Theorems · Definition · order theory
RelIso.subrelUnivIso
{α : Type u_1} → {r : α → α → Prop} → {p : α → Prop} → (∀ (x : α), p x) → Subrel r p ≃r rIf a proposition holds for all elements, then the Subrel is equivalent to the original
relation.
- Defined in
- Mathlib.Order.RelIso.Set
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- RelIsostatement · cited by 456
- Subrelstatement · cited by 53
- Equiv.subtypeUnivEquivproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Set.partiallyWellOrderedOn_univ_iffproof · cited by 2
- RelIso.subrelUnivIso_applystatement and proof · cited by 0
- RelIso.subrelUnivIso_symm_applystatement and proof · cited by 0