Theorems · Theorem · order theory
Set.inter_compl_nonempty_iff
∀ {α : Type u_1} {s t : Set α}, (s ∩ tᶜ).Nonempty ↔ ¬s ⊆ t- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Compl.complstatement and proof · cited by 2,925
- Set.Nonemptystatement · cited by 2,627
- Set.not_subsetproof · cited by 31
Cited by6
Results whose statement or proof uses this declaration.
- subset_closure_inter_of_isPreirreducible_of_isOpenproof · cited by 6
- Set.sdiff_nonemptyproof · cited by 5
- Filter.mem_iff_inf_principal_complproof · cited by 4
- exists_subset_nhds_of_isCompact'proof · cited by 2
- closure_sUnion_irreducibleComponents_sdiff_singletonproof · cited by 2
- dense_compl_singleton_iff_not_openproof · cited by 1