Theorems · Definition · order theory
OrderIso
(α : Type u_6) → (β : Type u_7) → [LE α] → [LE β] → Type (max u_6 u_7)
An order isomorphism is an equivalence such that a ≤ b ↔ (f a) ≤ (f b).
This definition is an abbreviation of RelIso (≤) (≤).
- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 874 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RelIsoproof · cited by 456
Cited by1,260
Results whose statement or proof uses this declaration.
- OrderIso.symmstatement and proof · cited by 475
- NNReal.sqrtstatement · cited by 91
- OrderIso.apply_symm_applystatement and proof · cited by 45
- Cardinal.preAlephstatement · cited by 44
- OrderIso.symm_apply_applystatement and proof · cited by 41
- OrderIso.map_supstatement and proof · cited by 37
- OrderIso.to_galoisConnectionstatement and proof · cited by 32
- OrderIso.transstatement and proof · cited by 31
- OrderIso.map_botstatement and proof · cited by 30
- OrderIso.le_iff_lestatement and proof · cited by 29
- CategoryTheory.Sieve.overEquivstatement · cited by 28
- OrderIso.injectivestatement and proof · cited by 28
Showing the 200 most cited of 1,260.