Mathlib Map

Theorems · Definition · order theory

InitialSeg.trans

{α : Type u_1} →
  {β : Type u_2} →
    {γ : Type u_3} →
      {r : α → α → Prop} → {s : β → β → Prop} → {t : γ → γ → Prop} → InitialSeg r s → InitialSeg s t → InitialSeg r t

Composition of functions shows that ≼i is transitive

Defined in
Mathlib.Order.InitialSeg
Cited by
5 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Ordinal.lift_lift · cited by 3Ordinal.lift_liftCardinal.lift_preAleph · cited by 2Cardinal.lift_preAlephOrdinal.lift_type_le · cited by 1Ordinal.lift_type_leInitialSeg.trans_apply · cited by 0InitialSeg.trans_applyCategoryTheory.Limits.hasIterationOfShape_of_initialSeg · cited by 0Limits.hasIterationOfShap…DFunLike.coe · cited by 62936DFunLike.coeInitialSeg · cited by 70InitialSegRelEmbedding.trans · cited by 27RelEmbedding.transInitialSeg.toRelEmbedding · cited by 8InitialSeg.toRelEmbeddingInitialSeg.transCITED BYCITES

Cites4

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

Cited by5

Results whose statement or proof uses this declaration.