Theorems · Theorem · order theory
Set.Nontrivial.exists_ne
∀ {α : Type u} {s : Set α}, s.Nontrivial → ∀ (z : α), ∃ x ∈ s, x ≠ z- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
Cited by8
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycleOn.apply_neproof · cited by 4
- Finset.Nontrivial.exists_neproof · cited by 4
- IsPreconnected.preperfect_of_nontrivialproof · cited by 2
- SimpleGraph.isClique_map_iff_of_nontrivialproof · cited by 2
- closure_ordConnected_inter_ratproof · cited by 1
- Matroid.IsCocircuit.isNonloop_of_memproof · cited by 1
- Set.nontrivial_iff_exists_neproof · cited by 1
- Matroid.Indep.insert_isCircuit_of_forall_of_nontrivialproof · cited by 0