Theorems · Theorem · order theory

iSup_mem_countableSupClosure

∀ {ι : Sort u_1} {α : Type u_2} {s : Set α} [inst : CompleteLattice α] [Countable ι] [Nonempty ι] {A : ι → α},
  (∀ (n : ι), A n ∈ s) → ⨆ n, A n ∈ countableSupClosure s

Defined in

Mathlib.Order.CountableSupClosed

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompleteLatticeCountableNonempty