awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
A : C
hlp : Eq.{v + 1} (α := A ⟶ A) (CategoryStruct.comp (Y := Limits.prod.{v, u} A A) (prod.lift (𝟙 A) 0) prod.snd) 0
hp1 : IsLimit (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp) :=
  Fork.IsLimit.mk (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp)
    (fun (s : Fork.{v, u} (C := C) (X := Limits.prod.{v, u} A A) prod.snd 0) ↦ s.ι ≫ prod.fst) ⋯ ⋯
hp2 : IsColimit (CokernelCofork.ofπ prod.snd hlp) := epiIsCokernelOfKernel (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp) hp1
Z : C
z : cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A) ⟶ Z
hz : r A ≫ z = 0
h : prod.lift (𝟙 A) 0 ≫ cokernel.π (diag A) ≫ z = 0
t : (CokernelCofork.ofπ prod.snd hlp).pt ⟶ Z
ht : prod.snd ≫ t = cokernel.π (diag A) ≫ z
htt : t = 0
hf :
  Eq (α := Limits.prod.{v, u} A A ⟶ Z) (prod.snd ≫ t)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
⊢ cokernel.π (diag A) ≫ z =
    CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0
have hf₁ : Eq.{v + 1} (α := Limits.prod.{v, u} A A ⟶ Z) (prod.snd ≫ 0)
  (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
Tactic: rw [← ht, htt, comp_zero, comp_zero]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
A : C
hlp : Eq.{v + 1} (α := A ⟶ A) (CategoryStruct.comp (Y := Limits.prod.{v, u} A A) (prod.lift (𝟙 A) 0) prod.snd) 0
hp1 : IsLimit (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp) :=
  Fork.IsLimit.mk (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp)
    (fun (s : Fork.{v, u} (C := C) (X := Limits.prod.{v, u} A A) prod.snd 0) ↦ s.ι ≫ prod.fst) ⋯ ⋯
hp2 : IsColimit (CokernelCofork.ofπ prod.snd hlp) := epiIsCokernelOfKernel (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp) hp1
Z : C
z : cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A) ⟶ Z
hz : r A ≫ z = 0
h : prod.lift (𝟙 A) 0 ≫ cokernel.π (diag A) ≫ z = 0
t : (CokernelCofork.ofπ prod.snd hlp).pt ⟶ Z
ht : prod.snd ≫ t = cokernel.π (diag A) ≫ z
htt : t = 0
hf :
  Eq (α := Limits.prod.{v, u} A A ⟶ Z) (prod.snd ≫ t)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
hf₁ :
  Eq.{v + 1} (α := Limits.prod.{v, u} A A ⟶ Z) (prod.snd ≫ 0)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
⊢ cokernel.π (diag A) ≫ z =
    CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0
have hf₂ : Eq.{v + 1} (α := Limits.prod.{v, u} A A ⟶ Z) 0
  (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
Tactic: rw [← ht, htt, comp_zero, comp_zero]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
A : C
hlp : Eq.{v + 1} (α := A ⟶ A) (CategoryStruct.comp (Y := Limits.prod.{v, u} A A) (prod.lift (𝟙 A) 0) prod.snd) 0
hp1 : IsLimit (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp) :=
  Fork.IsLimit.mk (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp)
    (fun (s : Fork.{v, u} (C := C) (X := Limits.prod.{v, u} A A) prod.snd 0) ↦ s.ι ≫ prod.fst) ⋯ ⋯
hp2 : IsColimit (CokernelCofork.ofπ prod.snd hlp) := epiIsCokernelOfKernel (KernelFork.ofι (prod.lift (𝟙 A) 0) hlp) hp1
Z : C
z : cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A) ⟶ Z
hz : r A ≫ z = 0
h : prod.lift (𝟙 A) 0 ≫ cokernel.π (diag A) ≫ z = 0
t : (CokernelCofork.ofπ prod.snd hlp).pt ⟶ Z
ht : prod.snd ≫ t = cokernel.π (diag A) ≫ z
htt : t = 0
hf :
  Eq (α := Limits.prod.{v, u} A A ⟶ Z) (prod.snd ≫ t)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
hf₁ :
  Eq.{v + 1} (α := Limits.prod.{v, u} A A ⟶ Z) (prod.snd ≫ 0)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
hf₂ :
  Eq.{v + 1} (α := Limits.prod.{v, u} A A ⟶ Z) 0
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0)
⊢ cokernel.π (diag A) ≫ z =
    CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} A A) (diag A)) (cokernel.π (diag A)) 0
have hf₃ : Eq.{v + 1} (α := Limits.prod.{v, u} A A ⟶ Z) 0 0
Tactic: rw [← ht, htt, comp_zero, comp_zero]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X : C
⊢ Eq.{v + 1} (α := X ⟶ X)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (diag X : X ⟶ Limits.prod.{v, u} X X)
      (σ : Limits.prod.{v, u} X X ⟶ X))
    0
have rw : Eq.{v + 1} (α := X ⟶ X)
  (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) 0 (inv (r X))) 0
Tactic: rw [cokernel.condition_assoc, zero_comp]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X : C
rw :
  Eq.{v + 1} (α := X ⟶ X)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) 0 (inv (r X))) 0
⊢ Eq.{v + 1} (α := X ⟶ X)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (diag X : X ⟶ Limits.prod.{v, u} X X)
      (σ : Limits.prod.{v, u} X X ⟶ X))
    0
have rw₁ : Eq.{v + 1} (α := X ⟶ X) 0 0
Tactic: rw [cokernel.condition_assoc, zero_comp]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X : C
⊢ Eq.{v + 1} (α := X ⟶ X)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ : Limits.prod.{v, u} X X ⟶ X))
    (𝟙 X)
have rw : Eq.{v + 1} (α := X ⟶ X)
  (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X))
    (prod.lift (𝟙 X) 0 ≫ cokernel.π (diag X)) (inv (r X)))
  (𝟙 X)
Tactic: rw [← Category.assoc, IsIso.hom_inv_id]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X : C
rw :
  Eq.{v + 1} (α := X ⟶ X)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X))
      (prod.lift (𝟙 X) 0 ≫ cokernel.π (diag X)) (inv (r X)))
    (𝟙 X)
⊢ Eq.{v + 1} (α := X ⟶ X)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ : Limits.prod.{v, u} X X ⟶ X))
    (𝟙 X)
have rw₁ : Eq.{v + 1} (α := X ⟶ X) (𝟙 X) (𝟙 X)
Tactic: rw [← Category.assoc, IsIso.hom_inv_id]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X : C
⊢ Eq.{v + 1} (α := Limits.prod.{v, u} X X ⟶ X)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) (cokernel.π (diag X))
        (Iso.hom (Iso.symm (asIso (r X)))) :
      Limits.prod.{v, u} X X ⟶ X)
    (σ : Limits.prod.{v, u} X X ⟶ X)
have rw : Eq.{v + 1} (α := Limits.prod.{v, u} X X ⟶ X)
  (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) (cokernel.π (diag X))
      (Iso.inv (asIso (r X))) :
    Limits.prod.{v, u} X X ⟶ X)
  (σ : Limits.prod.{v, u} X X ⟶ X)
Tactic: rw [Iso.symm_hom, asIso_inv]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X : C
rw :
  Eq.{v + 1} (α := Limits.prod.{v, u} X X ⟶ X)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) (cokernel.π (diag X))
        (Iso.inv (asIso (r X))) :
      Limits.prod.{v, u} X X ⟶ X)
    (σ : Limits.prod.{v, u} X X ⟶ X)
⊢ Eq.{v + 1} (α := Limits.prod.{v, u} X X ⟶ X)
    (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) (cokernel.π (diag X))
        (Iso.hom (Iso.symm (asIso (r X)))) :
      Limits.prod.{v, u} X X ⟶ X)
    (σ : Limits.prod.{v, u} X X ⟶ X)
have rw₁ : Eq.{v + 1} (α := Limits.prod.{v, u} X X ⟶ X)
  (CategoryStruct.comp (Y := cokernel.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) (cokernel.π (diag X)) (inv (r X)) :
    Limits.prod.{v, u} X X ⟶ X)
  (σ : Limits.prod.{v, u} X X ⟶ X)
Tactic: rw [Iso.symm_hom, asIso_inv]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
⊢ CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (diag X)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
        (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y)) =
    0
have rw : f ≫
    CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (diag Y : Y ⟶ Limits.prod.{v, u} Y Y)
      (σ : Limits.prod.{v, u} Y Y ⟶ Y) =
  0
Tactic: rw [prod.diag_map_assoc, diag_σ, comp_zero]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
rw :
  f ≫
      CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (diag Y : Y ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) =
    0
⊢ CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (diag X)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
        (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y)) =
    0
have rw₁ : Eq (α := X ⟶ Y) (f ≫ 0) 0
Tactic: rw [prod.diag_map_assoc, diag_σ, comp_zero]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
rw :
  f ≫
      CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (diag Y : Y ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) =
    0
rw₁ : Eq (α := X ⟶ Y) (f ≫ 0) 0
⊢ CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (diag X)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
        (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y)) =
    0
have rw₂ : Eq.{v + 1} (α := X ⟶ Y) 0 0
Tactic: rw [prod.diag_map_assoc, diag_σ, comp_zero]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
⊢ Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
have obtain : ∀
  (g :
    Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
        (CokernelCofork.ofπ σ sorry : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
      Y)
  (hg :
    Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ sorry) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
          (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
        Limits.prod.{v, u} X X ⟶ Y)),
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
Tactic: obtain ⟨g, hg⟩ :=
    CokernelCofork.IsColimit.desc' isColimitσ (Limits.prod.map f f ≫ σ) (by
      rw [prod.diag_map_assoc, diag_σ, comp_zero])
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
hfg : f = g
⊢ Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
have rw : Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
  (Cofork.π (CokernelCofork.ofπ σ sorry) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
Tactic: rw [← hg, Cofork.π_ofπ, hfg]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
hfg : f = g
rw :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
⊢ Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
have rw₁ : Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y) (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
Tactic: rw [← hg, Cofork.π_ofπ, hfg]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
hfg : f = g
rw :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
rw₁ : Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y) (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
⊢ Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
have rw₂ : Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y) (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
Tactic: rw [← hg, Cofork.π_ofπ, hfg]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
⊢ Eq (α := Limits.prod.{v, u} X X ⟶ Y) (σ ≫ f : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
have suffices : f = g
Tactic: suffices hfg : f = g by rw [← hg, Cofork.π_ofπ, hfg]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
⊢ f =
    f ≫
      CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.lift (𝟙 Y) 0 : Y ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y)
have rw : f = f ≫ 𝟙 Y
Tactic: rw [lift_σ, Category.comp_id]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
rw : f = f ≫ 𝟙 Y
⊢ f =
    f ≫
      CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.lift (𝟙 Y) 0 : Y ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y)
have rw₁ : f = f
Tactic: rw [lift_σ, Category.comp_id]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
⊢ f ≫
      CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.lift (𝟙 Y) 0 : Y ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) =
    CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
        (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y))
have rw : f ≫
    CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.lift (𝟙 Y) 0 : Y ⟶ Limits.prod.{v, u} Y Y)
      (σ : Limits.prod.{v, u} Y Y ⟶ Y) =
  f ≫
    CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.lift (𝟙 Y) 0 : Y ⟶ Limits.prod.{v, u} Y Y)
      (σ : Limits.prod.{v, u} Y Y ⟶ Y)
Tactic: rw [lift_map_assoc]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
⊢ CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
        (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y)) =
    CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
have rw : CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
    (Cofork.π (CokernelCofork.ofπ σ sorry) ≫ g : Limits.prod.{v, u} X X ⟶ Y) =
  CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
    (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
Tactic: rw [← hg, CokernelCofork.π_ofπ]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
rw :
  CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y) =
    CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
⊢ CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0)
      (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y)
        (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y) (σ : Limits.prod.{v, u} Y Y ⟶ Y)) =
    CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
have rw₁ : CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
    (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y) =
  CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
    (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y)
Tactic: rw [← hg, CokernelCofork.π_ofπ]
-- Lean 4 proof step from Mathlib.CategoryTheory.Abelian.NonPreadditive (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : NonPreadditiveAbelian.{v, u} C
X Y : C
f : X ⟶ Y
g :
  Cocone.pt.{0, v, 0, u} (F := parallelPair (Y := Limits.prod.{v, u} X X) (diag X) 0)
      (CokernelCofork.ofπ σ ⋯ : CokernelCofork.{v, u} (Y := Limits.prod.{v, u} X X) (diag X)) ⟶
    Y
hg :
  Eq (α := Limits.prod.{v, u} X X ⟶ Y) (Cofork.π (CokernelCofork.ofπ σ ⋯) ≫ g : Limits.prod.{v, u} X X ⟶ Y)
    (CategoryStruct.comp (Y := Limits.prod.{v, u} Y Y) (prod.map f f : Limits.prod.{v, u} X X ⟶ Limits.prod.{v, u} Y Y)
        (σ : Limits.prod.{v, u} Y Y ⟶ Y) :
      Limits.prod.{v, u} X X ⟶ Y)
⊢ CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ ≫ g : Limits.prod.{v, u} X X ⟶ Y) =
    g
have rw : CategoryStruct.comp (Y := Limits.prod.{v, u} X X) (prod.lift (𝟙 X) 0 : X ⟶ Limits.prod.{v, u} X X)
      (σ : Limits.prod.{v, u} X X ⟶ X) ≫
    g =
  g
Tactic: rw [← Category.assoc, lift_σ, Category.id_comp]