Theorems · Theorem · order theory
nonempty_orderEmbedding_of_finite_infinite
∀ (α : Type u_1) [inst : LinearOrder α] [hα : Finite α] (β : Type u_2) [inst_1 : LinearOrder β] [hβ : Infinite β], Nonempty (α ↪o β)
Any finite linear order order-embeds into any infinite linear order.
- Defined in
- Mathlib.Data.Finset.Sort
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Finset.cardproof · cited by 2,327
- Fintype.cardproof · cited by 1,386
- OrderEmbeddingstatement · cited by 619
- OrderIso.symmproof · cited by 475
- Infinitestatement and proof · cited by 352
- Fintype.ofFiniteproof · cited by 255
- Finset.orderEmbOfFinproof · cited by 47
- RelEmbedding.transproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.dlo_ageproof · cited by 1