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Theorems · Theorem · order theory

StrictAnti.strictAntiOn

∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
  StrictAnti f → ∀ (s : Set α), StrictAntiOn f s
Defined in
Mathlib.Order.Monotone.Defs
Cited by
16 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
PreorderPreorder
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Around this declaration

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

StrictAnti.le_iff_ge · cited by 16StrictAnti.le_iff_geStrictAnti.lt_iff_gt · cited by 10StrictAnti.lt_iff_gtStrictAnti.cmp_map_eq · cited by 2StrictAnti.cmp_map_eqStrictAnti.compares · cited by 1StrictAnti.comparesstrictAntiOn_univ · cited by 1strictAntiOn_univStrictAnti.image_Ico_subset · cited by 0StrictAnti.image_Ico_subs…StrictAnti.image_Iio_subset · cited by 0StrictAnti.image_Iio_subs…StrictAnti.image_Ioc_subset · cited by 0StrictAnti.image_Ioc_subs…StrictAnti.image_Ioi_subset · cited by 0StrictAnti.image_Ioi_subs…StrictAnti.image_Ioo_subset · cited by 0StrictAnti.image_Ioo_subs…StrictAnti.mapsTo_Ico · cited by 0StrictAnti.mapsTo_IcoStrictAnti.mapsTo_Iio · cited by 0StrictAnti.mapsTo_IioStrictAnti.mapsTo_Ioc · cited by 0StrictAnti.mapsTo_IocStrictAnti.mapsTo_Ioi · cited by 0StrictAnti.mapsTo_IoiStrictAnti.mapsTo_Ioo · cited by 0StrictAnti.mapsTo_IooSet · cited by 53352SetPreorder · cited by 7952PreorderStrictAnti · cited by 204StrictAntiStrictAntiOn · cited by 120StrictAntiOnStrictAnti.imp · cited by 4StrictAnti.impStrictAnti.strictAntiOnCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.