Theorems · Theorem · order theory
Setoid.sSup_eq_eqvGen
∀ {α : Type u_1} (S : Set (Setoid α)), sSup S = Relation.EqvGen.setoid fun x y => ∃ r ∈ S, r x yThe supremum of a set S of equivalence relations is the equivalence closure of the binary
relation there exists r ∈ S relating x and y.
- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Set.extproof · cited by 2,266
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfproof · cited by 935
- Relation.EqvGen.setoidstatement · cited by 10
- Setoid.eqvGen_eqproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Setoid.sSup_defproof · cited by 0