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Theorems · Definition · order theory

OrderIso.toOrderEmbedding

{α : Type u_2} → {β : Type u_3} → [inst : LE α] → [inst_1 : LE β] → α ≃o β → α ↪o β

Reinterpret an order isomorphism as an order embedding.

Defined in
Mathlib.Order.Hom.Basic
Cited by
22 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
LELE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Finset.orderEmbOfFin · cited by 47Finset.orderEmbOfFinOrderIso.map_sup · cited by 37OrderIso.map_supOrderIso.strictMono · cited by 26OrderIso.strictMonoOrderIso.monotone · cited by 23OrderIso.monotoneOrderIso.map_inf · cited by 17OrderIso.map_infOrderIso.lt_iff_lt · cited by 16OrderIso.lt_iff_ltMonoidWithZeroHom.ValueGroup₀.embedding_strictMono · cited by 12ValueGroup₀.embedding_str…OrderIso.withTopCongr · cited by 6OrderIso.withTopCongrOrderEmbedding.birkhoffSet · cited by 6OrderEmbedding.birkhoffSetSimplexCategory.eqToHom_toOrderHom · cited by 5SimplexCategory.eqToHom_t…OrderEmbedding.birkhoffFinset · cited by 4OrderEmbedding.birkhoffFi…OrderIso.withBotCongr · cited by 4OrderIso.withBotCongrAugmentedSimplexCategory.inl'_eval · cited by 3AugmentedSimplexCategory.…AugmentedSimplexCategory.eqToHom_toOrderHom · cited by 3AugmentedSimplexCategory.…SSet.stdSimplex.face_eq_ofSimplex · cited by 3stdSimplex.face_eq_ofSimp…OrderIso · cited by 874OrderIsoOrderEmbedding · cited by 619OrderEmbeddingRelIso.toRelEmbedding · cited by 34RelIso.toRelEmbeddingOrderIso.toOrderEmbeddingCITED BYCITES

Cites3

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Cited by31

Results whose statement or proof uses this declaration.