Theorems · Theorem · order theory
Set.sInter_eq_iInter
∀ {α : Type u_1} {s : Set (Set α)}, ⋂₀ s = ⋂ i, ↑i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Elemstatement · cited by 7,166
- Set.iInterstatement · cited by 1,084
- Set.sInterstatement and proof · cited by 225
- Subtype.range_coeproof · cited by 98
Cited by8
Results whose statement or proof uses this declaration.
- Topology.IsLower.isTopologicalBasisproof · cited by 3
- IsCompact.extremePoints_nonemptyproof · 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
- IsCompact.nonempty_inter_sInterproof · cited by 1
- Matroid.isFlat_closureproof · cited by 1
- IsCompact.nonempty_sInter_of_directed_nonempty_isCompact_isClosedproof · cited by 0
- small_sInterproof · cited by 0