Theorems · Theorem
exists_pair_lt
∀ (α : Type u_3) [Nontrivial α] [inst : LinearOrder α], ∃ x y, x < y
- Defined in
- Mathlib.Logic.Nontrivial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- NontrivialLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Nontrivialstatement and proof · cited by 2,416
- lt_or_gt_of_neproof · cited by 41
- exists_pair_neproof · cited by 32
Cited by3
Results whose statement or proof uses this declaration.
- nontrivial_iff_ltproof · cited by 2
- Continuous.strictMono_of_injproof · cited by 1
- Order.embedding_from_countable_to_denseproof · cited by 0