Theorems · Theorem · order theory
Set.subset_compl_singleton_iff
∀ {α : Type u_1} {s : Set α} {a : α}, s ⊆ {a}ᶜ ↔ a ∉ s- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 58 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 · cited by 2,925
- Set.singleton_subset_iffproof · cited by 206
- Set.subset_compl_commproof · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- integral_invproof · cited by 5
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- TemperedDistribution.isVanishingOn_deltaproof · cited by 1
- Distribution.isVanishingOn_deltaproof · cited by 1
- WithSeminorms.T1_of_separatingproof · cited by 1
- compl_singleton_mem_nhdsSet_iffproof · cited by 0
- spectrum.subset_singleton_zero_complproof · cited by 0