case h
C : Type u₁
inst✝² : Category C
X Y Z : C
D : Type u₂
inst✝¹ : Category D
inst✝ : HasPullbacks C
f : X ⟶ Y
g : Y ⟶ Z
t : MonoOver Z
⊢ (pullback (f ≫ g)).obj (Quotient.mk'' t) = (pullback f).obj ((pullback g).obj (Quotient.mk'' t))
C : Type u₁
inst✝² : Category C
X Y Z : C
D : Type u₂
inst✝¹ : Category D
inst✝ : HasPullbacks C
f : X ⟶ Y
g : Y ⟶ Z
x : Subobject Z
⊢ (pullback (f ≫ g)).obj x = (pullback f).obj ((pullback g).obj x)
induction' x using Quotient.inductionOn' with t
no goals
case h
C : Type u₁
inst✝² : Category C
X Y Z : C
D : Type u₂
inst✝¹ : Category D
inst✝ : HasPullbacks C
f : X ⟶ Y
g : Y ⟶ Z
t : MonoOver Z
⊢ (pullback (f ≫ g)).obj (Quotient.mk'' t) = (pullback f).obj ((pullback g).obj (Quotient.mk'' t))
exact Quotient.sound ⟨(MonoOver.pullbackComp _ _).app t⟩