Theorem: AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality
File: Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean

tactic: unfold mapMono
state_before: C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
⊢ mapMono K i ≫ f.f Δ.len = f.f Δ'.len ≫ mapMono K' i
state_after: C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
⊢ (if h : Δ' = Δ then eqToHom ⋯ else if h : Isδ₀ i then K.d Δ'.len Δ.len else 0) ≫ f.f Δ.len =
    f.f Δ'.len ≫ if h : Δ' = Δ then eqToHom ⋯ else if h : Isδ₀ i then K'.d Δ'.len Δ.len else 0

tactic: split_ifs with h
state_before: C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
⊢ (if h : Δ' = Δ then eqToHom ⋯ else if h : Isδ₀ i then K.d Δ'.len Δ.len else 0) ≫ f.f Δ.len =
    f.f Δ'.len ≫ if h : Δ' = Δ then eqToHom ⋯ else if h : Isδ₀ i then K'.d Δ'.len Δ.len else 0
state_after: case pos
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
h : Δ' = Δ
⊢ eqToHom ⋯ ≫ f.f Δ.len = f.f Δ'.len ≫ eqToHom ⋯

case pos
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
h : ¬Δ' = Δ
h✝ : Isδ₀ i
⊢ K.d Δ'.len Δ.len ≫ f.f Δ.len = f.f Δ'.len ≫ K'.d Δ'.len Δ.len

case neg
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
h : ¬Δ' = Δ
h✝ : ¬Isδ₀ i
⊢ 0 ≫ f.f Δ.len = f.f Δ'.len ≫ 0

tactic: subst h
state_before: case pos
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
h : Δ' = Δ
⊢ eqToHom ⋯ ≫ f.f Δ.len = f.f Δ'.len ≫ eqToHom ⋯
state_after: case pos
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ' Δ'' : SimplexCategory
i : Δ' ⟶ Δ'
inst✝ : Mono i
⊢ eqToHom ⋯ ≫ f.f Δ'.len = f.f Δ'.len ≫ eqToHom ⋯

tactic: simp only [id_comp, eqToHom_refl, comp_id]
state_before: case pos
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ' Δ'' : SimplexCategory
i : Δ' ⟶ Δ'
inst✝ : Mono i
⊢ eqToHom ⋯ ≫ f.f Δ'.len = f.f Δ'.len ≫ eqToHom ⋯
state_after: no goals

tactic: rw [HomologicalComplex.Hom.comm]
state_before: case pos
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
h : ¬Δ' = Δ
h✝ : Isδ₀ i
⊢ K.d Δ'.len Δ.len ≫ f.f Δ.len = f.f Δ'.len ≫ K'.d Δ'.len Δ.len
state_after: no goals

tactic: rw [zero_comp, comp_zero]
state_before: case neg
C : Type u_1
inst✝² : Category.{u_2, u_1} C
inst✝¹ : Preadditive C
K K' : ChainComplex C ℕ
f : K ⟶ K'
Δ Δ' Δ'' : SimplexCategory
i : Δ ⟶ Δ'
inst✝ : Mono i
h : ¬Δ' = Δ
h✝ : ¬Isδ₀ i
⊢ 0 ≫ f.f Δ.len = f.f Δ'.len ≫ 0
state_after: no goals