Mathlib Map

Theorems · Definition · order theory

OrderIso.orderIsoCongr

{α : Type u_2} →
  {β : Type u_3} →
    {γ : Type u_4} →
      {δ : Type u_5} →
        [inst : LE α] → [inst_1 : LE β] → [inst_2 : LE γ] → [inst_3 : LE δ] → α ≃o γ → β ≃o δ → α ≃o β ≃ (γ ≃o δ)

Transport an OrderIso across a pair of OrderIsos, by pre- and post-composition. This is Equiv.equivCongr/RelIso.relIsoCongr for OrderIso.

Defined in
Mathlib.Order.Hom.Basic
Cited by
2 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
LELELELE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderIso.orderIsoCongr_apply · cited by 0OrderIso.orderIsoCongr_ap…OrderIso.orderIsoCongr_symm_apply · cited by 0OrderIso.orderIsoCongr_sy…Equiv · cited by 8337EquivOrderIso · cited by 874OrderIsoRelIso.relIsoCongr · cited by 4RelIso.relIsoCongrOrderIso.orderIsoCongrCITED BYCITES

Cites3

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

Cited by2

Results whose statement or proof uses this declaration.