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Theorems · Theorem · order theory

StrictAnti.compares

∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : Preorder β] {f : α → β},
  StrictAnti f → ∀ {a b : α} {o : Ordering}, o.Compares (f a) (f b) ↔ o.Compares b a
Defined in
Mathlib.Order.Monotone.Basic
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
LinearOrderPreorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

StrictAnti.injective · cited by 12StrictAnti.injectiveLinearOrder · cited by 8572LinearOrderPreorder · cited by 7952PreorderSet.univ · cited by 3945Set.univStrictAnti · cited by 204StrictAntiOrdering.Compares · cited by 31Ordering.ComparesStrictAnti.strictAntiOn · cited by 16StrictAnti.strictAntiOnStrictAntiOn.compares · cited by 1StrictAntiOn.comparesStrictAnti.comparesCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.