Theorems · Theorem · order theory

Order.exists_orderEmbedding_insert

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : LinearOrder β] [DenselyOrdered β] [NoMinOrder β]
  [NoMaxOrder β] [nonem : Nonempty β] (S : Finset α) (f : ↥S ↪o β) (a : α), ∃ g, ⇑g ∘ Set.inclusion ⋯ = ⇑f

Defined in

Mathlib.Order.CountableDenseLinearOrder

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderLinearOrderDenselyOrderedNoMinOrderNoMaxOrderNonempty