Theorems · Theorem · order theory
Set.Nontrivial.not_subset_singleton
∀ {α : Type u} {s : Set α} {x : α}, s.Nontrivial → ¬s ⊆ {x}- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 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.Nontrivialstatement and proof · cited by 145
- Set.subset_singleton_iff_eqproof · cited by 10
- Set.Nontrivial.ne_singletonproof · cited by 3
- Set.Nontrivial.ne_emptyproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Finset.Nontrivial.not_subset_singletonproof · cited by 2
- Set.singleton_ne_univproof · cited by 2
- Finset.nsmul_right_strictMonoOnproof · cited by 1
- Set.smul_univ₀'proof · cited by 1
- Finset.pow_right_strictMonoOnproof · cited by 1