case a
ι : Type ?u.69349
α : Type u_1
inst✝³ : Preorder α
inst✝² : LocallyFiniteOrderBot α
a : α
inst✝¹ : Fintype α
inst✝ : DecidablePred fun x => x ≤ a
a✝ : α
⊢ a✝ ∈ filter (fun x => x ≤ a) univ ↔ a✝ ∈ Iic a
ι : Type ?u.69349
α : Type u_1
inst✝³ : Preorder α
inst✝² : LocallyFiniteOrderBot α
a : α
inst✝¹ : Fintype α
inst✝ : DecidablePred fun x => x ≤ a
⊢ filter (fun x => x ≤ a) univ = Iic a
ext
no goals
case a
ι : Type ?u.69349
α : Type u_1
inst✝³ : Preorder α
inst✝² : LocallyFiniteOrderBot α
a : α
inst✝¹ : Fintype α
inst✝ : DecidablePred fun x => x ≤ a
a✝ : α
⊢ a✝ ∈ filter (fun x => x ≤ a) univ ↔ a✝ ∈ Iic a
simp