C : Type u₁
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
S : C ⥤ D
T : D
A : CostructuredArrow S T
P Q : (CostructuredArrow S T)ᵒᵖ
f : P ⟶ A.op
g : Q ⟶ A.op
inst✝¹ : Mono f.unop.left.op
inst✝ : Mono g.unop.left.op
h : Subobject.mk f.unop.left.op ≤ Subobject.mk g.unop.left.op
⊢ g.unop.left.op.unop ≫ (Subobject.ofMkLEMk f.unop.left.op g.unop.left.op h).unop = f.unop.left
C : Type u₁
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
S : C ⥤ D
T : D
A : CostructuredArrow S T
P Q : (CostructuredArrow S T)ᵒᵖ
f : P ⟶ A.op
g : Q ⟶ A.op
inst✝¹ : Mono f.unop.left.op
inst✝ : Mono g.unop.left.op
h : Subobject.mk f.unop.left.op ≤ Subobject.mk g.unop.left.op
⊢ g.unop.left ≫ (Subobject.ofMkLEMk f.unop.left.op g.unop.left.op h).unop = f.unop.left
conv_lhs =>
  congr
  rw [← Quiver.Hom.unop_op g.unop.left]
C : Type u₁
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
S : C ⥤ D
T : D
A : CostructuredArrow S T
P Q : (CostructuredArrow S T)ᵒᵖ
f : P ⟶ A.op
g : Q ⟶ A.op
inst✝¹ : Mono f.unop.left.op
inst✝ : Mono g.unop.left.op
h : Subobject.mk f.unop.left.op ≤ Subobject.mk g.unop.left.op
⊢ (Subobject.ofMkLEMk f.unop.left.op g.unop.left.op h ≫ g.unop.left.op).unop = f.unop.left
C : Type u₁
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
S : C ⥤ D
T : D
A : CostructuredArrow S T
P Q : (CostructuredArrow S T)ᵒᵖ
f : P ⟶ A.op
g : Q ⟶ A.op
inst✝¹ : Mono f.unop.left.op
inst✝ : Mono g.unop.left.op
h : Subobject.mk f.unop.left.op ≤ Subobject.mk g.unop.left.op
⊢ g.unop.left.op.unop ≫ (Subobject.ofMkLEMk f.unop.left.op g.unop.left.op h).unop = f.unop.left
rw [← unop_comp]
no goals
C : Type u₁
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
S : C ⥤ D
T : D
A : CostructuredArrow S T
P Q : (CostructuredArrow S T)ᵒᵖ
f : P ⟶ A.op
g : Q ⟶ A.op
inst✝¹ : Mono f.unop.left.op
inst✝ : Mono g.unop.left.op
h : Subobject.mk f.unop.left.op ≤ Subobject.mk g.unop.left.op
⊢ (Subobject.ofMkLEMk f.unop.left.op g.unop.left.op h ≫ g.unop.left.op).unop = f.unop.left
simp only [Subobject.ofMkLEMk_comp, Quiver.Hom.unop_op]