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Theorems · Theorem · order theory

StrictAntiOn.cmp_map_eq

∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : α → β} {s : Set α} {x y : α},
  StrictAntiOn f s → x ∈ s → y ∈ s → cmp (f x) (f y) = cmp y x
Defined in
Mathlib.Order.Monotone.Basic
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
LinearOrderLinearOrder
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Around this declaration

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

StrictAnti.cmp_map_eq · cited by 2StrictAnti.cmp_map_eqSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderStrictAntiOn · cited by 120StrictAntiOncmp · cited by 43cmpStrictAntiOn.dual_right · cited by 8StrictAntiOn.dual_rightStrictMonoOn.cmp_map_eq · cited by 3StrictMonoOn.cmp_map_eqStrictAntiOn.cmp_map_eqCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.