exact forAllRel_of_trans_forAll_forAll hab.left hbc.left
α✝ : Type ?u.8039
β✝ : Type ?u.8042
r✝ : α✝ → β✝ → Prop
α : Type u_1
β : Type u_2
γ : Type u_3
r₁ : α → β → Prop
r₂ : β → γ → Prop
r : α → γ → Prop
inst✝ : Trans r₁ r₂ r
as : List α
cs : List γ
b : β
bs : List β
hbs : b :: bs ≠ []
hab : forAll (fun x => r₁ x b) as ∧ List.forAllRel r₁ as bs
hbc : forAll (r₂ b) cs ∧ List.forAllRel r₂ bs cs
⊢ List.forAllRel r as cs
no goals