Theorem: CategoryTheory.Limits.inl_inl_pushoutAssoc_hom
File: Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean

tactic: trans f₁ ≫ l₁
state_before: C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ pushout.inl ≫ (pushoutAssoc g₁ g₂ g₃ g₄).hom = pushout.inl
state_after: C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ pushout.inl ≫ (pushoutAssoc g₁ g₂ g₃ g₄).hom =
    pushout.inl ≫ pushout.desc pushout.inl (pushout.inl ≫ pushout.inr) ⋯

C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ pushout.desc pushout.inl (pushout.inl ≫ pushout.inr) ⋯ = pushout.inl

tactic: congr 1
state_before: C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ pushout.inl ≫ (pushoutAssoc g₁ g₂ g₃ g₄).hom =
    pushout.inl ≫ pushout.desc pushout.inl (pushout.inl ≫ pushout.inr) ⋯
state_after: case e_a
C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ (pushoutAssoc g₁ g₂ g₃ g₄).hom = pushout.desc pushout.inl (pushout.inl ≫ pushout.inr) ⋯

tactic: exact
  (pushoutPushoutLeftIsPushout g₁ g₂ g₃ g₄).comp_coconePointUniqueUpToIso_hom _
    WalkingCospan.left
state_before: case e_a
C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ (pushoutAssoc g₁ g₂ g₃ g₄).hom = pushout.desc pushout.inl (pushout.inl ≫ pushout.inr) ⋯
state_after: no goals

tactic: exact pushout.inl_desc _ _ _
state_before: C : Type u
inst✝⁵ : Category.{v, u} C
D : Type u₂
inst✝⁴ : Category.{v₂, u₂} D
W X Y Z X₁ X₂ X₃ Z₁ Z₂ : C
g₁ : Z₁ ⟶ X₁
g₂ : Z₁ ⟶ X₂
g₃ : Z₂ ⟶ X₂
g₄ : Z₂ ⟶ X₃
inst✝³ : HasPushout g₁ g₂
inst✝² : HasPushout g₃ g₄
inst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄
inst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)
⊢ pushout.inl ≫ pushout.desc pushout.inl (pushout.inl ≫ pushout.inr) ⋯ = pushout.inl
state_after: no goals