Theorems · Definition · order theory
OrderIso.symm
{α : Type u_2} → {β : Type u_3} → [inst : LE α] → [inst_1 : LE β] → α ≃o β → β ≃o αInverse of an order isomorphism.
- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 475 results in Mathlib
- Foundations
- Depth 24 from the axioms, rests on 80 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- OrderIsostatement and proof · cited by 874
- RelIso.symmproof · cited by 193
Cited by545
Results whose statement or proof uses this declaration.
- Real.logproof · cited by 939
- Real.arcsinproof · cited by 125
- Real.arctanproof · cited by 111
- NNReal.sqrtproof · cited by 91
- OrderIso.apply_symm_applystatement · cited by 45
- OrderIso.symm_apply_applystatement · cited by 41
- OrderIso.map_supproof · cited by 37
- OrderIso.to_galoisConnectionstatement · cited by 32
- OrderIso.map_sInf_eq_sInf_symm_preimagestatement and proof · cited by 18
- OrderIso.map_sSup_eq_sSup_symm_preimagestatement and proof · cited by 18
- Real.continuousOn_logproof · cited by 17
- OrderIso.map_infproof · cited by 17
Showing the 200 most cited of 545.