Subsemigroup.coe_iSup_of_directed

∀ {ι : Sort u_1} {M : Type u_2} [inst : Mul M] {S : ι → Subsemigroup M},
  Directed (fun x1 x2 => x1 ≤ x2) S → ↑(⨆ i, S i) = ⋃ i, ↑(S i)

Defined in: Mathlib.Algebra.Group.Subsemigroup.Membership
Cited by: 5 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Mul

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