Theorems · Theorem
exists_ne
∀ {α : Type u_1} [Nontrivial α] (x : α), ∃ y, y ≠ x- Defined in
- Mathlib.Logic.Nontrivial.Defs
- Cited by
- 101 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 48 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Nontrivial
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.
- Nontrivialstatement and proof · cited by 2,416
- Decidable.exists_neproof · cited by 3
Cited by101
Results whose statement or proof uses this declaration.
- nontrivial_iff_exists_neproof · cited by 8
- Cardinal.mk_finsupp_lift_of_infiniteproof · cited by 6
- nhds_bot_basisproof · cited by 6
- SimpleGraph.eccent_ne_zeroproof · cited by 5
- isSimpleModule_iff_quot_maximalproof · cited by 5
- rank_zero_iff_forall_zeroproof · cited by 5
- nhds_top_basisproof · cited by 5
- associatedPrimes.nonemptyproof · cited by 4
- AlgEquiv.eq_linearEquivConjAlgEquivproof · cited by 4
- IsAtomic.exists_atomproof · cited by 4
- HahnEmbedding.Partial.orderTop_eq_archimedeanClassMkproof · cited by 3