Theorems · Definition · order theory
RelIso.ofSurjective
{α : Type u_1} →
{β : Type u_2} → {r : α → α → Prop} → {s : β → β → Prop} → (f : r ↪r s) → Function.Surjective ⇑f → r ≃r sA surjective relation embedding is a relation isomorphism.
- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RelIsostatement · cited by 456
- RelEmbeddingstatement and proof · cited by 281
- RelEmbedding.toEmbeddingproof · cited by 45
- RelEmbedding.map_rel_iffproof · cited by 25
- Function.Embedding.equivOfSurjectiveproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- Nat.Subtype.orderIsoOfNatproof · cited by 4
- OrderIso.supIrredLowerSetproof · cited by 3
- OrderIso.ofSurjectiveproof · cited by 3
- OrderIso.infIrredUpperSetproof · cited by 3
- InitialSeg.principalSumRelIsoproof · cited by 2
- RelIso.embeddingSurjectiveEquivIsoproof · cited by 2
- CategoryTheory.Limits.hasColimitsOfShape_of_initialSegproof · cited by 1
- RelIso.ofSurjective_applystatement and proof · cited by 1
- RelIso.ofSurjective.congr_simpstatement and proof · cited by 0
- RelIso.embeddingSurjectiveEquivIso_applystatement · cited by 0