Theorems · Inductive type · order theory
IsEquiv
(α : Sort u_1) → (α → α → Prop) → Prop
IsEquiv X r means that the binary relation r on X is an equivalence relation, that
is, IsPreorder X r and Std.Symm r.
- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by16
Results whose statement or proof uses this declaration.
- Relation.EqvGen.eqvGen_lestatement and proof · cited by 6
- Set.Nonempty.pairwise_iff_exists_forallstatement and proof · cited by 2
- List.IsChain.length_le_length_destutterstatement and proof · cited by 1
- Equivalence.of_isEquivstatement and proof · cited by 1
- Set.pairwise_iff_exists_forallstatement and proof · cited by 1
- Relation.EqvGen.eqvGen_eq_reflTransGenproof · cited by 1
- IsEquiv.of_equivalencestatement · cited by 1
- List.le_length_destutter'_consstatement and proof · cited by 1
- List.length_destutter'_congrstatement and proof · cited by 1
- List.length_destutter_le_length_destutter_consstatement and proof · cited by 1
- LocalizedModule.r.isEquivstatement · cited by 0
- Equivalence.isEquivstatement · cited by 0