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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
Assumes
LinearOrderFiniteLinearOrderInfinite

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