
@@ -131,7 +148,9 @@ theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶
     have : (ComplexShape.down ℕ).next (i + 1) = i + 1 - 1 := by rw [ChainComplex.next_nat_succ]; rfl
     congr 2
 #align d_next_nat dNext_nat
+-/
 
+#print prevD_nat /-
 theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     prevD i f = f i (i - 1) ≫ D.d (i - 1) i :=
   by
@@ -144,6 +163,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i 
     have : (ComplexShape.up ℕ).prev (i + 1) = i + 1 - 1 := by rw [CochainComplex.prev_nat_succ]; rfl
     congr 2
 #align prev_d_nat prevD_nat
+-/
 
 #print Homotopy /-
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic obviously' -/
@@ -166,6 +186,7 @@ namespace Homotopy
 
 restate_axiom Homotopy.zero'
 
+#print Homotopy.equivSubZero /-
 /-- `f` is homotopic to `g` iff `f - g` is homotopic to `0`.
 -/
 def equivSubZero : Homotopy f g ≃ Homotopy (f - g) 0
@@ -181,6 +202,7 @@ def equivSubZero : Homotopy f g ≃ Homotopy (f - g) 0
   left_inv := by tidy
   right_inv := by tidy
 #align homotopy.equiv_sub_zero Homotopy.equivSubZero
+-/
 
 #print Homotopy.ofEq /-
 /-- Equal chain maps are homotopic. -/
@@ -224,6 +246,7 @@ def trans {e f g : C ⟶ D} (h : Homotopy e f) (k : Homotopy f g) : Homotopy e g
 #align homotopy.trans Homotopy.trans
 -/
 
+#print Homotopy.add /-
 /-- the sum of two homotopies is a homotopy between the sum of the respective morphisms. -/
 @[simps]
 def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homotopy f₂ g₂) :
@@ -235,6 +258,7 @@ def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homo
     simp only [HomologicalComplex.add_f_apply, h₁.comm, h₂.comm, AddMonoidHom.map_add]
     abel
 #align homotopy.add Homotopy.add
+-/
 
 #print Homotopy.compRight /-
 /-- homotopy is closed under composition (on the right) -/
@@ -319,6 +343,7 @@ def nullHomotopicMap' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : C ⟶ D
 #align homotopy.null_homotopic_map' Homotopy.nullHomotopicMap'
 -/
 
+#print Homotopy.nullHomotopicMap_comp /-
 /-- Compatibility of `null_homotopic_map` with the postcomposition by a morphism
 of complexes. -/
 theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
@@ -328,7 +353,9 @@ theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
   dsimp [null_homotopic_map, fromNext, toPrev, AddMonoidHom.mk'_apply]
   simp only [preadditive.add_comp, category.assoc, g.comm]
 #align homotopy.null_homotopic_map_comp Homotopy.nullHomotopicMap_comp
+-/
 
+#print Homotopy.nullHomotopicMap'_comp /-
 /-- Compatibility of `null_homotopic_map'` with the postcomposition by a morphism
 of complexes. -/
 theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) (g : D ⟶ E) :
@@ -342,7 +369,9 @@ theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)
   · rfl
   · rw [zero_comp]
 #align homotopy.null_homotopic_map'_comp Homotopy.nullHomotopicMap'_comp
+-/
 
+#print Homotopy.comp_nullHomotopicMap /-
 /-- Compatibility of `null_homotopic_map` with the precomposition by a morphism
 of complexes. -/
 theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
@@ -352,7 +381,9 @@ theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
   dsimp [null_homotopic_map, fromNext, toPrev, AddMonoidHom.mk'_apply]
   simp only [preadditive.comp_add, category.assoc, f.comm_assoc]
 #align homotopy.comp_null_homotopic_map Homotopy.comp_nullHomotopicMap
+-/
 
+#print Homotopy.comp_nullHomotopicMap' /-
 /-- Compatibility of `null_homotopic_map'` with the precomposition by a morphism
 of complexes. -/
 theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt i ⟶ E.pt j)) :
@@ -366,7 +397,9 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt
   · rfl
   · rw [comp_zero]
 #align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'
+-/
 
+#print Homotopy.map_nullHomotopicMap /-
 /-- Compatibility of `null_homotopic_map` with the application of additive functors -/
 theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -377,7 +410,9 @@ theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V 
   dsimp [null_homotopic_map, dNext, prevD]
   simp only [G.map_comp, functor.map_add]
 #align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMap
+-/
 
+#print Homotopy.map_nullHomotopicMap' /-
 /-- Compatibility of `null_homotopic_map'` with the application of additive functors -/
 theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -392,6 +427,7 @@ theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V 
   · rfl
   · rw [G.map_zero]
 #align homotopy.map_null_homotopic_map' Homotopy.map_nullHomotopicMap'
+-/
 
 #print Homotopy.nullHomotopy /-
 /-- Tautological construction of the `homotopy` to zero for maps constructed by
@@ -425,13 +461,16 @@ the degreewise morphisms induced by the null homotopic maps constructed
 with `null_homotopic_map` or `null_homotopic_map'` -/
 
 
+#print Homotopy.nullHomotopicMap_f /-
 @[simp]
 theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
     (nullHomotopicMap hom).f k₁ = C.d k₁ k₀ ≫ hom k₀ k₁ + hom k₁ k₂ ≫ D.d k₂ k₁ := by
   dsimp only [null_homotopic_map]; rw [dNext_eq hom r₁₀, prevD_eq hom r₂₁]
 #align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_f
+-/
 
+#print Homotopy.nullHomotopicMap'_f /-
 @[simp]
 theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -443,7 +482,9 @@ theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
   split_ifs
   rfl
 #align homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_f
+-/
 
+#print Homotopy.nullHomotopicMap_f_of_not_rel_left /-
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -453,7 +494,9 @@ theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
   rw [prevD_eq hom r₁₀, dNext, AddMonoidHom.mk'_apply, C.shape, zero_comp, zero_add]
   exact hk₀ _
 #align homotopy.null_homotopic_map_f_of_not_rel_left Homotopy.nullHomotopicMap_f_of_not_rel_left
+-/
 
+#print Homotopy.nullHomotopicMap'_f_of_not_rel_left /-
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -465,7 +508,9 @@ theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
   split_ifs
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_left Homotopy.nullHomotopicMap'_f_of_not_rel_left
+-/
 
+#print Homotopy.nullHomotopicMap_f_of_not_rel_right /-
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -475,7 +520,9 @@ theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
   rw [dNext_eq hom r₁₀, prevD, AddMonoidHom.mk'_apply, D.shape, comp_zero, add_zero]
   exact hk₁ _
 #align homotopy.null_homotopic_map_f_of_not_rel_right Homotopy.nullHomotopicMap_f_of_not_rel_right
+-/
 
+#print Homotopy.nullHomotopicMap'_f_of_not_rel_right /-
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -487,7 +534,9 @@ theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
   split_ifs
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_right Homotopy.nullHomotopicMap'_f_of_not_rel_right
+-/
 
+#print Homotopy.nullHomotopicMap_f_eq_zero /-
 @[simp]
 theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
     (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -496,7 +545,9 @@ theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀
   dsimp [null_homotopic_map, dNext, prevD]
   rw [C.shape, D.shape, zero_comp, comp_zero, add_zero] <;> apply_assumption
 #align homotopy.null_homotopic_map_f_eq_zero Homotopy.nullHomotopicMap_f_eq_zero
+-/
 
+#print Homotopy.nullHomotopicMap'_f_eq_zero /-
 @[simp]
 theorem nullHomotopicMap'_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
     (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -505,6 +556,7 @@ theorem nullHomotopicMap'_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k
   simp only [← null_homotopic_map']
   exact null_homotopic_map_f_eq_zero hk₀ hk₀' fun i j => dite (c.rel j i) (h i j) fun _ => 0
 #align homotopy.null_homotopic_map'_f_eq_zero Homotopy.nullHomotopicMap'_f_eq_zero
+-/
 
 /-!
 `homotopy.mk_inductive` allows us to build a homotopy of chain complexes inductively,
@@ -525,6 +577,7 @@ section MkInductive
 
 variable {P Q : ChainComplex V ℕ}
 
+#print Homotopy.prevD_chainComplex /-
 @[simp]
 theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     prevD j f = f j (j + 1) ≫ Q.d _ _ := by
@@ -532,7 +585,9 @@ theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
   have : (ComplexShape.down ℕ).prev j = j + 1 := ChainComplex.prev ℕ j
   congr 2
 #align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplex
+-/
 
+#print Homotopy.dNext_succ_chainComplex /-
 @[simp]
 theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     dNext (i + 1) f = P.d _ _ ≫ f i (i + 1) :=
@@ -541,7 +596,9 @@ theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
   have : (ComplexShape.down ℕ).next (i + 1) = i := ChainComplex.next_nat_succ _
   congr 2
 #align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplex
+-/
 
+#print Homotopy.dNext_zero_chainComplex /-
 @[simp]
 theorem dNext_zero_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : dNext 0 f = 0 :=
   by
@@ -549,6 +606,7 @@ theorem dNext_zero_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : dNext 0 f = 0
   rw [P.shape, zero_comp]
   rw [ChainComplex.next_nat_zero]; dsimp; decide
 #align homotopy.d_next_zero_chain_complex Homotopy.dNext_zero_chainComplex
+-/
 
 variable (e : P ⟶ Q) (zero : P.pt 0 ⟶ Q.pt 1) (comm_zero : e.f 0 = zero ≫ Q.d 1 0)
   (one : P.pt 1 ⟶ Q.pt 2) (comm_one : e.f 1 = P.d 1 0 ≫ zero + one ≫ Q.d 2 1)
@@ -560,8 +618,7 @@ variable (e : P ⟶ Q) (zero : P.pt 0 ⟶ Q.pt 1) (comm_zero : e.f 0 = zero ≫
       Σ' f'' : P.pt (n + 2) ⟶ Q.pt (n + 3),
         e.f (n + 2) = P.d (n + 2) (n + 1) ≫ p.2.1 + f'' ≫ Q.d (n + 3) (n + 2))
 
-include comm_one comm_zero
-
+#print Homotopy.mkInductiveAux₁ /-
 /-- An auxiliary construction for `mk_inductive`.
 
 Here we build by induction a family of diagrams,
@@ -584,9 +641,11 @@ def mkInductiveAux₁ :
     ⟨(mk_inductive_aux₁ (n + 1)).2.1, (succ (n + 1) (mk_inductive_aux₁ (n + 1))).1,
       (succ (n + 1) (mk_inductive_aux₁ (n + 1))).2⟩
 #align homotopy.mk_inductive_aux₁ Homotopy.mkInductiveAux₁
+-/
 
 section
 
+#print Homotopy.mkInductiveAux₂ /-
 /-- An auxiliary construction for `mk_inductive`.
 -/
 @[simp]
@@ -597,13 +656,17 @@ def mkInductiveAux₂ :
     let I := mkInductiveAux₁ e zero comm_zero one comm_one succ n
     ⟨(P.xNextIso rfl).Hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv, by simpa using I.2.2⟩
 #align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂
+-/
 
+#print Homotopy.mkInductiveAux₃ /-
 theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).Hom =
       (P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 :=
   by subst j <;> rcases i with (_ | _ | i) <;> · dsimp; simp
 #align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃
+-/
 
+#print Homotopy.mkInductive /-
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed chain complexes,
 working by induction.
 
@@ -634,6 +697,7 @@ def mkInductive : Homotopy e 0
     · dsimp [toPrev]; rw [dif_pos]; swap; · simp only [ChainComplex.prev]
       dsimp [X_prev_iso]; erw [category.comp_id]
 #align homotopy.mk_inductive Homotopy.mkInductive
+-/
 
 end
 
@@ -650,6 +714,7 @@ section MkCoinductive
 
 variable {P Q : CochainComplex V ℕ}
 
+#print Homotopy.dNext_cochainComplex /-
 @[simp]
 theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     dNext j f = P.d _ _ ≫ f (j + 1) j := by
@@ -657,7 +722,9 @@ theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
   have : (ComplexShape.up ℕ).next j = j + 1 := CochainComplex.next ℕ j
   congr 2
 #align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplex
+-/
 
+#print Homotopy.prevD_succ_cochainComplex /-
 @[simp]
 theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     prevD (i + 1) f = f (i + 1) _ ≫ Q.d i (i + 1) :=
@@ -666,7 +733,9 @@ theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
   have : (ComplexShape.up ℕ).prev (i + 1) = i := CochainComplex.prev_nat_succ i
   congr 2
 #align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplex
+-/
 
+#print Homotopy.prevD_zero_cochainComplex /-
 @[simp]
 theorem prevD_zero_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : prevD 0 f = 0 :=
   by
@@ -674,6 +743,7 @@ theorem prevD_zero_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : prevD 0 f =
   rw [Q.shape, comp_zero]
   rw [CochainComplex.prev_nat_zero]; dsimp; decide
 #align homotopy.prev_d_zero_cochain_complex Homotopy.prevD_zero_cochainComplex
+-/
 
 variable (e : P ⟶ Q) (zero : P.pt 1 ⟶ Q.pt 0) (comm_zero : e.f 0 = P.d 0 1 ≫ zero)
   (one : P.pt 2 ⟶ Q.pt 1) (comm_one : e.f 1 = zero ≫ Q.d 0 1 + P.d 1 2 ≫ one)
@@ -685,8 +755,7 @@ variable (e : P ⟶ Q) (zero : P.pt 1 ⟶ Q.pt 0) (comm_zero : e.f 0 = P.d 0 1 
       Σ' f'' : P.pt (n + 3) ⟶ Q.pt (n + 2),
         e.f (n + 2) = p.2.1 ≫ Q.d (n + 1) (n + 2) + P.d (n + 2) (n + 3) ≫ f'')
 
-include comm_one comm_zero succ
-
+#print Homotopy.mkCoinductiveAux₁ /-
 /-- An auxiliary construction for `mk_coinductive`.
 
 Here we build by induction a family of diagrams,
@@ -709,9 +778,11 @@ def mkCoinductiveAux₁ :
     ⟨(mk_coinductive_aux₁ (n + 1)).2.1, (succ (n + 1) (mk_coinductive_aux₁ (n + 1))).1,
       (succ (n + 1) (mk_coinductive_aux₁ (n + 1))).2⟩
 #align homotopy.mk_coinductive_aux₁ Homotopy.mkCoinductiveAux₁
+-/
 
 section
 
+#print Homotopy.mkCoinductiveAux₂ /-
 /-- An auxiliary construction for `mk_inductive`.
 -/
 @[simp]
@@ -722,13 +793,17 @@ def mkCoinductiveAux₂ :
     let I := mkCoinductiveAux₁ e zero comm_zero one comm_one succ n
     ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).Hom ≫ I.2.1, by simpa using I.2.2⟩
 #align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂
+-/
 
+#print Homotopy.mkCoinductiveAux₃ /-
 theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
       (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).1 ≫ (Q.xPrevIso h).Hom :=
   by subst j <;> rcases i with (_ | _ | i) <;> · dsimp; simp
 #align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃
+-/
 
+#print Homotopy.mkCoinductive /-
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed cochain complexes,
 working by induction.
 
@@ -760,6 +835,7 @@ def mkCoinductive : Homotopy e 0
     · dsimp [fromNext]; rw [dif_pos]; swap; · simp only [CochainComplex.next]
       dsimp [X_next_iso]; erw [category.id_comp]
 #align homotopy.mk_coinductive Homotopy.mkCoinductive
+-/
 
 end
 
@@ -839,6 +915,7 @@ end HomotopyEquiv
 
 variable [HasEqualizers V] [HasCokernels V] [HasImages V] [HasImageMaps V]
 
+#print homology_map_eq_of_homotopy /-
 /-- Homotopic maps induce the same map on homology.
 -/
 theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
@@ -859,7 +936,9 @@ theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
   · rw [prevD_eq_toPrev_dTo, ← category.assoc]
     apply image_subobject_factors_comp_self
 #align homology_map_eq_of_homotopy homology_map_eq_of_homotopy
+-/
 
+#print homologyObjIsoOfHomotopyEquiv /-
 /-- Homotopy equivalent complexes have isomorphic homologies. -/
 def homologyObjIsoOfHomotopyEquiv (f : HomotopyEquiv C D) (i : ι) :
     (homologyFunctor V c i).obj C ≅ (homologyFunctor V c i).obj D
@@ -873,6 +952,7 @@ def homologyObjIsoOfHomotopyEquiv (f : HomotopyEquiv C D) (i : ι) :
     rw [← functor.map_comp, homology_map_eq_of_homotopy f.homotopy_inv_hom_id,
       CategoryTheory.Functor.map_id]
 #align homology_obj_iso_of_homotopy_equiv homologyObjIsoOfHomotopyEquiv
+-/
 
 end
 
@@ -880,6 +960,7 @@ namespace CategoryTheory
 
 variable {W : Type _} [Category W] [Preadditive W]
 
+#print CategoryTheory.Functor.mapHomotopy /-
 /-- An additive functor takes homotopies to homotopies. -/
 @[simps]
 def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy f g) :
@@ -893,7 +974,9 @@ def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy
     simp only [F.map_add, ← F.map_comp]
     rfl
 #align category_theory.functor.map_homotopy CategoryTheory.Functor.mapHomotopy
+-/
 
+#print CategoryTheory.Functor.mapHomotopyEquiv /-
 /-- An additive functor preserves homotopy equivalences. -/
 @[simps]
 def Functor.mapHomotopyEquiv (F : V ⥤ W) [F.Additive] (h : HomotopyEquiv C D) :
@@ -910,6 +993,7 @@ def Functor.mapHomotopyEquiv (F : V ⥤ W) [F.Additive] (h : HomotopyEquiv C D)
     rw [← (F.map_homological_complex c).map_comp, ← (F.map_homological_complex c).map_id]
     exact F.map_homotopy h.homotopy_inv_hom_id
 #align category_theory.functor.map_homotopy_equiv CategoryTheory.Functor.mapHomotopyEquiv
+-/
 
 end CategoryTheory

86d1873c

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -622,7 +622,7 @@ def mkInductive : Homotopy e 0
   zero' i j w := by rwa [dif_neg]
   comm i := by
     dsimp; simp only [add_zero]
-    convert(mk_inductive_aux₂ e zero comm_zero one comm_one succ i).2.2
+    convert (mk_inductive_aux₂ e zero comm_zero one comm_one succ i).2.2
     · cases i
       · dsimp [fromNext]; rw [dif_neg]
         simp only [ChainComplex.next_nat_zero, Nat.one_ne_zero, not_false_iff]
@@ -748,7 +748,7 @@ def mkCoinductive : Homotopy e 0
   comm i := by
     dsimp
     rw [add_zero, add_comm]
-    convert(mk_coinductive_aux₂ e zero comm_zero one comm_one succ i).2.2 using 2
+    convert (mk_coinductive_aux₂ e zero comm_zero one comm_one succ i).2.2 using 2
     · cases i
       · dsimp [toPrev]; rw [dif_neg]
         simp only [CochainComplex.prev_nat_zero, Nat.one_ne_zero, not_false_iff]

86d1873c

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -555,9 +555,9 @@ variable (e : P ⟶ Q) (zero : P.pt 0 ⟶ Q.pt 1) (comm_zero : e.f 0 = zero ≫
   (succ :
     ∀ (n : ℕ)
       (p :
-        Σ'(f : P.pt n ⟶ Q.pt (n + 1))(f' : P.pt (n + 1) ⟶ Q.pt (n + 2)),
+        Σ' (f : P.pt n ⟶ Q.pt (n + 1)) (f' : P.pt (n + 1) ⟶ Q.pt (n + 2)),
           e.f (n + 1) = P.d (n + 1) n ≫ f + f' ≫ Q.d (n + 2) (n + 1)),
-      Σ'f'' : P.pt (n + 2) ⟶ Q.pt (n + 3),
+      Σ' f'' : P.pt (n + 2) ⟶ Q.pt (n + 3),
         e.f (n + 2) = P.d (n + 2) (n + 1) ≫ p.2.1 + f'' ≫ Q.d (n + 3) (n + 2))
 
 include comm_one comm_zero
@@ -576,7 +576,7 @@ which we do in `mk_inductive_aux₂`.
 @[simp, nolint unused_arguments]
 def mkInductiveAux₁ :
     ∀ n,
-      Σ'(f : P.pt n ⟶ Q.pt (n + 1))(f' : P.pt (n + 1) ⟶ Q.pt (n + 2)),
+      Σ' (f : P.pt n ⟶ Q.pt (n + 1)) (f' : P.pt (n + 1) ⟶ Q.pt (n + 2)),
         e.f (n + 1) = P.d (n + 1) n ≫ f + f' ≫ Q.d (n + 2) (n + 1)
   | 0 => ⟨zero, one, comm_one⟩
   | 1 => ⟨one, (succ 0 ⟨zero, one, comm_one⟩).1, (succ 0 ⟨zero, one, comm_one⟩).2⟩
@@ -591,7 +591,7 @@ section
 -/
 @[simp]
 def mkInductiveAux₂ :
-    ∀ n, Σ'(f : P.xNext n ⟶ Q.pt n)(f' : P.pt n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
+    ∀ n, Σ' (f : P.xNext n ⟶ Q.pt n) (f' : P.pt n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
   | 0 => ⟨0, zero ≫ (Q.xPrevIso rfl).inv, by simpa using comm_zero⟩
   | n + 1 =>
     let I := mkInductiveAux₁ e zero comm_zero one comm_one succ n
@@ -680,9 +680,9 @@ variable (e : P ⟶ Q) (zero : P.pt 1 ⟶ Q.pt 0) (comm_zero : e.f 0 = P.d 0 1 
   (succ :
     ∀ (n : ℕ)
       (p :
-        Σ'(f : P.pt (n + 1) ⟶ Q.pt n)(f' : P.pt (n + 2) ⟶ Q.pt (n + 1)),
+        Σ' (f : P.pt (n + 1) ⟶ Q.pt n) (f' : P.pt (n + 2) ⟶ Q.pt (n + 1)),
           e.f (n + 1) = f ≫ Q.d n (n + 1) + P.d (n + 1) (n + 2) ≫ f'),
-      Σ'f'' : P.pt (n + 3) ⟶ Q.pt (n + 2),
+      Σ' f'' : P.pt (n + 3) ⟶ Q.pt (n + 2),
         e.f (n + 2) = p.2.1 ≫ Q.d (n + 1) (n + 2) + P.d (n + 2) (n + 3) ≫ f'')
 
 include comm_one comm_zero succ
@@ -701,7 +701,7 @@ which we do in `mk_inductive_aux₂`.
 @[simp, nolint unused_arguments]
 def mkCoinductiveAux₁ :
     ∀ n,
-      Σ'(f : P.pt (n + 1) ⟶ Q.pt n)(f' : P.pt (n + 2) ⟶ Q.pt (n + 1)),
+      Σ' (f : P.pt (n + 1) ⟶ Q.pt n) (f' : P.pt (n + 2) ⟶ Q.pt (n + 1)),
         e.f (n + 1) = f ≫ Q.d n (n + 1) + P.d (n + 1) (n + 2) ≫ f'
   | 0 => ⟨zero, one, comm_one⟩
   | 1 => ⟨one, (succ 0 ⟨zero, one, comm_one⟩).1, (succ 0 ⟨zero, one, comm_one⟩).2⟩
@@ -716,7 +716,7 @@ section
 -/
 @[simp]
 def mkCoinductiveAux₂ :
-    ∀ n, Σ'(f : P.pt n ⟶ Q.xPrev n)(f' : P.xNext n ⟶ Q.pt n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
+    ∀ n, Σ' (f : P.pt n ⟶ Q.xPrev n) (f' : P.xNext n ⟶ Q.pt n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
   | 0 => ⟨0, (P.xNextIso rfl).Hom ≫ zero, by simpa using comm_zero⟩
   | n + 1 =>
     let I := mkCoinductiveAux₁ e zero comm_zero one comm_one succ n

86d1873c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -23,7 +23,7 @@ We define chain homotopies, and prove that homotopic chain maps induce the same
 
 universe v u
 
-open Classical
+open scoped Classical
 
 noncomputable section

86d1873c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -57,34 +57,22 @@ def fromNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.xNext i ⟶ D.pt i)
 #align from_next fromNext
 -/
 
-/- warning: d_next_eq_d_from_from_next -> dNext_eq_dFrom_fromNext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNextₓ'. -/
 @[simp]
 theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
     dNext i f = C.dFrom i ≫ fromNext i f :=
   rfl
 #align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNext
 
-/- warning: d_next_eq -> dNext_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align d_next_eq dNext_eqₓ'. -/
 theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
     dNext i f = C.d i i' ≫ f i' i := by obtain rfl := c.next_eq' w; rfl
 #align d_next_eq dNext_eq
 
-/- warning: d_next_comp_left -> dNext_comp_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align d_next_comp_left dNext_comp_leftₓ'. -/
 @[simp]
 theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (i : ι) :
     (dNext i fun i j => f.f i ≫ g i j) = f.f i ≫ dNext i g :=
   (f.comm_assoc _ _ _).symm
 #align d_next_comp_left dNext_comp_left
 
-/- warning: d_next_comp_right -> dNext_comp_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align d_next_comp_right dNext_comp_rightₓ'. -/
 @[simp]
 theorem dNext_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (i : ι) :
     (dNext i fun i j => f i j ≫ g.f j) = dNext i f ≫ g.f i :=
@@ -109,43 +97,28 @@ def toPrev (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.xPrev j) :
 #align to_prev toPrev
 -/
 
-/- warning: prev_d_eq_to_prev_d_to -> prevD_eq_toPrev_dTo is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dToₓ'. -/
 @[simp]
 theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
     prevD j f = toPrev j f ≫ D.dTo j :=
   rfl
 #align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dTo
 
-/- warning: prev_d_eq -> prevD_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align prev_d_eq prevD_eqₓ'. -/
 theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
     prevD j f = f j j' ≫ D.d j' j := by obtain rfl := c.prev_eq' w; rfl
 #align prev_d_eq prevD_eq
 
-/- warning: prev_d_comp_left -> prevD_comp_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align prev_d_comp_left prevD_comp_leftₓ'. -/
 @[simp]
 theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι) :
     (prevD j fun i j => f.f i ≫ g i j) = f.f j ≫ prevD j g :=
   Category.assoc _ _ _
 #align prev_d_comp_left prevD_comp_left
 
-/- warning: prev_d_comp_right -> prevD_comp_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align prev_d_comp_right prevD_comp_rightₓ'. -/
 @[simp]
 theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι) :
     (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j := by dsimp [prevD];
   simp only [category.assoc, g.comm]
 #align prev_d_comp_right prevD_comp_right
 
-/- warning: d_next_nat -> dNext_nat is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align d_next_nat dNext_natₓ'. -/
 theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     dNext i f = C.d i (i - 1) ≫ f (i - 1) i :=
   by
@@ -159,9 +132,6 @@ theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶
     congr 2
 #align d_next_nat dNext_nat
 
-/- warning: prev_d_nat -> prevD_nat is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align prev_d_nat prevD_natₓ'. -/
 theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     prevD i f = f i (i - 1) ≫ D.d (i - 1) i :=
   by
@@ -196,9 +166,6 @@ namespace Homotopy
 
 restate_axiom Homotopy.zero'
 
-/- warning: homotopy.equiv_sub_zero -> Homotopy.equivSubZero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.equiv_sub_zero Homotopy.equivSubZeroₓ'. -/
 /-- `f` is homotopic to `g` iff `f - g` is homotopic to `0`.
 -/
 def equivSubZero : Homotopy f g ≃ Homotopy (f - g) 0
@@ -257,9 +224,6 @@ def trans {e f g : C ⟶ D} (h : Homotopy e f) (k : Homotopy f g) : Homotopy e g
 #align homotopy.trans Homotopy.trans
 -/
 
-/- warning: homotopy.add -> Homotopy.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.add Homotopy.addₓ'. -/
 /-- the sum of two homotopies is a homotopy between the sum of the respective morphisms. -/
 @[simps]
 def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homotopy f₂ g₂) :
@@ -355,12 +319,6 @@ def nullHomotopicMap' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : C ⟶ D
 #align homotopy.null_homotopic_map' Homotopy.nullHomotopicMap'
 -/
 
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-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_comp Homotopy.nullHomotopicMap_compₓ'. -/
 /-- Compatibility of `null_homotopic_map` with the postcomposition by a morphism
 of complexes. -/
 theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
@@ -371,12 +329,6 @@ theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
   simp only [preadditive.add_comp, category.assoc, g.comm]
 #align homotopy.null_homotopic_map_comp Homotopy.nullHomotopicMap_comp
 
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 /-- Compatibility of `null_homotopic_map'` with the postcomposition by a morphism
 of complexes. -/
 theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) (g : D ⟶ E) :
@@ -391,12 +343,6 @@ theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)
   · rw [zero_comp]
 #align homotopy.null_homotopic_map'_comp Homotopy.nullHomotopicMap'_comp
 
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 /-- Compatibility of `null_homotopic_map` with the precomposition by a morphism
 of complexes. -/
 theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
@@ -407,12 +353,6 @@ theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
   simp only [preadditive.comp_add, category.assoc, f.comm_assoc]
 #align homotopy.comp_null_homotopic_map Homotopy.comp_nullHomotopicMap
 
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-Case conversion may be inaccurate. Consider using '#align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'ₓ'. -/
 /-- Compatibility of `null_homotopic_map'` with the precomposition by a morphism
 of complexes. -/
 theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt i ⟶ E.pt j)) :
@@ -427,9 +367,6 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt
   · rw [comp_zero]
 #align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMapₓ'. -/
 /-- Compatibility of `null_homotopic_map` with the application of additive functors -/
 theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -441,9 +378,6 @@ theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V 
   simp only [G.map_comp, functor.map_add]
 #align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMap
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.map_null_homotopic_map' Homotopy.map_nullHomotopicMap'ₓ'. -/
 /-- Compatibility of `null_homotopic_map'` with the application of additive functors -/
 theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -491,9 +425,6 @@ the degreewise morphisms induced by the null homotopic maps constructed
 with `null_homotopic_map` or `null_homotopic_map'` -/
 
 
-/- warning: homotopy.null_homotopic_map_f -> Homotopy.nullHomotopicMap_f is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_fₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -501,9 +432,6 @@ theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
   dsimp only [null_homotopic_map]; rw [dNext_eq hom r₁₀, prevD_eq hom r₂₁]
 #align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_f
 
-/- warning: homotopy.null_homotopic_map'_f -> Homotopy.nullHomotopicMap'_f is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_fₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -516,12 +444,6 @@ theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
   rfl
 #align homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_f
 
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-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f_of_not_rel_left Homotopy.nullHomotopicMap_f_of_not_rel_leftₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -532,12 +454,6 @@ theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
   exact hk₀ _
 #align homotopy.null_homotopic_map_f_of_not_rel_left Homotopy.nullHomotopicMap_f_of_not_rel_left
 
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-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f_of_not_rel_left Homotopy.nullHomotopicMap'_f_of_not_rel_leftₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -550,12 +466,6 @@ theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_left Homotopy.nullHomotopicMap'_f_of_not_rel_left
 
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-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f_of_not_rel_right Homotopy.nullHomotopicMap_f_of_not_rel_rightₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -566,12 +476,6 @@ theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
   exact hk₁ _
 #align homotopy.null_homotopic_map_f_of_not_rel_right Homotopy.nullHomotopicMap_f_of_not_rel_right
 
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 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -584,12 +488,6 @@ theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_right Homotopy.nullHomotopicMap'_f_of_not_rel_right
 
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 @[simp]
 theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
     (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -599,12 +497,6 @@ theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀
   rw [C.shape, D.shape, zero_comp, comp_zero, add_zero] <;> apply_assumption
 #align homotopy.null_homotopic_map_f_eq_zero Homotopy.nullHomotopicMap_f_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f_eq_zero Homotopy.nullHomotopicMap'_f_eq_zeroₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
     (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -633,9 +525,6 @@ section MkInductive
 
 variable {P Q : ChainComplex V ℕ}
 
-/- warning: homotopy.prev_d_chain_complex -> Homotopy.prevD_chainComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplexₓ'. -/
 @[simp]
 theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     prevD j f = f j (j + 1) ≫ Q.d _ _ := by
@@ -644,9 +533,6 @@ theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
   congr 2
 #align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplex
 
-/- warning: homotopy.d_next_succ_chain_complex -> Homotopy.dNext_succ_chainComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplexₓ'. -/
 @[simp]
 theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     dNext (i + 1) f = P.d _ _ ≫ f i (i + 1) :=
@@ -656,9 +542,6 @@ theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
   congr 2
 #align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplex
 
-/- warning: homotopy.d_next_zero_chain_complex -> Homotopy.dNext_zero_chainComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.d_next_zero_chain_complex Homotopy.dNext_zero_chainComplexₓ'. -/
 @[simp]
 theorem dNext_zero_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : dNext 0 f = 0 :=
   by
@@ -679,9 +562,6 @@ variable (e : P ⟶ Q) (zero : P.pt 0 ⟶ Q.pt 1) (comm_zero : e.f 0 = zero ≫
 
 include comm_one comm_zero
 
-/- warning: homotopy.mk_inductive_aux₁ -> Homotopy.mkInductiveAux₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₁ Homotopy.mkInductiveAux₁ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 
 Here we build by induction a family of diagrams,
@@ -707,9 +587,6 @@ def mkInductiveAux₁ :
 
 section
 
-/- warning: homotopy.mk_inductive_aux₂ -> Homotopy.mkInductiveAux₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 -/
 @[simp]
@@ -721,18 +598,12 @@ def mkInductiveAux₂ :
     ⟨(P.xNextIso rfl).Hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv, by simpa using I.2.2⟩
 #align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂
 
-/- warning: homotopy.mk_inductive_aux₃ -> Homotopy.mkInductiveAux₃ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃ₓ'. -/
 theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).Hom =
       (P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 :=
   by subst j <;> rcases i with (_ | _ | i) <;> · dsimp; simp
 #align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃
 
-/- warning: homotopy.mk_inductive -> Homotopy.mkInductive is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive Homotopy.mkInductiveₓ'. -/
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed chain complexes,
 working by induction.
 
@@ -779,9 +650,6 @@ section MkCoinductive
 
 variable {P Q : CochainComplex V ℕ}
 
-/- warning: homotopy.d_next_cochain_complex -> Homotopy.dNext_cochainComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplexₓ'. -/
 @[simp]
 theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     dNext j f = P.d _ _ ≫ f (j + 1) j := by
@@ -790,9 +658,6 @@ theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
   congr 2
 #align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplex
 
-/- warning: homotopy.prev_d_succ_cochain_complex -> Homotopy.prevD_succ_cochainComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplexₓ'. -/
 @[simp]
 theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     prevD (i + 1) f = f (i + 1) _ ≫ Q.d i (i + 1) :=
@@ -802,9 +667,6 @@ theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
   congr 2
 #align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplex
 
-/- warning: homotopy.prev_d_zero_cochain_complex -> Homotopy.prevD_zero_cochainComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_zero_cochain_complex Homotopy.prevD_zero_cochainComplexₓ'. -/
 @[simp]
 theorem prevD_zero_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : prevD 0 f = 0 :=
   by
@@ -825,9 +687,6 @@ variable (e : P ⟶ Q) (zero : P.pt 1 ⟶ Q.pt 0) (comm_zero : e.f 0 = P.d 0 1 
 
 include comm_one comm_zero succ
 
-/- warning: homotopy.mk_coinductive_aux₁ -> Homotopy.mkCoinductiveAux₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₁ Homotopy.mkCoinductiveAux₁ₓ'. -/
 /-- An auxiliary construction for `mk_coinductive`.
 
 Here we build by induction a family of diagrams,
@@ -853,9 +712,6 @@ def mkCoinductiveAux₁ :
 
 section
 
-/- warning: homotopy.mk_coinductive_aux₂ -> Homotopy.mkCoinductiveAux₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 -/
 @[simp]
@@ -867,18 +723,12 @@ def mkCoinductiveAux₂ :
     ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).Hom ≫ I.2.1, by simpa using I.2.2⟩
 #align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂
 
-/- warning: homotopy.mk_coinductive_aux₃ -> Homotopy.mkCoinductiveAux₃ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃ₓ'. -/
 theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
       (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).1 ≫ (Q.xPrevIso h).Hom :=
   by subst j <;> rcases i with (_ | _ | i) <;> · dsimp; simp
 #align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃
 
-/- warning: homotopy.mk_coinductive -> Homotopy.mkCoinductive is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive Homotopy.mkCoinductiveₓ'. -/
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed cochain complexes,
 working by induction.
 
@@ -989,9 +839,6 @@ end HomotopyEquiv
 
 variable [HasEqualizers V] [HasCokernels V] [HasImages V] [HasImageMaps V]
 
-/- warning: homology_map_eq_of_homotopy -> homology_map_eq_of_homotopy is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homology_map_eq_of_homotopy homology_map_eq_of_homotopyₓ'. -/
 /-- Homotopic maps induce the same map on homology.
 -/
 theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
@@ -1013,12 +860,6 @@ theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
     apply image_subobject_factors_comp_self
 #align homology_map_eq_of_homotopy homology_map_eq_of_homotopy
 
-/- warning: homology_obj_iso_of_homotopy_equiv -> homologyObjIsoOfHomotopyEquiv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align homology_obj_iso_of_homotopy_equiv homologyObjIsoOfHomotopyEquivₓ'. -/
 /-- Homotopy equivalent complexes have isomorphic homologies. -/
 def homologyObjIsoOfHomotopyEquiv (f : HomotopyEquiv C D) (i : ι) :
     (homologyFunctor V c i).obj C ≅ (homologyFunctor V c i).obj D
@@ -1039,9 +880,6 @@ namespace CategoryTheory
 
 variable {W : Type _} [Category W] [Preadditive W]
 
-/- warning: category_theory.functor.map_homotopy -> CategoryTheory.Functor.mapHomotopy is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_homotopy CategoryTheory.Functor.mapHomotopyₓ'. -/
 /-- An additive functor takes homotopies to homotopies. -/
 @[simps]
 def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy f g) :
@@ -1056,12 +894,6 @@ def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy
     rfl
 #align category_theory.functor.map_homotopy CategoryTheory.Functor.mapHomotopy
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_homotopy_equiv CategoryTheory.Functor.mapHomotopyEquivₓ'. -/
 /-- An additive functor preserves homotopy equivalences. -/
 @[simps]
 def Functor.mapHomotopyEquiv (F : V ⥤ W) [F.Additive] (h : HomotopyEquiv C D) :

86d1873c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -70,10 +70,7 @@ theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align d_next_eq dNext_eqₓ'. -/
 theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
-    dNext i f = C.d i i' ≫ f i' i :=
-  by
-  obtain rfl := c.next_eq' w
-  rfl
+    dNext i f = C.d i i' ≫ f i' i := by obtain rfl := c.next_eq' w; rfl
 #align d_next_eq dNext_eq
 
 /- warning: d_next_comp_left -> dNext_comp_left is a dubious translation:
@@ -125,10 +122,7 @@ theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align prev_d_eq prevD_eqₓ'. -/
 theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
-    prevD j f = f j j' ≫ D.d j' j :=
-  by
-  obtain rfl := c.prev_eq' w
-  rfl
+    prevD j f = f j j' ≫ D.d j' j := by obtain rfl := c.prev_eq' w; rfl
 #align prev_d_eq prevD_eq
 
 /- warning: prev_d_comp_left -> prevD_comp_left is a dubious translation:
@@ -145,9 +139,7 @@ theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι)
 Case conversion may be inaccurate. Consider using '#align prev_d_comp_right prevD_comp_rightₓ'. -/
 @[simp]
 theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι) :
-    (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j :=
-  by
-  dsimp [prevD]
+    (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j := by dsimp [prevD];
   simp only [category.assoc, g.comm]
 #align prev_d_comp_right prevD_comp_right
 
@@ -163,10 +155,7 @@ theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶
     simp only [shape, ChainComplex.next_nat_zero, ComplexShape.down_Rel, Nat.one_ne_zero,
       not_false_iff, zero_comp]
   · dsimp only [Nat.succ_eq_add_one]
-    have : (ComplexShape.down ℕ).next (i + 1) = i + 1 - 1 :=
-      by
-      rw [ChainComplex.next_nat_succ]
-      rfl
+    have : (ComplexShape.down ℕ).next (i + 1) = i + 1 - 1 := by rw [ChainComplex.next_nat_succ]; rfl
     congr 2
 #align d_next_nat dNext_nat
 
@@ -182,10 +171,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i 
     simp only [shape, CochainComplex.prev_nat_zero, ComplexShape.up_Rel, Nat.one_ne_zero,
       not_false_iff, comp_zero]
   · dsimp only [Nat.succ_eq_add_one]
-    have : (ComplexShape.up ℕ).prev (i + 1) = i + 1 - 1 :=
-      by
-      rw [CochainComplex.prev_nat_succ]
-      rfl
+    have : (ComplexShape.up ℕ).prev (i + 1) = i + 1 - 1 := by rw [CochainComplex.prev_nat_succ]; rfl
     congr 2
 #align prev_d_nat prevD_nat
 
@@ -267,9 +253,7 @@ def trans {e f g : C ⟶ D} (h : Homotopy e f) (k : Homotopy f g) : Homotopy e g
     where
   Hom := h.Hom + k.Hom
   zero' i j w := by rw [Pi.add_apply, Pi.add_apply, h.zero i j w, k.zero i j w, zero_add]
-  comm i := by
-    rw [AddMonoidHom.map_add, AddMonoidHom.map_add, h.comm, k.comm]
-    abel
+  comm i := by rw [AddMonoidHom.map_add, AddMonoidHom.map_add, h.comm, k.comm]; abel
 #align homotopy.trans Homotopy.trans
 -/
 
@@ -483,10 +467,7 @@ def nullHomotopy (hom : ∀ i j, C.pt i ⟶ D.pt j) (zero' : ∀ i j, ¬c.Rel j
     Homotopy (nullHomotopicMap hom) 0 :=
   { Hom
     zero'
-    comm := by
-      intro i
-      rw [HomologicalComplex.zero_f_apply, add_zero]
-      rfl }
+    comm := by intro i; rw [HomologicalComplex.zero_f_apply, add_zero]; rfl }
 #align homotopy.null_homotopy Homotopy.nullHomotopy
 -/
 
@@ -516,10 +497,8 @@ Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopi
 @[simp]
 theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
-    (nullHomotopicMap hom).f k₁ = C.d k₁ k₀ ≫ hom k₀ k₁ + hom k₁ k₂ ≫ D.d k₂ k₁ :=
-  by
-  dsimp only [null_homotopic_map]
-  rw [dNext_eq hom r₁₀, prevD_eq hom r₂₁]
+    (nullHomotopicMap hom).f k₁ = C.d k₁ k₀ ≫ hom k₀ k₁ + hom k₁ k₂ ≫ D.d k₂ k₁ := by
+  dsimp only [null_homotopic_map]; rw [dNext_eq hom r₁₀, prevD_eq hom r₂₁]
 #align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_f
 
 /- warning: homotopy.null_homotopic_map'_f -> Homotopy.nullHomotopicMap'_f is a dubious translation:
@@ -748,10 +727,7 @@ Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_
 theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).Hom =
       (P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 :=
-  by
-  subst j <;> rcases i with (_ | _ | i) <;>
-    · dsimp
-      simp
+  by subst j <;> rcases i with (_ | _ | i) <;> · dsimp; simp
 #align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃
 
 /- warning: homotopy.mk_inductive -> Homotopy.mkInductive is a dubious translation:
@@ -777,24 +753,15 @@ def mkInductive : Homotopy e 0
     dsimp; simp only [add_zero]
     convert(mk_inductive_aux₂ e zero comm_zero one comm_one succ i).2.2
     · cases i
-      · dsimp [fromNext]
-        rw [dif_neg]
+      · dsimp [fromNext]; rw [dif_neg]
         simp only [ChainComplex.next_nat_zero, Nat.one_ne_zero, not_false_iff]
-      · dsimp [fromNext]
-        rw [dif_pos]
-        swap
-        · simp only [ChainComplex.next_nat_succ]
+      · dsimp [fromNext]; rw [dif_pos]; swap; · simp only [ChainComplex.next_nat_succ]
         have aux : (ComplexShape.down ℕ).next i.succ = i := ChainComplex.next_nat_succ i
         rw [mk_inductive_aux₃ e zero comm_zero one comm_one succ ((ComplexShape.down ℕ).next i.succ)
             (i + 1) (by rw [aux])]
-        dsimp [X_next_iso]
-        erw [category.id_comp]
-    · dsimp [toPrev]
-      rw [dif_pos]
-      swap
-      · simp only [ChainComplex.prev]
-      dsimp [X_prev_iso]
-      erw [category.comp_id]
+        dsimp [X_next_iso]; erw [category.id_comp]
+    · dsimp [toPrev]; rw [dif_pos]; swap; · simp only [ChainComplex.prev]
+      dsimp [X_prev_iso]; erw [category.comp_id]
 #align homotopy.mk_inductive Homotopy.mkInductive
 
 end
@@ -906,10 +873,7 @@ Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductiv
 theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
       (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).1 ≫ (Q.xPrevIso h).Hom :=
-  by
-  subst j <;> rcases i with (_ | _ | i) <;>
-    · dsimp
-      simp
+  by subst j <;> rcases i with (_ | _ | i) <;> · dsimp; simp
 #align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃
 
 /- warning: homotopy.mk_coinductive -> Homotopy.mkCoinductive is a dubious translation:
@@ -936,24 +900,15 @@ def mkCoinductive : Homotopy e 0
     rw [add_zero, add_comm]
     convert(mk_coinductive_aux₂ e zero comm_zero one comm_one succ i).2.2 using 2
     · cases i
-      · dsimp [toPrev]
-        rw [dif_neg]
+      · dsimp [toPrev]; rw [dif_neg]
         simp only [CochainComplex.prev_nat_zero, Nat.one_ne_zero, not_false_iff]
-      · dsimp [toPrev]
-        rw [dif_pos]
-        swap
-        · simp only [CochainComplex.prev_nat_succ]
+      · dsimp [toPrev]; rw [dif_pos]; swap; · simp only [CochainComplex.prev_nat_succ]
         have aux : (ComplexShape.up ℕ).prev i.succ = i := CochainComplex.prev_nat_succ i
         rw [mk_coinductive_aux₃ e zero comm_zero one comm_one succ ((ComplexShape.up ℕ).prev i.succ)
             (i + 1) (by rw [aux])]
-        dsimp [X_prev_iso]
-        erw [category.comp_id]
-    · dsimp [fromNext]
-      rw [dif_pos]
-      swap
-      · simp only [CochainComplex.next]
-      dsimp [X_next_iso]
-      erw [category.id_comp]
+        dsimp [X_prev_iso]; erw [category.comp_id]
+    · dsimp [fromNext]; rw [dif_pos]; swap; · simp only [CochainComplex.next]
+      dsimp [X_next_iso]; erw [category.id_comp]
 #align homotopy.mk_coinductive Homotopy.mkCoinductive
 
 end

86d1873c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -58,10 +58,7 @@ def fromNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.xNext i ⟶ D.pt i)
 -/
 
 /- warning: d_next_eq_d_from_from_next -> dNext_eq_dFrom_fromNext is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNextₓ'. -/
 @[simp]
 theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
@@ -70,10 +67,7 @@ theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
 #align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNext
 
 /- warning: d_next_eq -> dNext_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align d_next_eq dNext_eqₓ'. -/
 theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
     dNext i f = C.d i i' ≫ f i' i :=
@@ -83,10 +77,7 @@ theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
 #align d_next_eq dNext_eq
 
 /- warning: d_next_comp_left -> dNext_comp_left is a dubious translation:
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g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align d_next_comp_left dNext_comp_leftₓ'. -/
 @[simp]
 theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (i : ι) :
@@ -95,10 +86,7 @@ theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (i : ι)
 #align d_next_comp_left dNext_comp_left
 
 /- warning: d_next_comp_right -> dNext_comp_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align d_next_comp_right dNext_comp_rightₓ'. -/
 @[simp]
 theorem dNext_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (i : ι) :
@@ -125,10 +113,7 @@ def toPrev (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.xPrev j) :
 -/
 
 /- warning: prev_d_eq_to_prev_d_to -> prevD_eq_toPrev_dTo is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dToₓ'. -/
 @[simp]
 theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
@@ -137,10 +122,7 @@ theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
 #align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dTo
 
 /- warning: prev_d_eq -> prevD_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align prev_d_eq prevD_eqₓ'. -/
 theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
     prevD j f = f j j' ≫ D.d j' j :=
@@ -150,10 +132,7 @@ theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
 #align prev_d_eq prevD_eq
 
 /- warning: prev_d_comp_left -> prevD_comp_left is a dubious translation:
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g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align prev_d_comp_left prevD_comp_leftₓ'. -/
 @[simp]
 theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι) :
@@ -162,10 +141,7 @@ theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι)
 #align prev_d_comp_left prevD_comp_left
 
 /- warning: prev_d_comp_right -> prevD_comp_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align prev_d_comp_right prevD_comp_rightₓ'. -/
 @[simp]
 theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι) :
@@ -176,10 +152,7 @@ theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι)
 #align prev_d_comp_right prevD_comp_right
 
 /- warning: d_next_nat -> dNext_nat is a dubious translation:
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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) C (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) D i) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) C i (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align d_next_nat dNext_natₓ'. -/
 theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     dNext i f = C.d i (i - 1) ≫ f (i - 1) i :=
@@ -198,10 +171,7 @@ theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶
 #align d_next_nat dNext_nat
 
 /- warning: prev_d_nat -> prevD_nat is a dubious translation:
-lean 3 declaration is
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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D j)) (fun (i : Nat) => Pi.addZeroClass.{0, u1} Nat (fun (j : Nat) => Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 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(ComplexShape.up.{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)) C D i) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i) (f i (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align prev_d_nat prevD_natₓ'. -/
 theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     prevD i f = f i (i - 1) ≫ D.d (i - 1) i :=
@@ -241,10 +211,7 @@ namespace Homotopy
 restate_axiom Homotopy.zero'
 
 /- warning: homotopy.equiv_sub_zero -> Homotopy.equivSubZero is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {f : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c))) C D} {g : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c))) C D}, Equiv.{max (succ u3) (succ u1), max (succ u3) (succ u1)} 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 Case conversion may be inaccurate. Consider using '#align homotopy.equiv_sub_zero Homotopy.equivSubZeroₓ'. -/
 /-- `f` is homotopic to `g` iff `f - g` is homotopic to `0`.
 -/
@@ -307,10 +274,7 @@ def trans {e f g : C ⟶ D} (h : Homotopy e f) (k : Homotopy f g) : Homotopy e g
 -/
 
 /- warning: homotopy.add -> Homotopy.add is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.add Homotopy.addₓ'. -/
 /-- the sum of two homotopies is a homotopy between the sum of the respective morphisms. -/
 @[simps]
@@ -480,10 +444,7 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt
 #align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'
 
 /- warning: homotopy.map_null_homotopic_map -> Homotopy.map_nullHomotopicMap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMapₓ'. -/
 /-- Compatibility of `null_homotopic_map` with the application of additive functors -/
 theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
@@ -497,10 +458,7 @@ theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V 
 #align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMap
 
 /- warning: homotopy.map_null_homotopic_map' -> Homotopy.map_nullHomotopicMap' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align homotopy.map_null_homotopic_map' Homotopy.map_nullHomotopicMap'ₓ'. -/
 /-- Compatibility of `null_homotopic_map'` with the application of additive functors -/
 theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
@@ -553,10 +511,7 @@ with `null_homotopic_map` or `null_homotopic_map'` -/
 
 
 /- warning: homotopy.null_homotopic_map_f -> Homotopy.nullHomotopicMap_f is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_fₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
@@ -568,10 +523,7 @@ theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
 #align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_f
 
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁)))))))) (CategoryTheory.CategoryStruct.comp.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁) (HomologicalComplex.d.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁ k₀) (h k₀ k₁ r₁₀)) (CategoryTheory.CategoryStruct.comp.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₂) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁) (h k₁ k₂ r₂₁) (HomologicalComplex.d.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₂ k₁)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_fₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
@@ -703,10 +655,7 @@ section MkInductive
 variable {P Q : ChainComplex V ℕ}
 
 /- warning: homotopy.prev_d_chain_complex -> Homotopy.prevD_chainComplex is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplexₓ'. -/
 @[simp]
 theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
@@ -717,10 +666,7 @@ theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
 #align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplex
 
 /- warning: homotopy.d_next_succ_chain_complex -> Homotopy.dNext_succ_chainComplex is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplexₓ'. -/
 @[simp]
 theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
@@ -732,10 +678,7 @@ theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
 #align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplex
 
 /- warning: homotopy.d_next_zero_chain_complex -> Homotopy.dNext_zero_chainComplex is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.d_next_zero_chain_complex Homotopy.dNext_zero_chainComplexₓ'. -/
 @[simp]
 theorem dNext_zero_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : dNext 0 f = 0 :=
@@ -758,10 +701,7 @@ variable (e : P ⟶ Q) (zero : P.pt 0 ⟶ Q.pt 1) (comm_zero : e.f 0 = zero ≫
 include comm_one comm_zero
 
 /- warning: homotopy.mk_inductive_aux₁ -> Homotopy.mkInductiveAux₁ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₁ Homotopy.mkInductiveAux₁ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 
@@ -789,10 +729,7 @@ def mkInductiveAux₁ :
 section
 
 /- warning: homotopy.mk_inductive_aux₂ -> Homotopy.mkInductiveAux₂ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 -/
@@ -806,10 +743,7 @@ def mkInductiveAux₂ :
 #align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂
 
 /- warning: homotopy.mk_inductive_aux₃ -> Homotopy.mkInductiveAux₃ is a dubious translation:
-lean 3 declaration is
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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)) Q j))))) (Homotopy.mkInductiveAux₂.{u1, u2} V _inst_1 _inst_2 P Q e zero comm_zero one comm_one succ j)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃ₓ'. -/
 theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).Hom =
@@ -821,10 +755,7 @@ theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
 #align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃
 
 /- warning: homotopy.mk_inductive -> Homotopy.mkInductive is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive Homotopy.mkInductiveₓ'. -/
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed chain complexes,
 working by induction.
@@ -882,10 +813,7 @@ section MkCoinductive
 variable {P Q : CochainComplex V ℕ}
 
 /- warning: homotopy.d_next_cochain_complex -> Homotopy.dNext_cochainComplex is a dubious translation:
-lean 3 declaration is
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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P j) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplexₓ'. -/
 @[simp]
 theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
@@ -896,10 +824,7 @@ theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
 #align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplex
 
 /- warning: homotopy.prev_d_succ_cochain_complex -> Homotopy.prevD_succ_cochainComplex is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplexₓ'. -/
 @[simp]
 theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
@@ -911,10 +836,7 @@ theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
 #align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplex
 
 /- warning: homotopy.prev_d_zero_cochain_complex -> Homotopy.prevD_zero_cochainComplex is a dubious translation:
-lean 3 declaration is
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q j)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_zero_cochain_complex Homotopy.prevD_zero_cochainComplexₓ'. -/
 @[simp]
 theorem prevD_zero_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : prevD 0 f = 0 :=
@@ -937,10 +859,7 @@ variable (e : P ⟶ Q) (zero : P.pt 1 ⟶ Q.pt 0) (comm_zero : e.f 0 = P.d 0 1 
 include comm_one comm_zero succ
 
 /- warning: homotopy.mk_coinductive_aux₁ -> Homotopy.mkCoinductiveAux₁ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₁ Homotopy.mkCoinductiveAux₁ₓ'. -/
 /-- An auxiliary construction for `mk_coinductive`.
 
@@ -968,10 +887,7 @@ def mkCoinductiveAux₁ :
 section
 
 /- warning: homotopy.mk_coinductive_aux₂ -> Homotopy.mkCoinductiveAux₂ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 -/
@@ -985,10 +901,7 @@ def mkCoinductiveAux₂ :
 #align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂
 
 /- warning: homotopy.mk_coinductive_aux₃ -> Homotopy.mkCoinductiveAux₃ is a dubious translation:
-lean 3 declaration is
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(HomologicalComplex.xPrevIso.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q i j h)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃ₓ'. -/
 theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
@@ -1000,10 +913,7 @@ theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
 #align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃
 
 /- warning: homotopy.mk_coinductive -> Homotopy.mkCoinductive is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive Homotopy.mkCoinductiveₓ'. -/
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed cochain complexes,
 working by induction.
@@ -1125,10 +1035,7 @@ end HomotopyEquiv
 variable [HasEqualizers V] [HasCokernels V] [HasImages V] [HasImageMaps V]
 
 /- warning: homology_map_eq_of_homotopy -> homology_map_eq_of_homotopy is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homology_map_eq_of_homotopy homology_map_eq_of_homotopyₓ'. -/
 /-- Homotopic maps induce the same map on homology.
 -/
@@ -1178,10 +1085,7 @@ namespace CategoryTheory
 variable {W : Type _} [Category W] [Preadditive W]
 
 /- warning: category_theory.functor.map_homotopy -> CategoryTheory.Functor.mapHomotopy is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_homotopy CategoryTheory.Functor.mapHomotopyₓ'. -/
 /-- An additive functor takes homotopies to homotopies. -/
 @[simps]

86d1873c

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: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebra.homology.homotopy
-! leanprover-community/mathlib commit 618ea3d5c99240cd7000d8376924906a148bf9ff
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Tactic.Abel
 /-!
 # Chain homotopies
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define chain homotopies, and prove that homotopic chain maps induce the same map on homology.
 -/

618ea3d5

bump to nightly-2023-04-20-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

d6678ca6

Diff

@@ -36,26 +36,42 @@ variable (f g : C ⟶ D) (h k : D ⟶ E) (i : ι)
 
 section
 
+#print dNext /-
 /-- The composition of `C.d i i' ≫ f i' i` if there is some `i'` coming after `i`,
 and `0` otherwise. -/
 def dNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt i ⟶ D.pt i) :=
   AddMonoidHom.mk' (fun f => C.d i (c.next i) ≫ f (c.next i) i) fun f g =>
     Preadditive.comp_add _ _ _ _ _ _
 #align d_next dNext
+-/
 
+#print fromNext /-
 /-- `f i' i` if `i'` comes after `i`, and 0 if there's no such `i'`.
 Hopefully there won't be much need for this, except in `d_next_eq_d_from_from_next`
 to see that `d_next` factors through `C.d_from i`. -/
 def fromNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.xNext i ⟶ D.pt i) :=
   AddMonoidHom.mk' (fun f => f (c.next i) i) fun f g => rfl
 #align from_next fromNext
+-/
 
+/- warning: d_next_eq_d_from_from_next -> dNext_eq_dFrom_fromNext is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNextₓ'. -/
 @[simp]
 theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
     dNext i f = C.dFrom i ≫ fromNext i f :=
   rfl
 #align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNext
 
+/- warning: d_next_eq -> dNext_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align d_next_eq dNext_eqₓ'. -/
 theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
     dNext i f = C.d i i' ≫ f i' i :=
   by
@@ -63,38 +79,66 @@ theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
   rfl
 #align d_next_eq dNext_eq
 
+/- warning: d_next_comp_left -> dNext_comp_left is a dubious translation:
+lean 3 declaration is
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g))
+Case conversion may be inaccurate. Consider using '#align d_next_comp_left dNext_comp_leftₓ'. -/
 @[simp]
 theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (i : ι) :
     (dNext i fun i j => f.f i ≫ g i j) = f.f i ≫ dNext i g :=
   (f.comm_assoc _ _ _).symm
 #align d_next_comp_left dNext_comp_left
 
+/- warning: d_next_comp_right -> dNext_comp_right is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {E : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} (f : forall (i : ι) (j : ι), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C i) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D j)) (g : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c))) D E) (i : ι), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 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+Case conversion may be inaccurate. Consider using '#align d_next_comp_right dNext_comp_rightₓ'. -/
 @[simp]
 theorem dNext_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (i : ι) :
     (dNext i fun i j => f i j ≫ g.f j) = dNext i f ≫ g.f i :=
   (Category.assoc _ _ _).symm
 #align d_next_comp_right dNext_comp_right
 
+#print prevD /-
 /-- The composition of `f j j' ≫ D.d j' j` if there is some `j'` coming before `j`,
 and `0` otherwise. -/
 def prevD (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.pt j) :=
   AddMonoidHom.mk' (fun f => f j (c.prev j) ≫ D.d (c.prev j) j) fun f g =>
     Preadditive.add_comp _ _ _ _ _ _
 #align prev_d prevD
+-/
 
+#print toPrev /-
 /-- `f j j'` if `j'` comes after `j`, and 0 if there's no such `j'`.
 Hopefully there won't be much need for this, except in `d_next_eq_d_from_from_next`
 to see that `d_next` factors through `C.d_from i`. -/
 def toPrev (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.xPrev j) :=
   AddMonoidHom.mk' (fun f => f j (c.prev j)) fun f g => rfl
 #align to_prev toPrev
+-/
 
+/- warning: prev_d_eq_to_prev_d_to -> prevD_eq_toPrev_dTo is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dToₓ'. -/
 @[simp]
 theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
     prevD j f = toPrev j f ≫ D.dTo j :=
   rfl
 #align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dTo
 
+/- warning: prev_d_eq -> prevD_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align prev_d_eq prevD_eqₓ'. -/
 theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
     prevD j f = f j j' ≫ D.d j' j :=
   by
@@ -102,12 +146,24 @@ theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
   rfl
 #align prev_d_eq prevD_eq
 
+/- warning: prev_d_comp_left -> prevD_comp_left is a dubious translation:
+lean 3 declaration is
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g))
+Case conversion may be inaccurate. Consider using '#align prev_d_comp_left prevD_comp_leftₓ'. -/
 @[simp]
 theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι) :
     (prevD j fun i j => f.f i ≫ g i j) = f.f j ≫ prevD j g :=
   Category.assoc _ _ _
 #align prev_d_comp_left prevD_comp_left
 
+/- warning: prev_d_comp_right -> prevD_comp_right is a dubious translation:
+lean 3 declaration is
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V _inst_1 _inst_2) c D j)) (g : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c))) D E) (j : ι), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 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+Case conversion may be inaccurate. Consider using '#align prev_d_comp_right prevD_comp_rightₓ'. -/
 @[simp]
 theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι) :
     (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j :=
@@ -116,6 +172,12 @@ theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι)
   simp only [category.assoc, g.comm]
 #align prev_d_comp_right prevD_comp_right
 
+/- warning: d_next_nat -> dNext_nat is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] (C : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (D : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (i : Nat) (f : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D j)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D j)) (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (Pi.addZeroClass.{0, u1} Nat (fun (i : Nat) => forall (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D j)) (fun (i : Nat) => Pi.addZeroClass.{0, u1} Nat (fun (j : Nat) => Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D j)) (fun (i_1 : Nat) => AddMonoid.toAddZeroClass.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i_1)) (SubNegMonoid.toAddMonoid.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i_1)) (AddGroup.toSubNegMonoid.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i_1)) (AddCommGroup.toAddGroup.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (SubNegMonoid.toAddMonoid.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (AddCommGroup.toAddGroup.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (CategoryTheory.Preadditive.homGroup.{u1, u2} V _inst_1 _inst_2 (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) D i)) (SubNegMonoid.toAddMonoid.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (AddCommGroup.toAddGroup.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i)) (CategoryTheory.Preadditive.homGroup.{u1, u2} V _inst_1 _inst_2 (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i))))))) (dNext.{u1, u2, 0} Nat V _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) C D i) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) D i) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) C i (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i))
+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] (C : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) (D : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) D j)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) C (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) D i) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) C i (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
+Case conversion may be inaccurate. Consider using '#align d_next_nat dNext_natₓ'. -/
 theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     dNext i f = C.d i (i - 1) ≫ f (i - 1) i :=
   by
@@ -132,6 +194,12 @@ theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶
     congr 2
 #align d_next_nat dNext_nat
 
+/- warning: prev_d_nat -> prevD_nat is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) D i)) (CategoryTheory.Preadditive.homGroup.{u1, u2} V _inst_1 _inst_2 (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) C i) (HomologicalComplex.x.{u1, u2, 0} 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) C i) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) D (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} 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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) D (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i))
+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] (C : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) (D : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) (i : Nat) (f : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D j)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D j)) => Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D j)) (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i)) (Pi.addZeroClass.{0, u1} Nat (fun (i : Nat) => forall (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D j)) (fun (i : Nat) => Pi.addZeroClass.{0, u1} Nat (fun (j : Nat) => Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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Nat.canonicallyOrderedCommSemiring)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i_1)) (SubNegMonoid.toAddMonoid.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i_1)) (AddCommGroup.toAddGroup.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i_1)) (CategoryTheory.Preadditive.homGroup.{u1, u2} V _inst_1 _inst_2 (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat 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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)) C i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) D i)) (SubNegMonoid.toAddMonoid.{u1} (Quiver.Hom.{succ u1, u2} V 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instSubNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))
+Case conversion may be inaccurate. Consider using '#align prev_d_nat prevD_natₓ'. -/
 theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     prevD i f = f i (i - 1) ≫ D.d (i - 1) i :=
   by
@@ -148,6 +216,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i 
     congr 2
 #align prev_d_nat prevD_nat
 
+#print Homotopy /-
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic obviously' -/
 /-- A homotopy `h` between chain maps `f` and `g` consists of components `h i j : C.X i ⟶ D.X j`
 which are zero unless `c.rel j i`, satisfying the homotopy condition.
@@ -160,6 +229,7 @@ structure Homotopy (f g : C ⟶ D) where
     run_tac
       obviously'
 #align homotopy Homotopy
+-/
 
 variable {f g}
 
@@ -167,6 +237,12 @@ namespace Homotopy
 
 restate_axiom Homotopy.zero'
 
+/- warning: homotopy.equiv_sub_zero -> Homotopy.equivSubZero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align homotopy.equiv_sub_zero Homotopy.equivSubZeroₓ'. -/
 /-- `f` is homotopic to `g` iff `f - g` is homotopic to `0`.
 -/
 def equivSubZero : Homotopy f g ≃ Homotopy (f - g) 0
@@ -183,6 +259,7 @@ def equivSubZero : Homotopy f g ≃ Homotopy (f - g) 0
   right_inv := by tidy
 #align homotopy.equiv_sub_zero Homotopy.equivSubZero
 
+#print Homotopy.ofEq /-
 /-- Equal chain maps are homotopic. -/
 @[simps]
 def ofEq (h : f = g) : Homotopy f g where
@@ -190,13 +267,17 @@ def ofEq (h : f = g) : Homotopy f g where
   zero' _ _ _ := rfl
   comm _ := by simp only [AddMonoidHom.map_zero, zero_add, h]
 #align homotopy.of_eq Homotopy.ofEq
+-/
 
+#print Homotopy.refl /-
 /-- Every chain map is homotopic to itself. -/
 @[simps, refl]
 def refl (f : C ⟶ D) : Homotopy f f :=
   ofEq (rfl : f = f)
 #align homotopy.refl Homotopy.refl
+-/
 
+#print Homotopy.symm /-
 /-- `f` is homotopic to `g` iff `g` is homotopic to `f`. -/
 @[simps, symm]
 def symm {f g : C ⟶ D} (h : Homotopy f g) : Homotopy g f
@@ -207,7 +288,9 @@ def symm {f g : C ⟶ D} (h : Homotopy f g) : Homotopy g f
     rw [AddMonoidHom.map_neg, AddMonoidHom.map_neg, h.comm, ← neg_add, ← add_assoc, neg_add_self,
       zero_add]
 #align homotopy.symm Homotopy.symm
+-/
 
+#print Homotopy.trans /-
 /-- homotopy is a transitive relation. -/
 @[simps, trans]
 def trans {e f g : C ⟶ D} (h : Homotopy e f) (k : Homotopy f g) : Homotopy e g
@@ -218,7 +301,14 @@ def trans {e f g : C ⟶ D} (h : Homotopy e f) (k : Homotopy f g) : Homotopy e g
     rw [AddMonoidHom.map_add, AddMonoidHom.map_add, h.comm, k.comm]
     abel
 #align homotopy.trans Homotopy.trans
+-/
 
+/- warning: homotopy.add -> Homotopy.add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align homotopy.add Homotopy.addₓ'. -/
 /-- the sum of two homotopies is a homotopy between the sum of the respective morphisms. -/
 @[simps]
 def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homotopy f₂ g₂) :
@@ -231,6 +321,7 @@ def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homo
     abel
 #align homotopy.add Homotopy.add
 
+#print Homotopy.compRight /-
 /-- homotopy is closed under composition (on the right) -/
 @[simps]
 def compRight {e f : C ⟶ D} (h : Homotopy e f) (g : D ⟶ E) : Homotopy (e ≫ g) (f ≫ g)
@@ -240,7 +331,9 @@ def compRight {e f : C ⟶ D} (h : Homotopy e f) (g : D ⟶ E) : Homotopy (e ≫
   comm i := by
     simp only [h.comm i, dNext_comp_right, preadditive.add_comp, prevD_comp_right, comp_f]
 #align homotopy.comp_right Homotopy.compRight
+-/
 
+#print Homotopy.compLeft /-
 /-- homotopy is closed under composition (on the left) -/
 @[simps]
 def compLeft {f g : D ⟶ E} (h : Homotopy f g) (e : C ⟶ D) : Homotopy (e ≫ f) (e ≫ g)
@@ -249,25 +342,32 @@ def compLeft {f g : D ⟶ E} (h : Homotopy f g) (e : C ⟶ D) : Homotopy (e ≫
   zero' i j w := by rw [h.zero i j w, comp_zero]
   comm i := by simp only [h.comm i, dNext_comp_left, preadditive.comp_add, prevD_comp_left, comp_f]
 #align homotopy.comp_left Homotopy.compLeft
+-/
 
+#print Homotopy.comp /-
 /-- homotopy is closed under composition -/
 @[simps]
 def comp {C₁ C₂ C₃ : HomologicalComplex V c} {f₁ g₁ : C₁ ⟶ C₂} {f₂ g₂ : C₂ ⟶ C₃}
     (h₁ : Homotopy f₁ g₁) (h₂ : Homotopy f₂ g₂) : Homotopy (f₁ ≫ f₂) (g₁ ≫ g₂) :=
   (h₁.compRight _).trans (h₂.compLeft _)
 #align homotopy.comp Homotopy.comp
+-/
 
+#print Homotopy.compRightId /-
 /-- a variant of `homotopy.comp_right` useful for dealing with homotopy equivalences. -/
 @[simps]
 def compRightId {f : C ⟶ C} (h : Homotopy f (𝟙 C)) (g : C ⟶ D) : Homotopy (f ≫ g) g :=
   (h.compRight g).trans (ofEq <| Category.id_comp _)
 #align homotopy.comp_right_id Homotopy.compRightId
+-/
 
+#print Homotopy.compLeftId /-
 /-- a variant of `homotopy.comp_left` useful for dealing with homotopy equivalences. -/
 @[simps]
 def compLeftId {f : D ⟶ D} (h : Homotopy f (𝟙 D)) (g : C ⟶ D) : Homotopy (g ≫ f) g :=
   (h.compLeft g).trans (ofEq <| Category.comp_id _)
 #align homotopy.comp_left_id Homotopy.compLeftId
+-/
 
 /-!
 Null homotopic maps can be constructed using the formula `hd+dh`. We show that
@@ -277,6 +377,7 @@ two differentials going to and from a certain degree, only one, or none.
 -/
 
 
+#print Homotopy.nullHomotopicMap /-
 /-- The null homotopic map associated to a family `hom` of morphisms `C_i ⟶ D_j`.
 This is the same datum as for the field `hom` in the structure `homotopy`. For
 this definition, we do not need the field `zero` of that structure
@@ -293,13 +394,22 @@ def nullHomotopicMap (hom : ∀ i j, C.pt i ⟶ D.pt j) : C ⟶ D
     rw [dNext_eq hom hij, prevD_eq hom hij, preadditive.comp_add, preadditive.add_comp, eq1, eq2,
       add_zero, zero_add, category.assoc]
 #align homotopy.null_homotopic_map Homotopy.nullHomotopicMap
+-/
 
+#print Homotopy.nullHomotopicMap' /-
 /-- Variant of `null_homotopic_map` where the input consists only of the
 relevant maps `C_i ⟶ D_j` such that `c.rel j i`. -/
 def nullHomotopicMap' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : C ⟶ D :=
   nullHomotopicMap fun i j => dite (c.Rel j i) (h i j) fun _ => 0
 #align homotopy.null_homotopic_map' Homotopy.nullHomotopicMap'
+-/
 
+/- warning: homotopy.null_homotopic_map_comp -> Homotopy.nullHomotopicMap_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_comp Homotopy.nullHomotopicMap_compₓ'. -/
 /-- Compatibility of `null_homotopic_map` with the postcomposition by a morphism
 of complexes. -/
 theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
@@ -310,6 +420,12 @@ theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
   simp only [preadditive.add_comp, category.assoc, g.comm]
 #align homotopy.null_homotopic_map_comp Homotopy.nullHomotopicMap_comp
 
+/- warning: homotopy.null_homotopic_map'_comp -> Homotopy.nullHomotopicMap'_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_comp Homotopy.nullHomotopicMap'_compₓ'. -/
 /-- Compatibility of `null_homotopic_map'` with the postcomposition by a morphism
 of complexes. -/
 theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) (g : D ⟶ E) :
@@ -324,6 +440,12 @@ theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)
   · rw [zero_comp]
 #align homotopy.null_homotopic_map'_comp Homotopy.nullHomotopicMap'_comp
 
+/- warning: homotopy.comp_null_homotopic_map -> Homotopy.comp_nullHomotopicMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy.comp_null_homotopic_map Homotopy.comp_nullHomotopicMapₓ'. -/
 /-- Compatibility of `null_homotopic_map` with the precomposition by a morphism
 of complexes. -/
 theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
@@ -334,6 +456,12 @@ theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
   simp only [preadditive.comp_add, category.assoc, f.comm_assoc]
 #align homotopy.comp_null_homotopic_map Homotopy.comp_nullHomotopicMap
 
+/- warning: homotopy.comp_null_homotopic_map' -> Homotopy.comp_nullHomotopicMap' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'ₓ'. -/
 /-- Compatibility of `null_homotopic_map'` with the precomposition by a morphism
 of complexes. -/
 theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt i ⟶ E.pt j)) :
@@ -348,6 +476,12 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt
   · rw [comp_zero]
 #align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'
 
+/- warning: homotopy.map_null_homotopic_map -> Homotopy.map_nullHomotopicMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u1}} {V : Type.{u5}} [_inst_1 : CategoryTheory.Category.{u4, u5} V] [_inst_2 : CategoryTheory.Preadditive.{u4, u5} V _inst_1] {c : ComplexShape.{u1} ι} {C : HomologicalComplex.{u4, u5, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u5} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u4, u5, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u5} V _inst_1 _inst_2) c} {W : Type.{u3}} [_inst_3 : CategoryTheory.Category.{u2, u3} W] [_inst_4 : CategoryTheory.Preadditive.{u2, u3} W _inst_3] (G : CategoryTheory.Functor.{u4, u2, u5, u3} V _inst_1 W _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u5, u3, u4, u2} V W _inst_1 _inst_3 _inst_2 _inst_4 G] (hom : forall (i : ι) (j : ι), Quiver.Hom.{succ u4, u5} V (CategoryTheory.CategoryStruct.toQuiver.{u4, u5} V (CategoryTheory.Category.toCategoryStruct.{u4, u5} V _inst_1)) (HomologicalComplex.X.{u4, u5, u1} ι V _inst_1 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+Case conversion may be inaccurate. Consider using '#align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMapₓ'. -/
 /-- Compatibility of `null_homotopic_map` with the application of additive functors -/
 theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -359,6 +493,12 @@ theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V 
   simp only [G.map_comp, functor.map_add]
 #align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMap
 
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+Case conversion may be inaccurate. Consider using '#align homotopy.map_null_homotopic_map' Homotopy.map_nullHomotopicMap'ₓ'. -/
 /-- Compatibility of `null_homotopic_map'` with the application of additive functors -/
 theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -374,6 +514,7 @@ theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V 
   · rw [G.map_zero]
 #align homotopy.map_null_homotopic_map' Homotopy.map_nullHomotopicMap'
 
+#print Homotopy.nullHomotopy /-
 /-- Tautological construction of the `homotopy` to zero for maps constructed by
 `null_homotopic_map`, at least when we have the `zero'` condition. -/
 @[simps]
@@ -386,7 +527,9 @@ def nullHomotopy (hom : ∀ i j, C.pt i ⟶ D.pt j) (zero' : ∀ i j, ¬c.Rel j
       rw [HomologicalComplex.zero_f_apply, add_zero]
       rfl }
 #align homotopy.null_homotopy Homotopy.nullHomotopy
+-/
 
+#print Homotopy.nullHomotopy' /-
 /-- Homotopy to zero for maps constructed with `null_homotopic_map'` -/
 @[simps]
 def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : Homotopy (nullHomotopicMap' h) 0 :=
@@ -399,12 +542,19 @@ def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : Homotopy (n
   exfalso
   exact hij hij'
 #align homotopy.null_homotopy' Homotopy.nullHomotopy'
+-/
 
 /-! This lemma and the following ones can be used in order to compute
 the degreewise morphisms induced by the null homotopic maps constructed
 with `null_homotopic_map` or `null_homotopic_map'` -/
 
 
+/- warning: homotopy.null_homotopic_map_f -> Homotopy.nullHomotopicMap_f 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 homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_fₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -414,6 +564,12 @@ theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
   rw [dNext_eq hom r₁₀, prevD_eq hom r₂₁]
 #align homotopy.null_homotopic_map_f Homotopy.nullHomotopicMap_f
 
+/- warning: homotopy.null_homotopic_map'_f -> Homotopy.nullHomotopicMap'_f 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 homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_fₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
     (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -426,6 +582,12 @@ theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
   rfl
 #align homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_f
 
+/- warning: homotopy.null_homotopic_map_f_of_not_rel_left -> Homotopy.nullHomotopicMap_f_of_not_rel_left is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {k₁ : ι} {k₀ : ι}, (ComplexShape.Rel.{u3} ι c k₁ k₀) -> (forall (l : ι), Not (ComplexShape.Rel.{u3} ι c k₀ l)) -> (forall (hom : forall (i : ι) (j : ι), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C i) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D j)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D k₀)) (HomologicalComplex.Hom.f.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C D (Homotopy.nullHomotopicMap.{u1, u2, u3} ι V _inst_1 _inst_2 c C D hom) k₀) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D k₁) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D k₀) (hom k₀ k₁) (HomologicalComplex.d.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D k₁ k₀)))
+but is expected to have type
+  forall {ι : Type.{u1}} {V : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} V] [_inst_2 : CategoryTheory.Preadditive.{u2, u3} V _inst_1] {c : ComplexShape.{u1} ι} {C : HomologicalComplex.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c} {k₁ : ι} {k₀ : ι}, (ComplexShape.Rel.{u1} ι c k₁ k₀) -> (forall (l : ι), Not (ComplexShape.Rel.{u1} ι c k₀ l)) -> (forall (hom : forall (i : ι) (j : ι), Quiver.Hom.{succ u2, u3} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1)) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C i) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D j)), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1)) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₀)) (HomologicalComplex.Hom.f.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C D (Homotopy.nullHomotopicMap.{u2, u3, u1} ι V _inst_1 _inst_2 c C D hom) k₀) (CategoryTheory.CategoryStruct.comp.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₀) (hom k₀ k₁) (HomologicalComplex.d.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁ k₀)))
+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f_of_not_rel_left Homotopy.nullHomotopicMap_f_of_not_rel_leftₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -436,6 +598,12 @@ theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
   exact hk₀ _
 #align homotopy.null_homotopic_map_f_of_not_rel_left Homotopy.nullHomotopicMap_f_of_not_rel_left
 
+/- warning: homotopy.null_homotopic_map'_f_of_not_rel_left -> Homotopy.nullHomotopicMap'_f_of_not_rel_left is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f_of_not_rel_left Homotopy.nullHomotopicMap'_f_of_not_rel_leftₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -448,6 +616,12 @@ theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_left Homotopy.nullHomotopicMap'_f_of_not_rel_left
 
+/- warning: homotopy.null_homotopic_map_f_of_not_rel_right -> Homotopy.nullHomotopicMap_f_of_not_rel_right is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {k₁ : ι} {k₀ : ι}, (ComplexShape.Rel.{u3} ι c k₁ k₀) -> (forall (l : ι), Not (ComplexShape.Rel.{u3} ι c l k₁)) -> (forall (hom : forall (i : ι) (j : ι), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C i) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D j)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D k₁)) (HomologicalComplex.Hom.f.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C D (Homotopy.nullHomotopicMap.{u1, u2, u3} ι V _inst_1 _inst_2 c C D hom) k₁) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.x.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c D k₁) (HomologicalComplex.d.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c C k₁ k₀) (hom k₀ k₁)))
+but is expected to have type
+  forall {ι : Type.{u1}} {V : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} V] [_inst_2 : CategoryTheory.Preadditive.{u2, u3} V _inst_1] {c : ComplexShape.{u1} ι} {C : HomologicalComplex.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c} {k₁ : ι} {k₀ : ι}, (ComplexShape.Rel.{u1} ι c k₁ k₀) -> (forall (l : ι), Not (ComplexShape.Rel.{u1} ι c l k₁)) -> (forall (hom : forall (i : ι) (j : ι), Quiver.Hom.{succ u2, u3} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1)) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C i) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D j)), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1)) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁)) (HomologicalComplex.Hom.f.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C D (Homotopy.nullHomotopicMap.{u2, u3, u1} ι V _inst_1 _inst_2 c C D hom) k₁) (CategoryTheory.CategoryStruct.comp.{u2, u3} V (CategoryTheory.Category.toCategoryStruct.{u2, u3} V _inst_1) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₀) (HomologicalComplex.X.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c D k₁) (HomologicalComplex.d.{u2, u3, u1} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u3} V _inst_1 _inst_2) c C k₁ k₀) (hom k₀ k₁)))
+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f_of_not_rel_right Homotopy.nullHomotopicMap_f_of_not_rel_rightₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -458,6 +632,12 @@ theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
   exact hk₁ _
 #align homotopy.null_homotopic_map_f_of_not_rel_right Homotopy.nullHomotopicMap_f_of_not_rel_right
 
+/- warning: homotopy.null_homotopic_map'_f_of_not_rel_right -> Homotopy.nullHomotopicMap'_f_of_not_rel_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f_of_not_rel_right Homotopy.nullHomotopicMap'_f_of_not_rel_rightₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
     (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -470,6 +650,12 @@ theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_right Homotopy.nullHomotopicMap'_f_of_not_rel_right
 
+/- warning: homotopy.null_homotopic_map_f_eq_zero -> Homotopy.nullHomotopicMap_f_eq_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map_f_eq_zero Homotopy.nullHomotopicMap_f_eq_zeroₓ'. -/
 @[simp]
 theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
     (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
@@ -479,6 +665,12 @@ theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀
   rw [C.shape, D.shape, zero_comp, comp_zero, add_zero] <;> apply_assumption
 #align homotopy.null_homotopic_map_f_eq_zero Homotopy.nullHomotopicMap_f_eq_zero
 
+/- warning: homotopy.null_homotopic_map'_f_eq_zero -> Homotopy.nullHomotopicMap'_f_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align homotopy.null_homotopic_map'_f_eq_zero Homotopy.nullHomotopicMap'_f_eq_zeroₓ'. -/
 @[simp]
 theorem nullHomotopicMap'_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
     (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
@@ -507,6 +699,12 @@ section MkInductive
 
 variable {P Q : ChainComplex V ℕ}
 
+/- warning: homotopy.prev_d_chain_complex -> Homotopy.prevD_chainComplex is a dubious translation:
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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) Q j)) (SubNegMonoid.toAddMonoid.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P j) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q j)) (AddCommGroup.toAddGroup.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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Nat.strictOrderedSemiring))))) Nat.hasOne) P Q j) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P j) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q j) (f j (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) j))
+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (f : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q j)) (j : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} 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+Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplexₓ'. -/
 @[simp]
 theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     prevD j f = f j (j + 1) ≫ Q.d _ _ := by
@@ -515,6 +713,12 @@ theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
   congr 2
 #align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplex
 
+/- warning: homotopy.d_next_succ_chain_complex -> Homotopy.dNext_succ_chainComplex is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) 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+but is expected to have type
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q j)) (i : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} 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Nat.canonicallyOrderedCommSemiring)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (f i (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+Case conversion may be inaccurate. Consider using '#align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplexₓ'. -/
 @[simp]
 theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     dNext (i + 1) f = P.d _ _ ≫ f i (i + 1) :=
@@ -524,6 +728,12 @@ theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
   congr 2
 #align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplex
 
+/- warning: homotopy.d_next_zero_chain_complex -> Homotopy.dNext_zero_chainComplex is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))))) (dNext.{u1, u2, 0} Nat V _inst_1 _inst_2 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align homotopy.d_next_zero_chain_complex Homotopy.dNext_zero_chainComplexₓ'. -/
 @[simp]
 theorem dNext_zero_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : dNext 0 f = 0 :=
   by
@@ -548,7 +758,7 @@ include comm_one comm_zero
 lean 3 declaration is
   forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) 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(AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) zero (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) -> (forall (one : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) n) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P (HAdd.hAdd.{0, 0, 0} Nat 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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (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)))))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) f' (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (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) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))
 but is expected to have type
-  forall {V : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} V] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} V _inst_1] {P : ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} {Q : ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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)))) P Q) (zero 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(AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) P succ) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat 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(OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) succ) f) (CategoryTheory.CategoryStruct.comp.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) f' (HomologicalComplex.d.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (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) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (comm_zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.Hom.f.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P Q e (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{u1, u1, u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat 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V _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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat 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_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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P succ) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) succ) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f' (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₁ Homotopy.mkInductiveAux₁ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 
@@ -579,7 +789,7 @@ section
 lean 3 declaration is
   forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (HomologicalComplex.Hom.f.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P Q e (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) zero (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) -> (forall (one : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 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Nat.hasOne) P n) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) Q n) (HomologicalComplex.dFrom.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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) P n) f) 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) Q n)))))))
 but is expected to have type
-  forall {V : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} V] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} V _inst_1] {P : ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} {Q : ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) 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(CategoryTheory.CategoryStruct.comp.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) P n) (HomologicalComplex.xPrev.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) Q n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) Q n) f' (HomologicalComplex.dTo.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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) Q n)))))))
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (HomologicalComplex.Hom.f.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P Q e (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) zero (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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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)) Q n)))))))
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 -/
@@ -592,15 +802,27 @@ def mkInductiveAux₂ :
     ⟨(P.xNextIso rfl).Hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv, by simpa using I.2.2⟩
 #align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂
 
-theorem mk_inductive_aux₃ (i j : ℕ) (h : i + 1 = j) :
+/- warning: homotopy.mk_inductive_aux₃ -> Homotopy.mkInductiveAux₃ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (comm_zero : Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 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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)) Q j))))) (Homotopy.mkInductiveAux₂.{u1, u2} V _inst_1 _inst_2 P Q e zero comm_zero one comm_one succ j)))
+Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃ₓ'. -/
+theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).Hom =
       (P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 :=
   by
   subst j <;> rcases i with (_ | _ | i) <;>
     · dsimp
       simp
-#align homotopy.mk_inductive_aux₃ Homotopy.mk_inductive_aux₃
+#align homotopy.mk_inductive_aux₃ Homotopy.mkInductiveAux₃
 
+/- warning: homotopy.mk_inductive -> Homotopy.mkInductive is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) P Q) 0 (Zero.zero.{u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 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+Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive Homotopy.mkInductiveₓ'. -/
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed chain complexes,
 working by induction.
 
@@ -656,6 +878,12 @@ section MkCoinductive
 
 variable {P Q : CochainComplex V ℕ}
 
+/- warning: homotopy.d_next_cochain_complex -> Homotopy.dNext_cochainComplex is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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 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+but is expected to have type
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q j)) (j : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(ComplexShape.up.{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)) P Q j) f) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P j) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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instAddNat) j (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j))
+Case conversion may be inaccurate. Consider using '#align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplexₓ'. -/
 @[simp]
 theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     dNext j f = P.d _ _ ≫ f (j + 1) j := by
@@ -664,6 +892,12 @@ theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
   congr 2
 #align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplex
 
+/- warning: homotopy.prev_d_succ_cochain_complex -> Homotopy.prevD_succ_cochainComplex is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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 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(OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q j)) (i : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : forall (i : Nat) (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Pi.addZeroClass.{0, u1} Nat (fun (i : Nat) => forall (j : Nat), Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P i) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplexₓ'. -/
 @[simp]
 theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     prevD (i + 1) f = f (i + 1) _ ≫ Q.d i (i + 1) :=
@@ -673,6 +907,12 @@ theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
   congr 2
 #align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplex
 
+/- warning: homotopy.prev_d_zero_cochain_complex -> Homotopy.prevD_zero_cochainComplex is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy.prev_d_zero_cochain_complex Homotopy.prevD_zero_cochainComplexₓ'. -/
 @[simp]
 theorem prevD_zero_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : prevD 0 f = 0 :=
   by
@@ -697,7 +937,7 @@ include comm_one comm_zero succ
 lean 3 declaration is
   forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) 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_inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) zero)) -> (forall (one : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) P (HAdd.hAdd.{0, 0, 0} Nat 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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (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)))))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (HAdd.hAdd.{0, 0, 0} Nat 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.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) f'))))))
 but is expected to have type
-  forall {V : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} V] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} V _inst_1] {P : CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} {Q : CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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)))) P Q) (zero : Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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Nat.hasOne))))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) Q succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.CategoryStruct.comp.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.d.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) succ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) f')))))
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (comm_zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.Hom.f.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P Q e (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{u1, u1, u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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_inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddZeroClass.toAdd.{u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q succ) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) f')))))
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₁ Homotopy.mkCoinductiveAux₁ₓ'. -/
 /-- An auxiliary construction for `mk_coinductive`.
 
@@ -728,7 +968,7 @@ section
 lean 3 declaration is
   forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (HomologicalComplex.Hom.f.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P Q e (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.d.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) zero)) -> (forall (one : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 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Nat.hasOne) Q n) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n) f (HomologicalComplex.dTo.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) P n) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n) (HomologicalComplex.dFrom.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) f'))))))
 but is expected to have type
-  forall {V : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} V] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} V _inst_1] {P : CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} {Q : CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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)))) P Q) (zero : Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))), (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P Q e (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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_inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) zero)) -> (forall (one : Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.xNext.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) => Eq.{succ u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P Q e n) (HAdd.hAdd.{u2, u2, u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (instHAdd.{u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) Q n)) (AddMonoid.toAddZeroClass.{u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (AddGroup.toSubNegMonoid.{u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (AddCommGroup.toAddGroup.{u2} (Quiver.Hom.{succ u2, u1} V (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (CategoryTheory.Preadditive.homGroup.{u2, u1} V _inst_1 _inst_2 (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)))))))) (CategoryTheory.CategoryStruct.comp.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.xPrev.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n) f (HomologicalComplex.dTo.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n)) (CategoryTheory.CategoryStruct.comp.{u2, u1} V (CategoryTheory.Category.toCategoryStruct.{u2, u1} V _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.xNext.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) (HomologicalComplex.x.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) Q n) (HomologicalComplex.dFrom.{u2, u1, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} V _inst_1 _inst_2) (ComplexShape.up.{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) P n) f'))))))
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V 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(HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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Nat.canonicallyOrderedCommSemiring)) Q n) (HomologicalComplex.dFrom.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P n) f'))))))
 Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂ₓ'. -/
 /-- An auxiliary construction for `mk_inductive`.
 -/
@@ -741,15 +981,27 @@ def mkCoinductiveAux₂ :
     ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).Hom ≫ I.2.1, by simpa using I.2.2⟩
 #align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂
 
-theorem mk_coinductive_aux₃ (i j : ℕ) (h : i + 1 = j) :
+/- warning: homotopy.mk_coinductive_aux₃ -> Homotopy.mkCoinductiveAux₃ is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne} (e : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (HomologicalComplex.Hom.f.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P Q e (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (CategoryTheory.CategoryStruct.comp.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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_inst_1 _inst_2) (ComplexShape.up.{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) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) zero)) (one : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) Q j) (HomologicalComplex.dFrom.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) P j) f')))) (Homotopy.mkCoinductiveAux₂.{u1, u2} V _inst_1 _inst_2 P Q e zero comm_zero one comm_one succ j)) (CategoryTheory.Iso.hom.{u1, u2} V _inst_1 (HomologicalComplex.xPrev.{u1, u2, 0} Nat V _inst_1 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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) Q i j h)))
+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} (e : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (comm_zero : Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V 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Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) Q j) (HomologicalComplex.dFrom.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P j) f')))) (Homotopy.mkCoinductiveAux₂.{u1, u2} V _inst_1 _inst_2 P Q e zero comm_zero one comm_one succ j)) (CategoryTheory.Iso.hom.{u1, u2} V _inst_1 (HomologicalComplex.xPrev.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V 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(HomologicalComplex.xPrevIso.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q i j h)))
+Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃ₓ'. -/
+theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
       (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).1 ≫ (Q.xPrevIso h).Hom :=
   by
   subst j <;> rcases i with (_ | _ | i) <;>
     · dsimp
       simp
-#align homotopy.mk_coinductive_aux₃ Homotopy.mk_coinductive_aux₃
+#align homotopy.mk_coinductive_aux₃ Homotopy.mkCoinductiveAux₃
 
+/- warning: homotopy.mk_coinductive -> Homotopy.mkCoinductive is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {P : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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)} {Q : CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(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.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _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.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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))))) P Q) (zero : Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V (CategoryTheory.Category.toCategoryStruct.{u1, u2} V _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) P (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) (ComplexShape.up.{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)) Q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))), (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} V (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} V 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+Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductive Homotopy.mkCoinductiveₓ'. -/
 /-- A constructor for a `homotopy e 0`, for `e` a chain map between `ℕ`-indexed cochain complexes,
 working by induction.
 
@@ -797,6 +1049,7 @@ end MkCoinductive
 
 end Homotopy
 
+#print HomotopyEquiv /-
 /-- A homotopy equivalence between two chain complexes consists of a chain map each way,
 and homotopies from the compositions to the identity chain maps.
 
@@ -809,9 +1062,11 @@ structure HomotopyEquiv (C D : HomologicalComplex V c) where
   homotopyHomInvId : Homotopy (hom ≫ inv) (𝟙 C)
   homotopyInvHomId : Homotopy (inv ≫ hom) (𝟙 D)
 #align homotopy_equiv HomotopyEquiv
+-/
 
 namespace HomotopyEquiv
 
+#print HomotopyEquiv.refl /-
 /-- Any complex is homotopy equivalent to itself. -/
 @[refl]
 def refl (C : HomologicalComplex V c) : HomotopyEquiv C C
@@ -821,10 +1076,12 @@ def refl (C : HomologicalComplex V c) : HomotopyEquiv C C
   homotopyHomInvId := by simp
   homotopyInvHomId := by simp
 #align homotopy_equiv.refl HomotopyEquiv.refl
+-/
 
 instance : Inhabited (HomotopyEquiv C C) :=
   ⟨refl C⟩
 
+#print HomotopyEquiv.symm /-
 /-- Being homotopy equivalent is a symmetric relation. -/
 @[symm]
 def symm {C D : HomologicalComplex V c} (f : HomotopyEquiv C D) : HomotopyEquiv D C
@@ -834,7 +1091,9 @@ def symm {C D : HomologicalComplex V c} (f : HomotopyEquiv C D) : HomotopyEquiv
   homotopyHomInvId := f.homotopyInvHomId
   homotopyInvHomId := f.homotopyHomInvId
 #align homotopy_equiv.symm HomotopyEquiv.symm
+-/
 
+#print HomotopyEquiv.trans /-
 /-- Homotopy equivalence is a transitive relation. -/
 @[trans]
 def trans {C D E : HomologicalComplex V c} (f : HomotopyEquiv C D) (g : HomotopyEquiv D E) :
@@ -848,17 +1107,26 @@ def trans {C D E : HomologicalComplex V c} (f : HomotopyEquiv C D) (g : Homotopy
     simpa using
       ((f.homotopy_inv_hom_id.comp_right_id g.hom).compLeft g.inv).trans g.homotopy_inv_hom_id
 #align homotopy_equiv.trans HomotopyEquiv.trans
+-/
 
+#print HomotopyEquiv.ofIso /-
 /-- An isomorphism of complexes induces a homotopy equivalence. -/
 def ofIso {ι : Type _} {V : Type u} [Category.{v} V] [Preadditive V] {c : ComplexShape ι}
     {C D : HomologicalComplex V c} (f : C ≅ D) : HomotopyEquiv C D :=
   ⟨f.Hom, f.inv, Homotopy.ofEq f.3, Homotopy.ofEq f.4⟩
 #align homotopy_equiv.of_iso HomotopyEquiv.ofIso
+-/
 
 end HomotopyEquiv
 
 variable [HasEqualizers V] [HasCokernels V] [HasImages V] [HasImageMaps V]
 
+/- warning: homology_map_eq_of_homotopy -> homology_map_eq_of_homotopy is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align homology_map_eq_of_homotopy homology_map_eq_of_homotopyₓ'. -/
 /-- Homotopic maps induce the same map on homology.
 -/
 theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
@@ -880,6 +1148,12 @@ theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
     apply image_subobject_factors_comp_self
 #align homology_map_eq_of_homotopy homology_map_eq_of_homotopy
 
+/- warning: homology_obj_iso_of_homotopy_equiv -> homologyObjIsoOfHomotopyEquiv 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 homology_obj_iso_of_homotopy_equiv homologyObjIsoOfHomotopyEquivₓ'. -/
 /-- Homotopy equivalent complexes have isomorphic homologies. -/
 def homologyObjIsoOfHomotopyEquiv (f : HomotopyEquiv C D) (i : ι) :
     (homologyFunctor V c i).obj C ≅ (homologyFunctor V c i).obj D
@@ -900,6 +1174,12 @@ namespace CategoryTheory
 
 variable {W : Type _} [Category W] [Preadditive W]
 
+/- warning: category_theory.functor.map_homotopy -> CategoryTheory.Functor.mapHomotopy is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_homotopy CategoryTheory.Functor.mapHomotopyₓ'. -/
 /-- An additive functor takes homotopies to homotopies. -/
 @[simps]
 def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy f g) :
@@ -914,6 +1194,12 @@ def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy
     rfl
 #align category_theory.functor.map_homotopy CategoryTheory.Functor.mapHomotopy
 
+/- warning: category_theory.functor.map_homotopy_equiv -> CategoryTheory.Functor.mapHomotopyEquiv is a dubious translation:
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+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {W : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u5, u4} W] [_inst_4 : CategoryTheory.Preadditive.{u5, u4} W _inst_3] (F : CategoryTheory.Functor.{u1, u5, u2, u4} V _inst_1 W _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u2, u4, u1, u5} V W _inst_1 _inst_3 _inst_2 _inst_4 F], (HomotopyEquiv.{u1, u2, u3} ι V _inst_1 _inst_2 c C D) -> (HomotopyEquiv.{u5, u4, u3} ι W _inst_3 _inst_4 c (CategoryTheory.Functor.obj.{max u3 u1, max u3 u5, max u2 u3 u1, max u4 u3 u5} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (HomologicalComplex.CategoryTheory.category.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.Functor.mapHomologicalComplex.{u1, u2, u3, u4, u5} ι V _inst_1 _inst_2 W _inst_3 _inst_4 F _inst_5 c) C) (CategoryTheory.Functor.obj.{max u3 u1, max u3 u5, max u2 u3 u1, max u4 u3 u5} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (HomologicalComplex.CategoryTheory.category.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.Functor.mapHomologicalComplex.{u1, u2, u3, u4, u5} ι V _inst_1 _inst_2 W _inst_3 _inst_4 F _inst_5 c) D))
+but is expected to have type
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} V _inst_1] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c} {W : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u5, u4} W] [_inst_4 : CategoryTheory.Preadditive.{u5, u4} W _inst_3] (F : CategoryTheory.Functor.{u1, u5, u2, u4} V _inst_1 W _inst_3) [_inst_5 : CategoryTheory.Functor.Additive.{u2, u4, u1, u5} V W _inst_1 _inst_3 _inst_2 _inst_4 F], (HomotopyEquiv.{u1, u2, u3} ι V _inst_1 _inst_2 c C D) -> (HomotopyEquiv.{u5, u4, u3} ι W _inst_3 _inst_4 c (Prefunctor.obj.{max (succ u1) (succ u3), max (succ u3) (succ u5), max (max u2 u1) u3, max (max u3 u4) u5} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c))) (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u5, max (max u3 u4) u5} (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.Category.toCategoryStruct.{max u3 u5, max (max u3 u4) u5} (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c))) (CategoryTheory.Functor.toPrefunctor.{max u1 u3, max u3 u5, max (max u2 u1) u3, max (max u3 u4) u5} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.Functor.mapHomologicalComplex.{u1, u2, u3, u4, u5} ι V _inst_1 _inst_2 W _inst_3 _inst_4 F _inst_5 c)) C) (Prefunctor.obj.{max (succ u1) (succ u3), max (succ u3) (succ u5), max (max u2 u1) u3, max (max u3 u4) u5} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c))) (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u5, max (max u3 u4) u5} (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.Category.toCategoryStruct.{max u3 u5, max (max u3 u4) u5} (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c))) (CategoryTheory.Functor.toPrefunctor.{max u1 u3, max u3 u5, max (max u2 u1) u3, max (max u3 u4) u5} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} V _inst_1 _inst_2) c) (HomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι W _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} W _inst_3 _inst_4) c) (CategoryTheory.Functor.mapHomologicalComplex.{u1, u2, u3, u4, u5} ι V _inst_1 _inst_2 W _inst_3 _inst_4 F _inst_5 c)) D))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_homotopy_equiv CategoryTheory.Functor.mapHomotopyEquivₓ'. -/
 /-- An additive functor preserves homotopy equivalences. -/
 @[simps]
 def Functor.mapHomotopyEquiv (F : V ⥤ W) [F.Additive] (h : HomotopyEquiv C D) :

618ea3d5

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -619,7 +619,7 @@ def mkInductive : Homotopy e 0
   zero' i j w := by rwa [dif_neg]
   comm i := by
     dsimp; simp only [add_zero]
-    convert (mk_inductive_aux₂ e zero comm_zero one comm_one succ i).2.2
+    convert(mk_inductive_aux₂ e zero comm_zero one comm_one succ i).2.2
     · cases i
       · dsimp [fromNext]
         rw [dif_neg]
@@ -769,7 +769,7 @@ def mkCoinductive : Homotopy e 0
   comm i := by
     dsimp
     rw [add_zero, add_comm]
-    convert (mk_coinductive_aux₂ e zero comm_zero one comm_one succ i).2.2 using 2
+    convert(mk_coinductive_aux₂ e zero comm_zero one comm_one succ i).2.2 using 2
     · cases i
       · dsimp [toPrev]
         rw [dif_neg]

618ea3d5

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -148,7 +148,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i 
     congr 2
 #align prev_d_nat prevD_nat
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic obviously' -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic obviously' -/
 /-- A homotopy `h` between chain maps `f` and `g` consists of components `h i j : C.X i ⟶ D.X j`
 which are zero unless `c.rel j i`, satisfying the homotopy condition.
 -/

618ea3d5

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -38,7 +38,7 @@ section
 
 /-- The composition of `C.d i i' ≫ f i' i` if there is some `i'` coming after `i`,
 and `0` otherwise. -/
-def dNext (i : ι) : (∀ i j, C.x i ⟶ D.x j) →+ (C.x i ⟶ D.x i) :=
+def dNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt i ⟶ D.pt i) :=
   AddMonoidHom.mk' (fun f => C.d i (c.next i) ≫ f (c.next i) i) fun f g =>
     Preadditive.comp_add _ _ _ _ _ _
 #align d_next dNext
@@ -46,17 +46,17 @@ def dNext (i : ι) : (∀ i j, C.x i ⟶ D.x j) →+ (C.x i ⟶ D.x i) :=
 /-- `f i' i` if `i'` comes after `i`, and 0 if there's no such `i'`.
 Hopefully there won't be much need for this, except in `d_next_eq_d_from_from_next`
 to see that `d_next` factors through `C.d_from i`. -/
-def fromNext (i : ι) : (∀ i j, C.x i ⟶ D.x j) →+ (C.xNext i ⟶ D.x i) :=
+def fromNext (i : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.xNext i ⟶ D.pt i) :=
   AddMonoidHom.mk' (fun f => f (c.next i) i) fun f g => rfl
 #align from_next fromNext
 
 @[simp]
-theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.x i ⟶ D.x j) (i : ι) :
+theorem dNext_eq_dFrom_fromNext (f : ∀ i j, C.pt i ⟶ D.pt j) (i : ι) :
     dNext i f = C.dFrom i ≫ fromNext i f :=
   rfl
 #align d_next_eq_d_from_from_next dNext_eq_dFrom_fromNext
 
-theorem dNext_eq (f : ∀ i j, C.x i ⟶ D.x j) {i i' : ι} (w : c.Rel i i') :
+theorem dNext_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {i i' : ι} (w : c.Rel i i') :
     dNext i f = C.d i i' ≫ f i' i :=
   by
   obtain rfl := c.next_eq' w
@@ -64,20 +64,20 @@ theorem dNext_eq (f : ∀ i j, C.x i ⟶ D.x j) {i i' : ι} (w : c.Rel i i') :
 #align d_next_eq dNext_eq
 
 @[simp]
-theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.x i ⟶ E.x j) (i : ι) :
+theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (i : ι) :
     (dNext i fun i j => f.f i ≫ g i j) = f.f i ≫ dNext i g :=
   (f.comm_assoc _ _ _).symm
 #align d_next_comp_left dNext_comp_left
 
 @[simp]
-theorem dNext_comp_right (f : ∀ i j, C.x i ⟶ D.x j) (g : D ⟶ E) (i : ι) :
+theorem dNext_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (i : ι) :
     (dNext i fun i j => f i j ≫ g.f j) = dNext i f ≫ g.f i :=
   (Category.assoc _ _ _).symm
 #align d_next_comp_right dNext_comp_right
 
 /-- The composition of `f j j' ≫ D.d j' j` if there is some `j'` coming before `j`,
 and `0` otherwise. -/
-def prevD (j : ι) : (∀ i j, C.x i ⟶ D.x j) →+ (C.x j ⟶ D.x j) :=
+def prevD (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.pt j) :=
   AddMonoidHom.mk' (fun f => f j (c.prev j) ≫ D.d (c.prev j) j) fun f g =>
     Preadditive.add_comp _ _ _ _ _ _
 #align prev_d prevD
@@ -85,16 +85,17 @@ def prevD (j : ι) : (∀ i j, C.x i ⟶ D.x j) →+ (C.x j ⟶ D.x j) :=
 /-- `f j j'` if `j'` comes after `j`, and 0 if there's no such `j'`.
 Hopefully there won't be much need for this, except in `d_next_eq_d_from_from_next`
 to see that `d_next` factors through `C.d_from i`. -/
-def toPrev (j : ι) : (∀ i j, C.x i ⟶ D.x j) →+ (C.x j ⟶ D.xPrev j) :=
+def toPrev (j : ι) : (∀ i j, C.pt i ⟶ D.pt j) →+ (C.pt j ⟶ D.xPrev j) :=
   AddMonoidHom.mk' (fun f => f j (c.prev j)) fun f g => rfl
 #align to_prev toPrev
 
 @[simp]
-theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.x i ⟶ D.x j) (j : ι) : prevD j f = toPrev j f ≫ D.dTo j :=
+theorem prevD_eq_toPrev_dTo (f : ∀ i j, C.pt i ⟶ D.pt j) (j : ι) :
+    prevD j f = toPrev j f ≫ D.dTo j :=
   rfl
 #align prev_d_eq_to_prev_d_to prevD_eq_toPrev_dTo
 
-theorem prevD_eq (f : ∀ i j, C.x i ⟶ D.x j) {j j' : ι} (w : c.Rel j' j) :
+theorem prevD_eq (f : ∀ i j, C.pt i ⟶ D.pt j) {j j' : ι} (w : c.Rel j' j) :
     prevD j f = f j j' ≫ D.d j' j :=
   by
   obtain rfl := c.prev_eq' w
@@ -102,20 +103,20 @@ theorem prevD_eq (f : ∀ i j, C.x i ⟶ D.x j) {j j' : ι} (w : c.Rel j' j) :
 #align prev_d_eq prevD_eq
 
 @[simp]
-theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.x i ⟶ E.x j) (j : ι) :
+theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.pt i ⟶ E.pt j) (j : ι) :
     (prevD j fun i j => f.f i ≫ g i j) = f.f j ≫ prevD j g :=
   Category.assoc _ _ _
 #align prev_d_comp_left prevD_comp_left
 
 @[simp]
-theorem prevD_comp_right (f : ∀ i j, C.x i ⟶ D.x j) (g : D ⟶ E) (j : ι) :
+theorem prevD_comp_right (f : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) (j : ι) :
     (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j :=
   by
   dsimp [prevD]
   simp only [category.assoc, g.comm]
 #align prev_d_comp_right prevD_comp_right
 
-theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.x i ⟶ D.x j) :
+theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     dNext i f = C.d i (i - 1) ≫ f (i - 1) i :=
   by
   dsimp [dNext]
@@ -131,7 +132,7 @@ theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.x i ⟶ D
     congr 2
 #align d_next_nat dNext_nat
 
-theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.x i ⟶ D.x j) :
+theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.pt i ⟶ D.pt j) :
     prevD i f = f i (i - 1) ≫ D.d (i - 1) i :=
   by
   dsimp [prevD]
@@ -153,7 +154,7 @@ which are zero unless `c.rel j i`, satisfying the homotopy condition.
 -/
 @[ext, nolint has_nonempty_instance]
 structure Homotopy (f g : C ⟶ D) where
-  Hom : ∀ i j, C.x i ⟶ D.x j
+  Hom : ∀ i j, C.pt i ⟶ D.pt j
   zero' : ∀ i j, ¬c.Rel j i → hom i j = 0 := by obviously
   comm : ∀ i, f.f i = dNext i hom + prevD i hom + g.f i := by
     run_tac
@@ -280,7 +281,7 @@ two differentials going to and from a certain degree, only one, or none.
 This is the same datum as for the field `hom` in the structure `homotopy`. For
 this definition, we do not need the field `zero` of that structure
 as this definition uses only the maps `C_i ⟶ C_j` when `c.rel j i`. -/
-def nullHomotopicMap (hom : ∀ i j, C.x i ⟶ D.x j) : C ⟶ D
+def nullHomotopicMap (hom : ∀ i j, C.pt i ⟶ D.pt j) : C ⟶ D
     where
   f i := dNext i hom + prevD i hom
   comm' i j hij :=
@@ -295,13 +296,13 @@ def nullHomotopicMap (hom : ∀ i j, C.x i ⟶ D.x j) : C ⟶ D
 
 /-- Variant of `null_homotopic_map` where the input consists only of the
 relevant maps `C_i ⟶ D_j` such that `c.rel j i`. -/
-def nullHomotopicMap' (h : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) : C ⟶ D :=
+def nullHomotopicMap' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : C ⟶ D :=
   nullHomotopicMap fun i j => dite (c.Rel j i) (h i j) fun _ => 0
 #align homotopy.null_homotopic_map' Homotopy.nullHomotopicMap'
 
 /-- Compatibility of `null_homotopic_map` with the postcomposition by a morphism
 of complexes. -/
-theorem nullHomotopicMap_comp (hom : ∀ i j, C.x i ⟶ D.x j) (g : D ⟶ E) :
+theorem nullHomotopicMap_comp (hom : ∀ i j, C.pt i ⟶ D.pt j) (g : D ⟶ E) :
     nullHomotopicMap hom ≫ g = nullHomotopicMap fun i j => hom i j ≫ g.f j :=
   by
   ext n
@@ -311,7 +312,7 @@ theorem nullHomotopicMap_comp (hom : ∀ i j, C.x i ⟶ D.x j) (g : D ⟶ E) :
 
 /-- Compatibility of `null_homotopic_map'` with the postcomposition by a morphism
 of complexes. -/
-theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) (g : D ⟶ E) :
+theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) (g : D ⟶ E) :
     nullHomotopicMap' hom ≫ g = nullHomotopicMap' fun i j hij => hom i j hij ≫ g.f j :=
   by
   ext n
@@ -325,7 +326,7 @@ theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j))
 
 /-- Compatibility of `null_homotopic_map` with the precomposition by a morphism
 of complexes. -/
-theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.x i ⟶ E.x j) :
+theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.pt i ⟶ E.pt j) :
     f ≫ nullHomotopicMap hom = nullHomotopicMap fun i j => f.f i ≫ hom i j :=
   by
   ext n
@@ -335,7 +336,7 @@ theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.x i ⟶ E.x j) :
 
 /-- Compatibility of `null_homotopic_map'` with the precomposition by a morphism
 of complexes. -/
-theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.x i ⟶ E.x j)) :
+theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.pt i ⟶ E.pt j)) :
     f ≫ nullHomotopicMap' hom = nullHomotopicMap' fun i j hij => f.f i ≫ hom i j hij :=
   by
   ext n
@@ -349,7 +350,7 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.x
 
 /-- Compatibility of `null_homotopic_map` with the application of additive functors -/
 theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
-    (hom : ∀ i j, C.x i ⟶ D.x j) :
+    (hom : ∀ i j, C.pt i ⟶ D.pt j) :
     (G.mapHomologicalComplex c).map (nullHomotopicMap hom) =
       nullHomotopicMap fun i j => G.map (hom i j) :=
   by
@@ -360,7 +361,7 @@ theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V 
 
 /-- Compatibility of `null_homotopic_map'` with the application of additive functors -/
 theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
-    (hom : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) :
+    (hom : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
     (G.mapHomologicalComplex c).map (nullHomotopicMap' hom) =
       nullHomotopicMap' fun i j hij => G.map (hom i j hij) :=
   by
@@ -376,7 +377,7 @@ theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V 
 /-- Tautological construction of the `homotopy` to zero for maps constructed by
 `null_homotopic_map`, at least when we have the `zero'` condition. -/
 @[simps]
-def nullHomotopy (hom : ∀ i j, C.x i ⟶ D.x j) (zero' : ∀ i j, ¬c.Rel j i → hom i j = 0) :
+def nullHomotopy (hom : ∀ i j, C.pt i ⟶ D.pt j) (zero' : ∀ i j, ¬c.Rel j i → hom i j = 0) :
     Homotopy (nullHomotopicMap hom) 0 :=
   { Hom
     zero'
@@ -388,7 +389,7 @@ def nullHomotopy (hom : ∀ i j, C.x i ⟶ D.x j) (zero' : ∀ i j, ¬c.Rel j i
 
 /-- Homotopy to zero for maps constructed with `null_homotopic_map'` -/
 @[simps]
-def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) : Homotopy (nullHomotopicMap' h) 0 :=
+def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) : Homotopy (nullHomotopicMap' h) 0 :=
   by
   apply null_homotopy fun i j => dite (c.rel j i) (h i j) fun _ => 0
   intro i j hij
@@ -406,7 +407,7 @@ with `null_homotopic_map` or `null_homotopic_map'` -/
 
 @[simp]
 theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
-    (hom : ∀ i j, C.x i ⟶ D.x j) :
+    (hom : ∀ i j, C.pt i ⟶ D.pt j) :
     (nullHomotopicMap hom).f k₁ = C.d k₁ k₀ ≫ hom k₀ k₁ + hom k₁ k₂ ≫ D.d k₂ k₁ :=
   by
   dsimp only [null_homotopic_map]
@@ -415,7 +416,7 @@ theorem nullHomotopicMap_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
 
 @[simp]
 theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r₁₀ : c.Rel k₁ k₀)
-    (h : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) :
+    (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
     (nullHomotopicMap' h).f k₁ = C.d k₁ k₀ ≫ h k₀ k₁ r₁₀ + h k₁ k₂ r₂₁ ≫ D.d k₂ k₁ :=
   by
   simp only [← null_homotopic_map']
@@ -427,7 +428,7 @@ theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
 
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
-    (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (hom : ∀ i j, C.x i ⟶ D.x j) :
+    (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
     (nullHomotopicMap hom).f k₀ = hom k₀ k₁ ≫ D.d k₁ k₀ :=
   by
   dsimp only [null_homotopic_map]
@@ -437,7 +438,7 @@ theorem nullHomotopicMap_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
 
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
-    (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (h : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) :
+    (hk₀ : ∀ l : ι, ¬c.Rel k₀ l) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
     (nullHomotopicMap' h).f k₀ = h k₀ k₁ r₁₀ ≫ D.d k₁ k₀ :=
   by
   simp only [← null_homotopic_map']
@@ -449,7 +450,7 @@ theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
 
 @[simp]
 theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
-    (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (hom : ∀ i j, C.x i ⟶ D.x j) :
+    (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
     (nullHomotopicMap hom).f k₁ = C.d k₁ k₀ ≫ hom k₀ k₁ :=
   by
   dsimp only [null_homotopic_map]
@@ -459,7 +460,7 @@ theorem nullHomotopicMap_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
 
 @[simp]
 theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k₁ k₀)
-    (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (h : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) :
+    (hk₁ : ∀ l : ι, ¬c.Rel l k₁) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
     (nullHomotopicMap' h).f k₁ = C.d k₁ k₀ ≫ h k₀ k₁ r₁₀ :=
   by
   simp only [← null_homotopic_map']
@@ -471,7 +472,8 @@ theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
 
 @[simp]
 theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
-    (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (hom : ∀ i j, C.x i ⟶ D.x j) : (nullHomotopicMap hom).f k₀ = 0 :=
+    (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (hom : ∀ i j, C.pt i ⟶ D.pt j) :
+    (nullHomotopicMap hom).f k₀ = 0 :=
   by
   dsimp [null_homotopic_map, dNext, prevD]
   rw [C.shape, D.shape, zero_comp, comp_zero, add_zero] <;> apply_assumption
@@ -479,7 +481,7 @@ theorem nullHomotopicMap_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀
 
 @[simp]
 theorem nullHomotopicMap'_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k₀ l)
-    (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (h : ∀ i j, c.Rel j i → (C.x i ⟶ D.x j)) :
+    (hk₀' : ∀ l : ι, ¬c.Rel l k₀) (h : ∀ i j, c.Rel j i → (C.pt i ⟶ D.pt j)) :
     (nullHomotopicMap' h).f k₀ = 0 :=
   by
   simp only [← null_homotopic_map']
@@ -506,15 +508,15 @@ section MkInductive
 variable {P Q : ChainComplex V ℕ}
 
 @[simp]
-theorem prevD_chainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (j : ℕ) : prevD j f = f j (j + 1) ≫ Q.d _ _ :=
-  by
+theorem prevD_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
+    prevD j f = f j (j + 1) ≫ Q.d _ _ := by
   dsimp [prevD]
   have : (ComplexShape.down ℕ).prev j = j + 1 := ChainComplex.prev ℕ j
   congr 2
 #align homotopy.prev_d_chain_complex Homotopy.prevD_chainComplex
 
 @[simp]
-theorem dNext_succ_chainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (i : ℕ) :
+theorem dNext_succ_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     dNext (i + 1) f = P.d _ _ ≫ f i (i + 1) :=
   by
   dsimp [dNext]
@@ -523,21 +525,21 @@ theorem dNext_succ_chainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (i : ℕ) :
 #align homotopy.d_next_succ_chain_complex Homotopy.dNext_succ_chainComplex
 
 @[simp]
-theorem dNext_zero_chainComplex (f : ∀ i j, P.x i ⟶ Q.x j) : dNext 0 f = 0 :=
+theorem dNext_zero_chainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : dNext 0 f = 0 :=
   by
   dsimp [dNext]
   rw [P.shape, zero_comp]
   rw [ChainComplex.next_nat_zero]; dsimp; decide
 #align homotopy.d_next_zero_chain_complex Homotopy.dNext_zero_chainComplex
 
-variable (e : P ⟶ Q) (zero : P.x 0 ⟶ Q.x 1) (comm_zero : e.f 0 = zero ≫ Q.d 1 0)
-  (one : P.x 1 ⟶ Q.x 2) (comm_one : e.f 1 = P.d 1 0 ≫ zero + one ≫ Q.d 2 1)
+variable (e : P ⟶ Q) (zero : P.pt 0 ⟶ Q.pt 1) (comm_zero : e.f 0 = zero ≫ Q.d 1 0)
+  (one : P.pt 1 ⟶ Q.pt 2) (comm_one : e.f 1 = P.d 1 0 ≫ zero + one ≫ Q.d 2 1)
   (succ :
     ∀ (n : ℕ)
       (p :
-        Σ'(f : P.x n ⟶ Q.x (n + 1))(f' : P.x (n + 1) ⟶ Q.x (n + 2)),
+        Σ'(f : P.pt n ⟶ Q.pt (n + 1))(f' : P.pt (n + 1) ⟶ Q.pt (n + 2)),
           e.f (n + 1) = P.d (n + 1) n ≫ f + f' ≫ Q.d (n + 2) (n + 1)),
-      Σ'f'' : P.x (n + 2) ⟶ Q.x (n + 3),
+      Σ'f'' : P.pt (n + 2) ⟶ Q.pt (n + 3),
         e.f (n + 2) = P.d (n + 2) (n + 1) ≫ p.2.1 + f'' ≫ Q.d (n + 3) (n + 2))
 
 include comm_one comm_zero
@@ -562,7 +564,7 @@ which we do in `mk_inductive_aux₂`.
 @[simp, nolint unused_arguments]
 def mkInductiveAux₁ :
     ∀ n,
-      Σ'(f : P.x n ⟶ Q.x (n + 1))(f' : P.x (n + 1) ⟶ Q.x (n + 2)),
+      Σ'(f : P.pt n ⟶ Q.pt (n + 1))(f' : P.pt (n + 1) ⟶ Q.pt (n + 2)),
         e.f (n + 1) = P.d (n + 1) n ≫ f + f' ≫ Q.d (n + 2) (n + 1)
   | 0 => ⟨zero, one, comm_one⟩
   | 1 => ⟨one, (succ 0 ⟨zero, one, comm_one⟩).1, (succ 0 ⟨zero, one, comm_one⟩).2⟩
@@ -583,7 +585,7 @@ Case conversion may be inaccurate. Consider using '#align homotopy.mk_inductive_
 -/
 @[simp]
 def mkInductiveAux₂ :
-    ∀ n, Σ'(f : P.xNext n ⟶ Q.x n)(f' : P.x n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
+    ∀ n, Σ'(f : P.xNext n ⟶ Q.pt n)(f' : P.pt n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
   | 0 => ⟨0, zero ≫ (Q.xPrevIso rfl).inv, by simpa using comm_zero⟩
   | n + 1 =>
     let I := mkInductiveAux₁ e zero comm_zero one comm_one succ n
@@ -655,7 +657,7 @@ section MkCoinductive
 variable {P Q : CochainComplex V ℕ}
 
 @[simp]
-theorem dNext_cochainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (j : ℕ) :
+theorem dNext_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (j : ℕ) :
     dNext j f = P.d _ _ ≫ f (j + 1) j := by
   dsimp [dNext]
   have : (ComplexShape.up ℕ).next j = j + 1 := CochainComplex.next ℕ j
@@ -663,7 +665,7 @@ theorem dNext_cochainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (j : ℕ) :
 #align homotopy.d_next_cochain_complex Homotopy.dNext_cochainComplex
 
 @[simp]
-theorem prevD_succ_cochainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (i : ℕ) :
+theorem prevD_succ_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) (i : ℕ) :
     prevD (i + 1) f = f (i + 1) _ ≫ Q.d i (i + 1) :=
   by
   dsimp [prevD]
@@ -672,21 +674,21 @@ theorem prevD_succ_cochainComplex (f : ∀ i j, P.x i ⟶ Q.x j) (i : ℕ) :
 #align homotopy.prev_d_succ_cochain_complex Homotopy.prevD_succ_cochainComplex
 
 @[simp]
-theorem prevD_zero_cochainComplex (f : ∀ i j, P.x i ⟶ Q.x j) : prevD 0 f = 0 :=
+theorem prevD_zero_cochainComplex (f : ∀ i j, P.pt i ⟶ Q.pt j) : prevD 0 f = 0 :=
   by
   dsimp [prevD]
   rw [Q.shape, comp_zero]
   rw [CochainComplex.prev_nat_zero]; dsimp; decide
 #align homotopy.prev_d_zero_cochain_complex Homotopy.prevD_zero_cochainComplex
 
-variable (e : P ⟶ Q) (zero : P.x 1 ⟶ Q.x 0) (comm_zero : e.f 0 = P.d 0 1 ≫ zero)
-  (one : P.x 2 ⟶ Q.x 1) (comm_one : e.f 1 = zero ≫ Q.d 0 1 + P.d 1 2 ≫ one)
+variable (e : P ⟶ Q) (zero : P.pt 1 ⟶ Q.pt 0) (comm_zero : e.f 0 = P.d 0 1 ≫ zero)
+  (one : P.pt 2 ⟶ Q.pt 1) (comm_one : e.f 1 = zero ≫ Q.d 0 1 + P.d 1 2 ≫ one)
   (succ :
     ∀ (n : ℕ)
       (p :
-        Σ'(f : P.x (n + 1) ⟶ Q.x n)(f' : P.x (n + 2) ⟶ Q.x (n + 1)),
+        Σ'(f : P.pt (n + 1) ⟶ Q.pt n)(f' : P.pt (n + 2) ⟶ Q.pt (n + 1)),
           e.f (n + 1) = f ≫ Q.d n (n + 1) + P.d (n + 1) (n + 2) ≫ f'),
-      Σ'f'' : P.x (n + 3) ⟶ Q.x (n + 2),
+      Σ'f'' : P.pt (n + 3) ⟶ Q.pt (n + 2),
         e.f (n + 2) = p.2.1 ≫ Q.d (n + 1) (n + 2) + P.d (n + 2) (n + 3) ≫ f'')
 
 include comm_one comm_zero succ
@@ -711,7 +713,7 @@ which we do in `mk_inductive_aux₂`.
 @[simp, nolint unused_arguments]
 def mkCoinductiveAux₁ :
     ∀ n,
-      Σ'(f : P.x (n + 1) ⟶ Q.x n)(f' : P.x (n + 2) ⟶ Q.x (n + 1)),
+      Σ'(f : P.pt (n + 1) ⟶ Q.pt n)(f' : P.pt (n + 2) ⟶ Q.pt (n + 1)),
         e.f (n + 1) = f ≫ Q.d n (n + 1) + P.d (n + 1) (n + 2) ≫ f'
   | 0 => ⟨zero, one, comm_one⟩
   | 1 => ⟨one, (succ 0 ⟨zero, one, comm_one⟩).1, (succ 0 ⟨zero, one, comm_one⟩).2⟩
@@ -732,7 +734,7 @@ Case conversion may be inaccurate. Consider using '#align homotopy.mk_coinductiv
 -/
 @[simp]
 def mkCoinductiveAux₂ :
-    ∀ n, Σ'(f : P.x n ⟶ Q.xPrev n)(f' : P.xNext n ⟶ Q.x n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
+    ∀ n, Σ'(f : P.pt n ⟶ Q.xPrev n)(f' : P.xNext n ⟶ Q.pt n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
   | 0 => ⟨0, (P.xNextIso rfl).Hom ≫ zero, by simpa using comm_zero⟩
   | n + 1 =>
     let I := mkCoinductiveAux₁ e zero comm_zero one comm_one succ n

618ea3d5

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

618ea3d5

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

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

c5b5490c

Diff

@@ -130,7 +130,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.X i ⟶
   · congr <;> simp
 #align prev_d_nat prevD_nat
 
--- Porting note: removed @[has_nonempty_instance]
+-- Porting note(#5171): removed @[has_nonempty_instance]
 /-- A homotopy `h` between chain maps `f` and `g` consists of components `h i j : C.X i ⟶ D.X j`
 which are zero unless `c.Rel j i`, satisfying the homotopy condition.
 -/

618ea3d5

chore: remove @[eqns] in Algebra/Homology/Homotopy (#11648)

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

f7c6a4c6

Diff

@@ -542,21 +542,22 @@ def mkInductiveAux₂ :
     ⟨(P.xNextIso rfl).hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv, by simpa using I.2.2⟩
 #align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂
 
-theorem mkInductiveAux₂_zero :
+-- Adaptation note:
+-- During the port we marked these lemmas with `@[eqns]` to emulate the old Lean 3 behaviour.
+-- See https://github.com/leanprover-community/mathlib4/issues/11647
+
+@[simp] theorem mkInductiveAux₂_zero :
     mkInductiveAux₂ e zero comm_zero one comm_one succ 0 =
       ⟨0, zero ≫ (Q.xPrevIso rfl).inv, mkInductiveAux₂.proof_2 e zero comm_zero⟩ :=
   rfl
 
-theorem mkInductiveAux₂_add_one (n) :
+@[simp] theorem mkInductiveAux₂_add_one (n) :
     mkInductiveAux₂ e zero comm_zero one comm_one succ (n + 1) =
       let I := mkInductiveAux₁ e zero one comm_one succ n
       ⟨(P.xNextIso rfl).hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv,
         mkInductiveAux₂.proof_5 e zero one comm_one succ n⟩ :=
   rfl
 
-attribute [eqns mkInductiveAux₂_zero mkInductiveAux₂_add_one] mkInductiveAux₂
-attribute [simp] mkInductiveAux₂
-
 theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).hom =
       (P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 := by
@@ -680,21 +681,22 @@ def mkCoinductiveAux₂ :
     ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).hom ≫ I.2.1, by simpa using I.2.2⟩
 #align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂
 
-theorem mkCoinductiveAux₂_zero :
+-- Adaptation note:
+-- During the port we marked these lemmas with `@[eqns]` to emulate the old Lean 3 behaviour.
+-- See https://github.com/leanprover-community/mathlib4/issues/11647
+
+@[simp] theorem mkCoinductiveAux₂_zero :
     mkCoinductiveAux₂ e zero comm_zero one comm_one succ 0 =
       ⟨0, (P.xNextIso rfl).hom ≫ zero, mkCoinductiveAux₂.proof_2 e zero comm_zero⟩ :=
   rfl
 
-theorem mkCoinductiveAux₂_add_one (n) :
+@[simp] theorem mkCoinductiveAux₂_add_one (n) :
     mkCoinductiveAux₂ e zero comm_zero one comm_one succ (n + 1) =
       let I := mkCoinductiveAux₁ e zero one comm_one succ n
       ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).hom ≫ I.2.1,
         mkCoinductiveAux₂.proof_5 e zero one comm_one succ n⟩ :=
   rfl
 
-attribute [eqns mkCoinductiveAux₂_zero mkCoinductiveAux₂_add_one] mkCoinductiveAux₂
-attribute [simp] mkCoinductiveAux₂
-
 theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
       (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).1 ≫ (Q.xPrevIso h).hom := by

618ea3d5

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

@@ -25,11 +25,8 @@ noncomputable section
 open CategoryTheory Category Limits HomologicalComplex
 
 variable {ι : Type*}
-
 variable {V : Type u} [Category.{v} V] [Preadditive V]
-
 variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
-
 variable (f g : C ⟶ D) (h k : D ⟶ E) (i : ι)
 
 section

618ea3d5

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -18,7 +18,7 @@ We define chain homotopies, and prove that homotopic chain maps induce the same
 
 universe v u
 
-open Classical
+open scoped Classical
 
 noncomputable section

618ea3d5

feat(Algebra/Homology): the category of homological complexes is linear (#10891)

In this PR, it is shown that if C is a R-linear category, then the category of homological complexes in C is R-linear. (This is also obtained for the homotopy category.)

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

f5aa22df

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
+import Mathlib.Algebra.Homology.Linear
 import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
 import Mathlib.Tactic.Abel
 
@@ -206,6 +207,20 @@ def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homo
     abel
 #align homotopy.add Homotopy.add
 
+/-- the scalar multiplication of an homotopy -/
+@[simps!]
+def smul {R : Type*} [Semiring R] [Linear R V] (h : Homotopy f g) (a : R) :
+    Homotopy (a • f) (a • g) where
+  hom i j := a • h.hom i j
+  zero i j hij := by
+    dsimp
+    rw [h.zero i j hij, smul_zero]
+  comm i := by
+    dsimp
+    rw [h.comm]
+    dsimp [fromNext, toPrev]
+    simp only [smul_add, Linear.comp_smul, Linear.smul_comp]
+
 /-- homotopy is closed under composition (on the right) -/
 @[simps]
 def compRight {e f : C ⟶ D} (h : Homotopy e f) (g : D ⟶ E) : Homotopy (e ≫ g) (f ≫ g) where

618ea3d5

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -132,7 +132,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.X i ⟶
   · congr <;> simp
 #align prev_d_nat prevD_nat
 
--- porting note: removed @[has_nonempty_instance]
+-- Porting note: removed @[has_nonempty_instance]
 /-- A homotopy `h` between chain maps `f` and `g` consists of components `h i j : C.X i ⟶ D.X j`
 which are zero unless `c.Rel j i`, satisfying the homotopy condition.
 -/

618ea3d5

feat(Algebra/Homology): construction of the homotopy cofiber (#8969)

e0f4e431

Diff

@@ -56,6 +56,11 @@ theorem dNext_eq (f : ∀ i j, C.X i ⟶ D.X j) {i i' : ι} (w : c.Rel i i') :
   rfl
 #align d_next_eq dNext_eq
 
+lemma dNext_eq_zero (f : ∀ i j, C.X i ⟶ D.X j) (i : ι) (hi : ¬ c.Rel i (c.next i)) :
+    dNext i f = 0 := by
+  dsimp [dNext]
+  rw [shape _ _ _ hi, zero_comp]
+
 @[simp 1100]
 theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.X i ⟶ E.X j) (i : ι) :
     (dNext i fun i j => f.f i ≫ g i j) = f.f i ≫ dNext i g :=
@@ -74,6 +79,11 @@ def prevD (j : ι) : (∀ i j, C.X i ⟶ D.X j) →+ (C.X j ⟶ D.X j) :=
     Preadditive.add_comp _ _ _ _ _ _
 #align prev_d prevD
 
+lemma prevD_eq_zero (f : ∀ i j, C.X i ⟶ D.X j) (i : ι) (hi : ¬ c.Rel (c.prev i) i) :
+    prevD i f = 0 := by
+  dsimp [prevD]
+  rw [shape _ _ _ hi, comp_zero]
+
 /-- `f j (c.prev j)`. -/
 def toPrev (j : ι) : (∀ i j, C.X i ⟶ D.X j) →+ (C.X j ⟶ D.xPrev j) :=
   AddMonoidHom.mk' (fun f => f j (c.prev j)) fun _ _ => rfl

618ea3d5

feat: the homology functor on the homotopy category for the new API (#8595)

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

b112cb6b

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathlib.Algebra.Homology.Additive
+import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
 import Mathlib.Tactic.Abel
 
 #align_import algebra.homology.homotopy from "leanprover-community/mathlib"@"618ea3d5c99240cd7000d8376924906a148bf9ff"
@@ -21,7 +21,7 @@ open Classical
 
 noncomputable section
 
-open CategoryTheory CategoryTheory.Limits HomologicalComplex
+open CategoryTheory Category Limits HomologicalComplex
 
 variable {ι : Type*}
 
@@ -65,7 +65,7 @@ theorem dNext_comp_left (f : C ⟶ D) (g : ∀ i j, D.X i ⟶ E.X j) (i : ι) :
 @[simp 1100]
 theorem dNext_comp_right (f : ∀ i j, C.X i ⟶ D.X j) (g : D ⟶ E) (i : ι) :
     (dNext i fun i j => f i j ≫ g.f j) = dNext i f ≫ g.f i :=
-  (Category.assoc _ _ _).symm
+  (assoc _ _ _).symm
 #align d_next_comp_right dNext_comp_right
 
 /-- The composition `f j (c.prev j) ≫ D.d (c.prev j) j`. -/
@@ -94,14 +94,14 @@ theorem prevD_eq (f : ∀ i j, C.X i ⟶ D.X j) {j j' : ι} (w : c.Rel j' j) :
 @[simp 1100]
 theorem prevD_comp_left (f : C ⟶ D) (g : ∀ i j, D.X i ⟶ E.X j) (j : ι) :
     (prevD j fun i j => f.f i ≫ g i j) = f.f j ≫ prevD j g :=
-  Category.assoc _ _ _
+  assoc _ _ _
 #align prev_d_comp_left prevD_comp_left
 
 @[simp 1100]
 theorem prevD_comp_right (f : ∀ i j, C.X i ⟶ D.X j) (g : D ⟶ E) (j : ι) :
     (prevD j fun i j => f i j ≫ g.f j) = prevD j f ≫ g.f j := by
   dsimp [prevD]
-  simp only [Category.assoc, g.comm]
+  simp only [assoc, g.comm]
 #align prev_d_comp_right prevD_comp_right
 
 theorem dNext_nat (C D : ChainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.X i ⟶ D.X j) :
@@ -224,13 +224,13 @@ def comp {C₁ C₂ C₃ : HomologicalComplex V c} {f₁ g₁ : C₁ ⟶ C₂} {
 /-- a variant of `Homotopy.compRight` useful for dealing with homotopy equivalences. -/
 @[simps!]
 def compRightId {f : C ⟶ C} (h : Homotopy f (𝟙 C)) (g : C ⟶ D) : Homotopy (f ≫ g) g :=
-  (h.compRight g).trans (ofEq <| Category.id_comp _)
+  (h.compRight g).trans (ofEq <| id_comp _)
 #align homotopy.comp_right_id Homotopy.compRightId
 
 /-- a variant of `Homotopy.compLeft` useful for dealing with homotopy equivalences. -/
 @[simps!]
 def compLeftId {f : D ⟶ D} (h : Homotopy f (𝟙 D)) (g : C ⟶ D) : Homotopy (g ≫ f) g :=
-  (h.compLeft g).trans (ofEq <| Category.comp_id _)
+  (h.compLeft g).trans (ofEq <| comp_id _)
 #align homotopy.comp_left_id Homotopy.compLeftId
 
 /-!
@@ -249,12 +249,12 @@ def nullHomotopicMap (hom : ∀ i j, C.X i ⟶ D.X j) : C ⟶ D where
   f i := dNext i hom + prevD i hom
   comm' i j hij := by
     have eq1 : prevD i hom ≫ D.d i j = 0 := by
-      simp only [prevD, AddMonoidHom.mk'_apply, Category.assoc, d_comp_d, comp_zero]
+      simp only [prevD, AddMonoidHom.mk'_apply, assoc, d_comp_d, comp_zero]
     have eq2 : C.d i j ≫ dNext j hom = 0 := by
       simp only [dNext, AddMonoidHom.mk'_apply, d_comp_d_assoc, zero_comp]
     dsimp only
     rw [dNext_eq hom hij, prevD_eq hom hij, Preadditive.comp_add, Preadditive.add_comp, eq1, eq2,
-      add_zero, zero_add, Category.assoc]
+      add_zero, zero_add, assoc]
 #align homotopy.null_homotopic_map Homotopy.nullHomotopicMap
 
 /-- Variant of `nullHomotopicMap` where the input consists only of the
@@ -269,7 +269,7 @@ theorem nullHomotopicMap_comp (hom : ∀ i j, C.X i ⟶ D.X j) (g : D ⟶ E) :
     nullHomotopicMap hom ≫ g = nullHomotopicMap fun i j => hom i j ≫ g.f j := by
   ext n
   dsimp [nullHomotopicMap, fromNext, toPrev, AddMonoidHom.mk'_apply]
-  simp only [Preadditive.add_comp, Category.assoc, g.comm]
+  simp only [Preadditive.add_comp, assoc, g.comm]
 #align homotopy.null_homotopic_map_comp Homotopy.nullHomotopicMap_comp
 
 /-- Compatibility of `nullHomotopicMap'` with the postcomposition by a morphism
@@ -291,7 +291,7 @@ theorem comp_nullHomotopicMap (f : C ⟶ D) (hom : ∀ i j, D.X i ⟶ E.X j) :
     f ≫ nullHomotopicMap hom = nullHomotopicMap fun i j => f.f i ≫ hom i j := by
   ext n
   dsimp [nullHomotopicMap, fromNext, toPrev, AddMonoidHom.mk'_apply]
-  simp only [Preadditive.comp_add, Category.assoc, f.comm_assoc]
+  simp only [Preadditive.comp_add, assoc, f.comm_assoc]
 #align homotopy.comp_null_homotopic_map Homotopy.comp_nullHomotopicMap
 
 /-- Compatibility of `nullHomotopicMap'` with the precomposition by a morphism
@@ -570,9 +570,9 @@ def mkInductive : Homotopy e 0 where
         simp only [ChainComplex.next_nat_succ, dite_true]
         rw [mkInductiveAux₃ e zero comm_zero one comm_one succ]
         dsimp [xNextIso]
-        rw [Category.id_comp]
+        rw [id_comp]
     · dsimp [toPrev]
-      erw [dif_pos, Category.comp_id]
+      erw [dif_pos, comp_id]
       simp only [ChainComplex.prev]
 #align homotopy.mk_inductive Homotopy.mkInductive
 
@@ -709,9 +709,9 @@ def mkCoinductive : Homotopy e 0 where
         simp only [CochainComplex.prev_nat_succ, dite_true]
         rw [mkCoinductiveAux₃ e zero comm_zero one comm_one succ]
         dsimp [xPrevIso]
-        rw [Category.comp_id]
+        rw [comp_id]
     · dsimp [fromNext]
-      erw [dif_pos, Category.id_comp]
+      erw [dif_pos, id_comp]
       simp only [CochainComplex.next]
 #align homotopy.mk_coinductive Homotopy.mkCoinductive
 
@@ -734,6 +734,12 @@ structure HomotopyEquiv (C D : HomologicalComplex V c) where
   homotopyInvHomId : Homotopy (inv ≫ hom) (𝟙 D)
 #align homotopy_equiv HomotopyEquiv
 
+variable (V c) in
+/-- The morphism property on `HomologicalComplex V c` given by homotopy equivalences. -/
+def HomologicalComplex.homotopyEquivalences :
+    MorphismProperty (HomologicalComplex V c) :=
+  fun X Y f => ∃ (e : HomotopyEquiv X Y), e.hom = f
+
 namespace HomotopyEquiv
 
 /-- Any complex is homotopy equivalent to itself. -/
@@ -795,7 +801,7 @@ theorem homology'_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
   simp only [CategoryTheory.Subobject.factorThru_add_sub_factorThru_right]
   erw [Subobject.factorThru_ofLE (D.boundaries_le_cycles' i)]
   · simp
-  · rw [prevD_eq_toPrev_dTo, ← Category.assoc]
+  · rw [prevD_eq_toPrev_dTo, ← assoc]
     apply imageSubobject_factors_comp_self
 #align homology_map_eq_of_homotopy homology'_map_eq_of_homotopy
 
@@ -845,3 +851,65 @@ def Functor.mapHomotopyEquiv (F : V ⥤ W) [F.Additive] (h : HomotopyEquiv C D)
 #align category_theory.functor.map_homotopy_equiv CategoryTheory.Functor.mapHomotopyEquiv
 
 end CategoryTheory
+
+section
+
+open HomologicalComplex CategoryTheory
+
+variable {C : Type*} [Category C] [Preadditive C] {ι : Type _} {c : ComplexShape ι}
+  [DecidableRel c.Rel] {K L : HomologicalComplex C c} {f g : K ⟶ L}
+
+/-- A homotopy between morphisms of homological complexes `K ⟶ L` induces a homotopy
+between morphisms of short complexes `K.sc i ⟶ L.sc i`. -/
+noncomputable def Homotopy.toShortComplex (ho : Homotopy f g) (i : ι) :
+    ShortComplex.Homotopy ((shortComplexFunctor C c i).map f)
+      ((shortComplexFunctor C c i).map g) where
+  h₀ :=
+    if c.Rel (c.prev i) i
+    then ho.hom _ (c.prev (c.prev i)) ≫ L.d _ _
+    else f.f _ - g.f _ - K.d _ i ≫ ho.hom i _
+  h₁ := ho.hom _ _
+  h₂ := ho.hom _ _
+  h₃ :=
+    if c.Rel i (c.next i)
+    then K.d _ _ ≫ ho.hom (c.next (c.next i)) _
+    else f.f _ - g.f _ - ho.hom _ i ≫ L.d _ _
+  h₀_f := by
+    split_ifs with h
+    · dsimp
+      simp only [assoc, d_comp_d, comp_zero]
+    · dsimp
+      rw [L.shape _ _ h, comp_zero]
+  g_h₃ := by
+    split_ifs with h
+    · dsimp
+      simp
+    · dsimp
+      rw [K.shape _ _ h, zero_comp]
+  comm₁ := by
+    dsimp
+    split_ifs with h
+    · rw [ho.comm (c.prev i)]
+      dsimp [dFrom, dTo, fromNext, toPrev]
+      rw [congr_arg (fun j => d K (c.prev i) j ≫ ho.hom j (c.prev i)) (c.next_eq' h)]
+    · abel
+  comm₂ := ho.comm i
+  comm₃ := by
+    dsimp
+    split_ifs with h
+    · rw [ho.comm (c.next i)]
+      dsimp [dFrom, dTo, fromNext, toPrev]
+      rw [congr_arg (fun j => ho.hom (c.next i) j ≫ L.d j (c.next i)) (c.prev_eq' h)]
+    · abel
+
+lemma Homotopy.homologyMap_eq (ho : Homotopy f g) (i : ι) [K.HasHomology i] [L.HasHomology i] :
+    homologyMap f i = homologyMap g i :=
+  ShortComplex.Homotopy.homologyMap_congr (ho.toShortComplex i)
+
+/-- The isomorphism in homology induced by an homotopy equivalence. -/
+noncomputable def HomotopyEquiv.toHomologyIso (h : HomotopyEquiv K L) (i : ι)
+    [K.HasHomology i] [L.HasHomology i] : K.homology i ≅ L.homology i where
+  hom := homologyMap h.hom i
+  inv := homologyMap h.inv i
+  hom_inv_id := by rw [← homologyMap_comp, h.homotopyHomInvId.homologyMap_eq, homologyMap_id]
+  inv_hom_id := by rw [← homologyMap_comp, h.homotopyInvHomId.homologyMap_eq, homologyMap_id]

618ea3d5

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -565,7 +565,7 @@ def mkInductive : Homotopy e 0 where
     · cases i
       · dsimp [fromNext, mkInductiveAux₂]
         rw [dif_neg]
-        simp only
+        decide
       · dsimp [fromNext]
         simp only [ChainComplex.next_nat_succ, dite_true]
         rw [mkInductiveAux₃ e zero comm_zero one comm_one succ]
@@ -704,7 +704,7 @@ def mkCoinductive : Homotopy e 0 where
     · cases i
       · dsimp [toPrev, mkCoinductiveAux₂]
         rw [dif_neg]
-        simp only
+        decide
       · dsimp [toPrev]
         simp only [CochainComplex.prev_nat_succ, dite_true]
         rw [mkCoinductiveAux₃ e zero comm_zero one comm_one succ]

618ea3d5

refactor: introduce the new homology API for homological complex and rename the old one (#7954)

This PR renames definitions of the current homology API (adding a ' to homology, cycles, QuasiIso) so as to create space for the development of the new homology API of homological complexes: this PR also contains the new definition of HomologicalComplex.homology which involves the homology theory of short complexes.

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

c5fe4511

Diff

@@ -781,34 +781,34 @@ variable [HasEqualizers V] [HasCokernels V] [HasImages V] [HasImageMaps V]
 
 /-- Homotopic maps induce the same map on homology.
 -/
-theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
-    (homologyFunctor V c i).map f = (homologyFunctor V c i).map g := by
-  dsimp [homologyFunctor]
+theorem homology'_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
+    (homology'Functor V c i).map f = (homology'Functor V c i).map g := by
+  dsimp [homology'Functor]
   apply eq_of_sub_eq_zero
   ext
-  simp only [homology.π_map, comp_zero, Preadditive.comp_sub]
+  simp only [homology'.π_map, comp_zero, Preadditive.comp_sub]
   dsimp [kernelSubobjectMap]
   simp_rw [h.comm i]
   simp only [zero_add, zero_comp, dNext_eq_dFrom_fromNext, kernelSubobject_arrow_comp_assoc,
     Preadditive.comp_add]
   rw [← Preadditive.sub_comp]
   simp only [CategoryTheory.Subobject.factorThru_add_sub_factorThru_right]
-  erw [Subobject.factorThru_ofLE (D.boundaries_le_cycles i)]
+  erw [Subobject.factorThru_ofLE (D.boundaries_le_cycles' i)]
   · simp
   · rw [prevD_eq_toPrev_dTo, ← Category.assoc]
     apply imageSubobject_factors_comp_self
-#align homology_map_eq_of_homotopy homology_map_eq_of_homotopy
+#align homology_map_eq_of_homotopy homology'_map_eq_of_homotopy
 
 /-- Homotopy equivalent complexes have isomorphic homologies. -/
 def homologyObjIsoOfHomotopyEquiv (f : HomotopyEquiv C D) (i : ι) :
-    (homologyFunctor V c i).obj C ≅ (homologyFunctor V c i).obj D where
-  hom := (homologyFunctor V c i).map f.hom
-  inv := (homologyFunctor V c i).map f.inv
+    (homology'Functor V c i).obj C ≅ (homology'Functor V c i).obj D where
+  hom := (homology'Functor V c i).map f.hom
+  inv := (homology'Functor V c i).map f.inv
   hom_inv_id := by
-    rw [← Functor.map_comp, homology_map_eq_of_homotopy f.homotopyHomInvId,
+    rw [← Functor.map_comp, homology'_map_eq_of_homotopy f.homotopyHomInvId,
       CategoryTheory.Functor.map_id]
   inv_hom_id := by
-    rw [← Functor.map_comp, homology_map_eq_of_homotopy f.homotopyInvHomId,
+    rw [← Functor.map_comp, homology'_map_eq_of_homotopy f.homotopyInvHomId,
       CategoryTheory.Functor.map_id]
 #align homology_obj_iso_of_homotopy_equiv homologyObjIsoOfHomotopyEquiv

618ea3d5

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -349,7 +349,6 @@ def nullHomotopy (hom : ∀ i j, C.X i ⟶ D.X j) (zero : ∀ i j, ¬c.Rel j i 
 def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.X i ⟶ D.X j)) : Homotopy (nullHomotopicMap' h) 0 := by
   apply nullHomotopy fun i j => dite (c.Rel j i) (h i j) fun _ => 0
   intro i j hij
-  dsimp
   rw [dite_eq_right_iff]
   intro hij'
   exfalso
@@ -375,7 +374,6 @@ theorem nullHomotopicMap'_f {k₂ k₁ k₀ : ι} (r₂₁ : c.Rel k₂ k₁) (r
     (nullHomotopicMap' h).f k₁ = C.d k₁ k₀ ≫ h k₀ k₁ r₁₀ + h k₁ k₂ r₂₁ ≫ D.d k₂ k₁ := by
   simp only [nullHomotopicMap']
   rw [nullHomotopicMap_f r₂₁ r₁₀]
-  dsimp
   split_ifs
   rfl
 #align homotopy.null_homotopic_map'_f Homotopy.nullHomotopicMap'_f
@@ -395,7 +393,6 @@ theorem nullHomotopicMap'_f_of_not_rel_left {k₁ k₀ : ι} (r₁₀ : c.Rel k
     (nullHomotopicMap' h).f k₀ = h k₀ k₁ r₁₀ ≫ D.d k₁ k₀ := by
   simp only [nullHomotopicMap']
   rw [nullHomotopicMap_f_of_not_rel_left r₁₀ hk₀]
-  dsimp
   split_ifs
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_left Homotopy.nullHomotopicMap'_f_of_not_rel_left
@@ -415,7 +412,6 @@ theorem nullHomotopicMap'_f_of_not_rel_right {k₁ k₀ : ι} (r₁₀ : c.Rel k
     (nullHomotopicMap' h).f k₁ = C.d k₁ k₀ ≫ h k₀ k₁ r₁₀ := by
   simp only [nullHomotopicMap']
   rw [nullHomotopicMap_f_of_not_rel_right r₁₀ hk₁]
-  dsimp
   split_ifs
   rfl
 #align homotopy.null_homotopic_map'_f_of_not_rel_right Homotopy.nullHomotopicMap'_f_of_not_rel_right

618ea3d5

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

@@ -23,7 +23,7 @@ noncomputable section
 
 open CategoryTheory CategoryTheory.Limits HomologicalComplex
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 variable {V : Type u} [Category.{v} V] [Preadditive V]
 
@@ -308,7 +308,7 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.X
 #align homotopy.comp_null_homotopic_map' Homotopy.comp_nullHomotopicMap'
 
 /-- Compatibility of `nullHomotopicMap` with the application of additive functors -/
-theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
+theorem map_nullHomotopicMap {W : Type*} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, C.X i ⟶ D.X j) :
     (G.mapHomologicalComplex c).map (nullHomotopicMap hom) =
       nullHomotopicMap (fun i j => by exact G.map (hom i j)) := by
@@ -318,7 +318,7 @@ theorem map_nullHomotopicMap {W : Type _} [Category W] [Preadditive W] (G : V 
 #align homotopy.map_null_homotopic_map Homotopy.map_nullHomotopicMap
 
 /-- Compatibility of `nullHomotopicMap'` with the application of additive functors -/
-theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
+theorem map_nullHomotopicMap' {W : Type*} [Category W] [Preadditive W] (G : V ⥤ W) [G.Additive]
     (hom : ∀ i j, c.Rel j i → (C.X i ⟶ D.X j)) :
     (G.mapHomologicalComplex c).map (nullHomotopicMap' hom) =
       nullHomotopicMap' fun i j hij => by exact G.map (hom i j hij) := by
@@ -774,7 +774,7 @@ def trans {C D E : HomologicalComplex V c} (f : HomotopyEquiv C D) (g : Homotopy
 #align homotopy_equiv.trans HomotopyEquiv.trans
 
 /-- An isomorphism of complexes induces a homotopy equivalence. -/
-def ofIso {ι : Type _} {V : Type u} [Category.{v} V] [Preadditive V] {c : ComplexShape ι}
+def ofIso {ι : Type*} {V : Type u} [Category.{v} V] [Preadditive V] {c : ComplexShape ι}
     {C D : HomologicalComplex V c} (f : C ≅ D) : HomotopyEquiv C D :=
   ⟨f.hom, f.inv, Homotopy.ofEq f.3, Homotopy.ofEq f.4⟩
 #align homotopy_equiv.of_iso HomotopyEquiv.ofIso
@@ -820,7 +820,7 @@ end
 
 namespace CategoryTheory
 
-variable {W : Type _} [Category W] [Preadditive W]
+variable {W : Type*} [Category W] [Preadditive W]
 
 /-- An additive functor takes homotopies to homotopies. -/
 @[simps]

618ea3d5

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.homology.homotopy
-! leanprover-community/mathlib commit 618ea3d5c99240cd7000d8376924906a148bf9ff
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Homology.Additive
 import Mathlib.Tactic.Abel
 
+#align_import algebra.homology.homotopy from "leanprover-community/mathlib"@"618ea3d5c99240cd7000d8376924906a148bf9ff"
+
 /-!
 # Chain homotopies

618ea3d5

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

@@ -518,7 +518,6 @@ section
 
 /-- An auxiliary construction for `mkInductive`.
 -/
-@[simp]
 def mkInductiveAux₂ :
     ∀ n, Σ' (f : P.xNext n ⟶ Q.X n) (f' : P.X n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
   | 0 => ⟨0, zero ≫ (Q.xPrevIso rfl).inv, by simpa using comm_zero⟩
@@ -528,6 +527,21 @@ def mkInductiveAux₂ :
     ⟨(P.xNextIso rfl).hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv, by simpa using I.2.2⟩
 #align homotopy.mk_inductive_aux₂ Homotopy.mkInductiveAux₂
 
+theorem mkInductiveAux₂_zero :
+    mkInductiveAux₂ e zero comm_zero one comm_one succ 0 =
+      ⟨0, zero ≫ (Q.xPrevIso rfl).inv, mkInductiveAux₂.proof_2 e zero comm_zero⟩ :=
+  rfl
+
+theorem mkInductiveAux₂_add_one (n) :
+    mkInductiveAux₂ e zero comm_zero one comm_one succ (n + 1) =
+      let I := mkInductiveAux₁ e zero one comm_one succ n
+      ⟨(P.xNextIso rfl).hom ≫ I.1, I.2.1 ≫ (Q.xPrevIso rfl).inv,
+        mkInductiveAux₂.proof_5 e zero one comm_one succ n⟩ :=
+  rfl
+
+attribute [eqns mkInductiveAux₂_zero mkInductiveAux₂_add_one] mkInductiveAux₂
+attribute [simp] mkInductiveAux₂
+
 theorem mkInductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).hom =
       (P.xNextIso h).inv ≫ (mkInductiveAux₂ e zero comm_zero one comm_one succ j).1 := by
@@ -643,7 +657,6 @@ section
 
 /-- An auxiliary construction for `mkInductive`.
 -/
-@[simp]
 def mkCoinductiveAux₂ :
     ∀ n, Σ' (f : P.X n ⟶ Q.xPrev n) (f' : P.xNext n ⟶ Q.X n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
   | 0 => ⟨0, (P.xNextIso rfl).hom ≫ zero, by simpa using comm_zero⟩
@@ -652,6 +665,21 @@ def mkCoinductiveAux₂ :
     ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).hom ≫ I.2.1, by simpa using I.2.2⟩
 #align homotopy.mk_coinductive_aux₂ Homotopy.mkCoinductiveAux₂
 
+theorem mkCoinductiveAux₂_zero :
+    mkCoinductiveAux₂ e zero comm_zero one comm_one succ 0 =
+      ⟨0, (P.xNextIso rfl).hom ≫ zero, mkCoinductiveAux₂.proof_2 e zero comm_zero⟩ :=
+  rfl
+
+theorem mkCoinductiveAux₂_add_one (n) :
+    mkCoinductiveAux₂ e zero comm_zero one comm_one succ (n + 1) =
+      let I := mkCoinductiveAux₁ e zero one comm_one succ n
+      ⟨I.1 ≫ (Q.xPrevIso rfl).inv, (P.xNextIso rfl).hom ≫ I.2.1,
+        mkCoinductiveAux₂.proof_5 e zero one comm_one succ n⟩ :=
+  rfl
+
+attribute [eqns mkCoinductiveAux₂_zero mkCoinductiveAux₂_add_one] mkCoinductiveAux₂
+attribute [simp] mkCoinductiveAux₂
+
 theorem mkCoinductiveAux₃ (i j : ℕ) (h : i + 1 = j) :
     (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.1 =
       (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).1 ≫ (Q.xPrevIso h).hom := by

618ea3d5

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

@@ -203,7 +203,7 @@ def add {f₁ g₁ f₂ g₂ : C ⟶ D} (h₁ : Homotopy f₁ g₁) (h₂ : Homo
 @[simps]
 def compRight {e f : C ⟶ D} (h : Homotopy e f) (g : D ⟶ E) : Homotopy (e ≫ g) (f ≫ g) where
   hom i j := h.hom i j ≫ g.f j
-  zero i j w := by dsimp ; rw [h.zero i j w, zero_comp]
+  zero i j w := by dsimp; rw [h.zero i j w, zero_comp]
   comm i := by rw [comp_f, h.comm i, dNext_comp_right, prevD_comp_right, Preadditive.add_comp,
     comp_f, Preadditive.add_comp]
 #align homotopy.comp_right Homotopy.compRight
@@ -212,7 +212,7 @@ def compRight {e f : C ⟶ D} (h : Homotopy e f) (g : D ⟶ E) : Homotopy (e ≫
 @[simps]
 def compLeft {f g : D ⟶ E} (h : Homotopy f g) (e : C ⟶ D) : Homotopy (e ≫ f) (e ≫ g) where
   hom i j := e.f i ≫ h.hom i j
-  zero i j w := by dsimp ; rw [h.zero i j w, comp_zero]
+  zero i j w := by dsimp; rw [h.zero i j w, comp_zero]
   comm i := by rw [comp_f, h.comm i, dNext_comp_left, prevD_comp_left, comp_f,
     Preadditive.comp_add, Preadditive.comp_add]
 #align homotopy.comp_left Homotopy.compLeft
@@ -549,7 +549,7 @@ def mkInductive : Homotopy e 0 where
     if h : i + 1 = j then
       (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.1 ≫ (Q.xPrevIso h).hom
     else 0
-  zero i j w := by dsimp ; rw [dif_neg] ; exact w
+  zero i j w := by dsimp; rw [dif_neg]; exact w
   comm i := by
     dsimp
     simp only [add_zero]
@@ -673,7 +673,7 @@ def mkCoinductive : Homotopy e 0 where
     if h : j + 1 = i then
       (P.xNextIso h).inv ≫ (mkCoinductiveAux₂ e zero comm_zero one comm_one succ j).2.1
     else 0
-  zero i j w := by dsimp ; rw [dif_neg] ; exact w
+  zero i j w := by dsimp; rw [dif_neg]; exact w
   comm i := by
     dsimp
     simp only [add_zero]
@@ -802,7 +802,7 @@ variable {W : Type _} [Category W] [Preadditive W]
 def Functor.mapHomotopy (F : V ⥤ W) [F.Additive] {f g : C ⟶ D} (h : Homotopy f g) :
     Homotopy ((F.mapHomologicalComplex c).map f) ((F.mapHomologicalComplex c).map g) where
   hom i j := F.map (h.hom i j)
-  zero i j w := by dsimp ; rw [h.zero i j w, F.map_zero]
+  zero i j w := by dsimp; rw [h.zero i j w, F.map_zero]
   comm i := by
     have H := h.comm i
     dsimp [dNext, prevD] at H ⊢

618ea3d5

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

@@ -122,7 +122,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.X i ⟶
   cases i
   · simp only [shape, CochainComplex.prev_nat_zero, ComplexShape.up_Rel, Nat.one_ne_zero,
       not_false_iff, comp_zero]
-  . congr <;> simp
+  · congr <;> simp
 #align prev_d_nat prevD_nat
 
 -- porting note: removed @[has_nonempty_instance]
@@ -555,16 +555,16 @@ def mkInductive : Homotopy e 0 where
     simp only [add_zero]
     refine' (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.2.trans _
     congr
-    . cases i
-      . dsimp [fromNext, mkInductiveAux₂]
+    · cases i
+      · dsimp [fromNext, mkInductiveAux₂]
         rw [dif_neg]
         simp only
-      . dsimp [fromNext]
+      · dsimp [fromNext]
         simp only [ChainComplex.next_nat_succ, dite_true]
         rw [mkInductiveAux₃ e zero comm_zero one comm_one succ]
         dsimp [xNextIso]
         rw [Category.id_comp]
-    . dsimp [toPrev]
+    · dsimp [toPrev]
       erw [dif_pos, Category.comp_id]
       simp only [ChainComplex.prev]
 #align homotopy.mk_inductive Homotopy.mkInductive
@@ -680,16 +680,16 @@ def mkCoinductive : Homotopy e 0 where
     rw [add_comm]
     refine' (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.2.trans _
     congr
-    . cases i
-      . dsimp [toPrev, mkCoinductiveAux₂]
+    · cases i
+      · dsimp [toPrev, mkCoinductiveAux₂]
         rw [dif_neg]
         simp only
-      . dsimp [toPrev]
+      · dsimp [toPrev]
         simp only [CochainComplex.prev_nat_succ, dite_true]
         rw [mkCoinductiveAux₃ e zero comm_zero one comm_one succ]
         dsimp [xPrevIso]
         rw [Category.comp_id]
-    . dsimp [fromNext]
+    · dsimp [fromNext]
       erw [dif_pos, Category.id_comp]
       simp only [CochainComplex.next]
 #align homotopy.mk_coinductive Homotopy.mkCoinductive

618ea3d5

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -282,7 +282,7 @@ theorem nullHomotopicMap'_comp (hom : ∀ i j, c.Rel j i → (C.X i ⟶ D.X j))
   ext n
   erw [nullHomotopicMap_comp]
   congr
-  ext (i j)
+  ext i j
   split_ifs
   · rfl
   · rw [zero_comp]
@@ -304,7 +304,7 @@ theorem comp_nullHomotopicMap' (f : C ⟶ D) (hom : ∀ i j, c.Rel j i → (D.X
   ext n
   erw [comp_nullHomotopicMap]
   congr
-  ext (i j)
+  ext i j
   split_ifs
   · rfl
   · rw [comp_zero]
@@ -328,7 +328,7 @@ theorem map_nullHomotopicMap' {W : Type _} [Category W] [Preadditive W] (G : V 
   ext n
   erw [map_nullHomotopicMap]
   congr
-  ext (i j)
+  ext i j
   split_ifs
   · rfl
   · rw [G.map_zero]

618ea3d5

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -486,9 +486,9 @@ variable (e : P ⟶ Q) (zero : P.X 0 ⟶ Q.X 1) (comm_zero : e.f 0 = zero ≫ Q.
   (succ :
     ∀ (n : ℕ)
       (p :
-        Σ'(f : P.X n ⟶ Q.X (n + 1))(f' : P.X (n + 1) ⟶ Q.X (n + 2)),
+        Σ' (f : P.X n ⟶ Q.X (n + 1)) (f' : P.X (n + 1) ⟶ Q.X (n + 2)),
           e.f (n + 1) = P.d (n + 1) n ≫ f + f' ≫ Q.d (n + 2) (n + 1)),
-      Σ'f'' : P.X (n + 2) ⟶ Q.X (n + 3),
+      Σ' f'' : P.X (n + 2) ⟶ Q.X (n + 3),
         e.f (n + 2) = P.d (n + 2) (n + 1) ≫ p.2.1 + f'' ≫ Q.d (n + 3) (n + 2))
 
 /-- An auxiliary construction for `mkInductive`.
@@ -505,7 +505,7 @@ which we do in `mkInductiveAux₂`.
 @[simp, nolint unusedArguments]
 def mkInductiveAux₁ :
     ∀ n,
-      Σ'(f : P.X n ⟶ Q.X (n + 1))(f' : P.X (n + 1) ⟶ Q.X (n + 2)),
+      Σ' (f : P.X n ⟶ Q.X (n + 1)) (f' : P.X (n + 1) ⟶ Q.X (n + 2)),
         e.f (n + 1) = P.d (n + 1) n ≫ f + f' ≫ Q.d (n + 2) (n + 1)
   | 0 => ⟨zero, one, comm_one⟩
   | 1 => ⟨one, (succ 0 ⟨zero, one, comm_one⟩).1, (succ 0 ⟨zero, one, comm_one⟩).2⟩
@@ -520,7 +520,7 @@ section
 -/
 @[simp]
 def mkInductiveAux₂ :
-    ∀ n, Σ'(f : P.xNext n ⟶ Q.X n)(f' : P.X n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
+    ∀ n, Σ' (f : P.xNext n ⟶ Q.X n) (f' : P.X n ⟶ Q.xPrev n), e.f n = P.dFrom n ≫ f + f' ≫ Q.dTo n
   | 0 => ⟨0, zero ≫ (Q.xPrevIso rfl).inv, by simpa using comm_zero⟩
   | n + 1 =>
     let I := mkInductiveAux₁ e zero --comm_zero
@@ -611,9 +611,9 @@ variable (e : P ⟶ Q) (zero : P.X 1 ⟶ Q.X 0) (comm_zero : e.f 0 = P.d 0 1 ≫
   (succ :
     ∀ (n : ℕ)
       (p :
-        Σ'(f : P.X (n + 1) ⟶ Q.X n)(f' : P.X (n + 2) ⟶ Q.X (n + 1)),
+        Σ' (f : P.X (n + 1) ⟶ Q.X n) (f' : P.X (n + 2) ⟶ Q.X (n + 1)),
           e.f (n + 1) = f ≫ Q.d n (n + 1) + P.d (n + 1) (n + 2) ≫ f'),
-      Σ'f'' : P.X (n + 3) ⟶ Q.X (n + 2),
+      Σ' f'' : P.X (n + 3) ⟶ Q.X (n + 2),
         e.f (n + 2) = p.2.1 ≫ Q.d (n + 1) (n + 2) + P.d (n + 2) (n + 3) ≫ f'')
 
 /-- An auxiliary construction for `mkCoinductive`.
@@ -630,7 +630,7 @@ which we do in `mkInductiveAux₂`.
 @[simp]
 def mkCoinductiveAux₁ :
     ∀ n,
-      Σ'(f : P.X (n + 1) ⟶ Q.X n)(f' : P.X (n + 2) ⟶ Q.X (n + 1)),
+      Σ' (f : P.X (n + 1) ⟶ Q.X n) (f' : P.X (n + 2) ⟶ Q.X (n + 1)),
         e.f (n + 1) = f ≫ Q.d n (n + 1) + P.d (n + 1) (n + 2) ≫ f'
   | 0 => ⟨zero, one, comm_one⟩
   | 1 => ⟨one, (succ 0 ⟨zero, one, comm_one⟩).1, (succ 0 ⟨zero, one, comm_one⟩).2⟩
@@ -645,7 +645,7 @@ section
 -/
 @[simp]
 def mkCoinductiveAux₂ :
-    ∀ n, Σ'(f : P.X n ⟶ Q.xPrev n)(f' : P.xNext n ⟶ Q.X n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
+    ∀ n, Σ' (f : P.X n ⟶ Q.xPrev n) (f' : P.xNext n ⟶ Q.X n), e.f n = f ≫ Q.dTo n + P.dFrom n ≫ f'
   | 0 => ⟨0, (P.xNextIso rfl).hom ≫ zero, by simpa using comm_zero⟩
   | n + 1 =>
     let I := mkCoinductiveAux₁ e zero one comm_one succ n

618ea3d5

chore: fix upper/lowercase in comments (#4360)

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

27d257fc

Diff

@@ -444,7 +444,7 @@ theorem nullHomotopicMap'_f_eq_zero {k₀ : ι} (hk₀ : ∀ l : ι, ¬c.Rel k
 so that as we construct each component, we have available the previous two components,
 and the fact that they satisfy the homotopy condition.
 
-To simplify the situation, we only construct homotopies of the form `homotopy e 0`.
+To simplify the situation, we only construct homotopies of the form `Homotopy e 0`.
 `Homotopy.equivSubZero` can provide the general case.
 
 Notice however, that this construction does not have particularly good definitional properties:

618ea3d5

chore: tidy various files (#3848)

66cb7cc4

Diff

@@ -772,7 +772,7 @@ theorem homology_map_eq_of_homotopy (h : Homotopy f g) (i : ι) :
     Preadditive.comp_add]
   rw [← Preadditive.sub_comp]
   simp only [CategoryTheory.Subobject.factorThru_add_sub_factorThru_right]
-  erw [Subobject.factorThru_ofLe (D.boundaries_le_cycles i)]
+  erw [Subobject.factorThru_ofLE (D.boundaries_le_cycles i)]
   · simp
   · rw [prevD_eq_toPrev_dTo, ← Category.assoc]
     apply imageSubobject_factors_comp_self

618ea3d5

chore: bye-bye, solo bys! (#3825)

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

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

14167e48

Diff

@@ -349,8 +349,7 @@ def nullHomotopy (hom : ∀ i j, C.X i ⟶ D.X j) (zero : ∀ i j, ¬c.Rel j i 
 
 /-- Homotopy to zero for maps constructed with `nullHomotopicMap'` -/
 @[simps!]
-def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.X i ⟶ D.X j)) : Homotopy (nullHomotopicMap' h) 0 :=
-  by
+def nullHomotopy' (h : ∀ i j, c.Rel j i → (C.X i ⟶ D.X j)) : Homotopy (nullHomotopicMap' h) 0 := by
   apply nullHomotopy fun i j => dite (c.Rel j i) (h i j) fun _ => 0
   intro i j hij
   dsimp

618ea3d5

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -206,7 +206,6 @@ def compRight {e f : C ⟶ D} (h : Homotopy e f) (g : D ⟶ E) : Homotopy (e ≫
   zero i j w := by dsimp ; rw [h.zero i j w, zero_comp]
   comm i := by rw [comp_f, h.comm i, dNext_comp_right, prevD_comp_right, Preadditive.add_comp,
     comp_f, Preadditive.add_comp]
-
 #align homotopy.comp_right Homotopy.compRight
 
 /-- homotopy is closed under composition (on the left) -/

618ea3d5

feat: port Algebra.Homology.Homotopy (#3524)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

4f99e001

`algebra.homology.homotopy` ⟷ `Mathlib.Algebra.Homology.Homotopy`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 3 + 325

algebra.homology.homotopy ⟷ Mathlib.Algebra.Homology.Homotopy

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 3 + 325

`algebra.homology.homotopy` ⟷ `Mathlib.Algebra.Homology.Homotopy`