intro habsb hbc
α✝ : Type ?u.5956
β✝ : Type ?u.5959
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
b : β
cs : List γ
a : α
as : List α
h_ind : forAll (fun x => r₁ x b) as → forAll (r₂ b) cs → List.forAllRel r as cs
⊢ r₁ a b ∧ forAll (fun x => r₁ x b) as → forAll (r₂ b) cs → forAll (r a) cs ∧ forAll (fun a => forAll (r a) cs) as
α✝ : Type ?u.5956
β✝ : Type ?u.5959
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
b : β
cs : List γ
a : α
as : List α
h_ind : forAll (fun x => r₁ x b) as → forAll (r₂ b) cs → List.forAllRel r as cs
habsb : r₁ a b ∧ forAll (fun x => r₁ x b) as
hbc : forAll (r₂ b) cs
⊢ forAll (r a) cs ∧ forAll (fun a => forAll (r a) cs) as