α : Type u_1
r : α → α → Prop
s t : Set α
inst✝¹ : LinearOrder α
inst✝ : NoMaxOrder α
a : α
⊢ Bounded (fun x x_1 => x < x_1) (s ∩ {b | a < b}) ↔ Bounded (fun x x_1 => x < x_1) s
α : Type u_1
r : α → α → Prop
s t : Set α
inst✝¹ : LinearOrder α
inst✝ : NoMaxOrder α
a : α
⊢ Unbounded (fun x x_1 => x < x_1) (s ∩ {b | a < b}) ↔ Unbounded (fun x x_1 => x < x_1) s
rw [← not_bounded_iff, ← not_bounded_iff, not_iff_not]
no goals
α : Type u_1
r : α → α → Prop
s t : Set α
inst✝¹ : LinearOrder α
inst✝ : NoMaxOrder α
a : α
⊢ Bounded (fun x x_1 => x < x_1) (s ∩ {b | a < b}) ↔ Bounded (fun x x_1 => x < x_1) s
exact bounded_lt_inter_lt a