Theorems · Inductive type · order theory
IsPreorder
(α : Sort u_1) → (α → α → Prop) → Prop
IsPreorder X r means that the binary relation r on X is a pre-order, that is, reflexive
and transitive.
- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 20 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 by30
Results whose statement or proof uses this declaration.
- Antisymmetrizationstatement and proof · cited by 25
- toAntisymmetrizationstatement and proof · cited by 12
- Set.PartiallyWellOrderedOn.exists_monotone_subseqstatement and proof · cited by 9
- AntisymmRel.setoidstatement and proof · cited by 7
- WellQuasiOrdered.exists_monotone_subseqstatement and proof · cited by 4
- ofAntisymmetrizationstatement and proof · cited by 4
- Set.PartiallyWellOrderedOn.wellFoundedOnstatement and proof · cited by 3
- Set.PartiallyWellOrderedOn.partiallyWellOrderedOn_sublistForall₂statement and proof · cited by 2
- WellQuasiOrdered.wellFoundedstatement and proof · cited by 2
- Antisymmetrization.indstatement and proof · cited by 2
- Set.partiallyWellOrderedOn_iff_exists_monotone_subseqstatement and proof · cited by 2
- wellQuasiOrdered_iff_exists_monotone_subseqstatement and proof · cited by 2