Theorems · Definition · order theory
RelIso.toRelEmbedding
{α : Type u_1} → {β : Type u_2} → {r : α → α → Prop} → {s : β → β → Prop} → r ≃r s → r ↪r sConvert a RelIso to a RelEmbedding. This function is also available as a coercion
but often it is easier to write f.toRelEmbedding than to write explicitly r and s
in the target type.
- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RelIsostatement and proof · cited by 456
- RelEmbeddingstatement · cited by 281
- Equiv.toEmbeddingproof · cited by 254
- RelIso.toEquivproof · cited by 113
- RelIso.map_rel_iff'proof · cited by 2
Cited by49
Results whose statement or proof uses this declaration.
- Cardinal.alephproof · cited by 76
- OrderIso.toOrderEmbeddingproof · cited by 22
- SimpleGraph.Iso.toEmbeddingproof · cited by 9
- SimpleGraph.Iso.connectedComponentEquivproof · cited by 5
- RelIso.relEmbeddingCongrproof · cited by 4
- RelIso.relHomCongrproof · cited by 4
- PrincipalSeg.relIsoTransproof · cited by 4
- RelIso.toInitialSegproof · cited by 4
- SimpleGraph.Iso.mapEdgeSetproof · cited by 3
- PartOrdEmb.Iso.mkproof · cited by 3
- apply_covBy_apply_iffproof · cited by 3
- OrderIso.equivEmbeddingSurjectiveproof · cited by 2