Theorems · Theorem · order theory
StrictAnti.image_Ioc_subset
∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : PartialOrder α] [inst_1 : Preorder β] {a b : α},
StrictAnti f → f '' Set.Ioc a b ⊆ Set.Ico (f b) (f a)- Defined in
- Mathlib.Order.Interval.Set.Image
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPreorder
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- PartialOrderstatement and proof · cited by 6,410
- Set.imagestatement · cited by 5,609
- Set.Iccproof · cited by 1,702
- Set.Iocstatement · cited by 971
- Set.Icostatement · cited by 799
- StrictAntistatement and proof · cited by 204
- StrictAnti.strictAntiOnproof · cited by 16
- StrictAntiOn.image_Ioc_subsetproof · cited by 2
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