Theorems · Definition · order theory
Ordering.Compares
{α : Type u_1} → [LT α] → Ordering → α → α → PropCompares o a b means that a and b have the ordering relation o between them, assuming
that the relation a < b is defined.
- Defined in
- Mathlib.Data.Ordering.Basic
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- LT
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 by32
Results whose statement or proof uses this declaration.
- StrictMono.injectiveproof · cited by 94
- StrictMonoOn.injOnproof · cited by 22
- StrictAnti.injectiveproof · cited by 12
- cmp_comparesstatement and proof · cited by 5
- Ordering.Compares.eq_ltstatement and proof · cited by 4
- StrictMonoOn.comparesstatement and proof · cited by 4
- ONote.cmp_comparesstatement · cited by 3
- Ordering.Compares.eq_gtstatement and proof · cited by 2
- Ordering.Compares.injstatement and proof · cited by 2
- ONote.repr_injproof · cited by 2
- Ordering.Compares.swapstatement · cited by 2
- Ordering.compares_swapstatement · cited by 2