Subsemigroup.mem_iSup_of_directed

∀ {M : Type u_2} [inst : Mul M] {ι : Sort u_3} {S : ι → Subsemigroup M},
  Directed (fun x1 x2 => x1 ≤ x2) S → ∀ {x : M}, x ∈ ⨆ i, S i ↔ ∃ i, x ∈ S i

Defined in: Mathlib.Algebra.Group.Subsemigroup.Membership
Cited by: 3 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Mul

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