Theorems · Theorem · order theory
Set.sdiff_nonempty
∀ {α : Type u_1} {s t : Set α}, (s \ t).Nonempty ↔ ¬s ⊆ t- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Nonemptystatement · cited by 2,627
- Set.inter_compl_nonempty_iffproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- ZFSet.IsOrdinal.subset_iff_eq_or_memproof · cited by 2
- IsClosed.two_pow_mk_le_two_pow_mk_denseproof · cited by 2
- IsCountablyCompact.elim_directed_coverproof · cited by 1
- Set.diff_nonemptyproof · cited by 0