Theorems · Definition · order theory
RelIso.symm
{α : Type u_1} → {β : Type u_2} → {r : α → α → Prop} → {s : β → β → Prop} → r ≃r s → s ≃r rInverse map of a relation isomorphism is a relation isomorphism.
- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 193 results in Mathlib
- Foundations
- Depth 23 from the axioms, rests on 76 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.symmproof · cited by 3,681
- RelIsostatement and proof · cited by 456
- RelIso.toEquivproof · cited by 113
Cited by205
Results whose statement or proof uses this declaration.
- OrderIso.symmproof · cited by 475
- SimpleGraph.Iso.symmproof · cited by 34
- RelIso.apply_symm_applystatement · cited by 8
- PrincipalSeg.subrelIsoproof · cited by 6
- Ordinal.lift_addproof · cited by 6
- RelIso.relEmbeddingCongrproof · cited by 4
- RelIso.relHomCongrproof · cited by 4
- RelIso.symm_apply_applystatement · cited by 4
- RelIso.relIsoCongrproof · cited by 4
- OrderHom.onDiagproof · cited by 3
- RelIso.ordinal_lift_type_eqproof · cited by 3
- PrincipalSeg.orderIsoIioproof · cited by 2
Showing the 200 most cited of 205.