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Theorems · Definition · order theory

OrderEmbedding.comp

{α : Type u_2} →
  {β : Type u_3} → {γ : Type u_4} → [inst : LE α] → [inst_1 : LE β] → [inst_2 : LE γ] → α ↪o β → β ↪o γ → α ↪o γ

Composition of two order embeddings is an order embedding

Defined in
Mathlib.Order.Hom.Basic
Cited by
4 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
LELELE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderEmbedding.comp_assoc · cited by 0OrderEmbedding.comp_assocOrderEmbedding.comp_id · cited by 0OrderEmbedding.comp_idOrderEmbedding.id_comp · cited by 0OrderEmbedding.id_compOrderEmbedding.coe_comp · cited by 0OrderEmbedding.coe_compOrderEmbedding · cited by 619OrderEmbeddingRelEmbedding.trans · cited by 27RelEmbedding.transOrderEmbedding.compCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.