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Theorems · Definition · order theory

OrderIso.ofSurjective

{α : Type u_2} → {β : Type u_3} → [inst : LE α] → [inst_1 : LE β] → (f : α ↪o β) → Function.Surjective ⇑f → α ≃o β

A surjective order embedding is an order isomorphism.

Defined in
Mathlib.Order.Hom.Basic
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses Classical.choice, Quot.sound
Assumes
LELE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OrderIso.equivEmbeddingSurjective · cited by 2OrderIso.equivEmbeddingSu…OrderIso.ofSurjective_apply · cited by 0OrderIso.ofSurjective_app…OrderIso.ofSurjective_symm_apply · cited by 0OrderIso.ofSurjective_sym…OrderIso.equivEmbeddingSurjective_symm_apply · cited by 0OrderIso.equivEmbeddingSu…DFunLike.coe · cited by 62936DFunLike.coeOrderIso · cited by 874OrderIsoOrderEmbedding · cited by 619OrderEmbeddingRelIso.ofSurjective · cited by 4RelIso.ofSurjectiveOrderIso.ofSurjectiveCITED BYCITES

Cites4

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Cited by4

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