IsLUB.of_subset_of_superset

∀ {α : Type u_1} [inst : Preorder α] {a : α} {s t p : Set α}, IsLUB s a → IsLUB p a → s ⊆ t → t ⊆ p → IsLUB t a

If a is a least upper bound for sets s and p, then it is a least upper bound for any set t, s ⊆ t ⊆ p.

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.