Theorems · Theorem
exists_pair_ne
∀ (α : Type u_3) [Nontrivial α], ∃ x y, x ≠ y
- Defined in
- Mathlib.Logic.Nontrivial.Defs
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- 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
- Nontrivial.exists_pair_neproof · cited by 12
Cited by32
Results whose statement or proof uses this declaration.
- Function.Injective.nontrivialproof · cited by 17
- Set.nontrivial_univproof · cited by 4
- Function.Surjective.nontrivialproof · cited by 4
- exists_pair_ltproof · cited by 3
- Decidable.exists_neproof · cited by 3
- Function.not_injective_constproof · cited by 2
- Filter.disjoint_atBot_atTopproof · cited by 2
- Filter.disjoint_atTop_atBotproof · cited by 2
- Fintype.exists_pair_of_one_lt_cardproof · cited by 2
- SimpleGraph.ediam_ne_zeroproof · cited by 2
- IsLeftRegular.ne_zeroproof · cited by 1
- Equiv.Perm.sign_surjectiveproof · cited by 1