Theorems · Theorem
Set.mem_sInter
∀ {α : Type u} {x : α} {S : Set (Set α)}, x ∈ ⋂₀ S ↔ ∀ t ∈ S, x ∈ t- Defined in
- Mathlib.Order.SetNotation
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.sInterstatement · cited by 225
Cited by7
Results whose statement or proof uses this declaration.
- ChainCompletePartialOrder.bot_isAdmissibleproof · cited by 4
- IsClub.sInter_of_orderTopproof · cited by 2
- exists_idempotent_of_compact_t2_of_continuous_add_leftproof · cited by 2
- exists_idempotent_of_compact_t2_of_continuous_mul_leftproof · cited by 2
- CountableInfClosed.sInterproof · cited by 1
- Filter.mem_kerproof · cited by 0
- countableInfClosure_eq_sInterproof · cited by 0