Theorems · Theorem · order theory
Infinite.exists_strictMono_or_strictAnti
∀ (α : Type u_2) [inst : LinearOrder α] [Infinite α], ∃ f, StrictMono f ∨ StrictAnti f
Every infinite linear order contains either a strictly increasing or a strictly decreasing
sequence indexed by ℕ.
- Defined in
- Mathlib.Order.OrderIsoNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderInfinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Function.Embeddingproof · cited by 988
- StrictMonostatement · cited by 706
- OrderEmbeddingproof · cited by 619
- Infinitestatement and proof · cited by 352
- lt_of_le_of_neproof · cited by 230
- StrictAntistatement · cited by 204
- Function.Embedding.injectiveproof · cited by 111
- RelEmbedding.injectiveproof · cited by 41
- Infinite.natEmbeddingproof · cited by 12
- exists_increasing_or_nonincreasing_subseqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finite.of_wellFoundedLT_wellFoundedGTproof · cited by 0