α : Type u_1
β : Type ?u.226217
inst✝² : Preorder α
p : α → Prop
inst✝¹ : DecidablePred p
inst✝ : LocallyFiniteOrderBot α
a : Subtype p
hp : ∀ ⦃a x : α⦄, x ≤ a → p a → p x
⊢ map (Embedding.subtype p) (Finset.subtype p (Iio ↑a)) = Iio ↑a
α : Type u_1
β : Type ?u.226217
inst✝² : Preorder α
p : α → Prop
inst✝¹ : DecidablePred p
inst✝ : LocallyFiniteOrderBot α
a : Subtype p
hp : ∀ ⦃a x : α⦄, x ≤ a → p a → p x
⊢ map (Embedding.subtype p) (Iio a) = Iio ↑a
rw [subtype_Iio_eq]
no goals
α : Type u_1
β : Type ?u.226217
inst✝² : Preorder α
p : α → Prop
inst✝¹ : DecidablePred p
inst✝ : LocallyFiniteOrderBot α
a : Subtype p
hp : ∀ ⦃a x : α⦄, x ≤ a → p a → p x
⊢ map (Embedding.subtype p) (Finset.subtype p (Iio ↑a)) = Iio ↑a
exact Finset.subtype_map_of_mem fun x hx => hp (mem_Iio.1 hx).le a.prop