Theorems · Theorem · order theory
surjOn_Ioc_of_monotone_surjective
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : PartialOrder β] {f : α → β},
Monotone f → Function.Surjective f → ∀ (a b : α), Set.SurjOn f (Set.Ioc a b) (Set.Ioc (f a) (f b))- Defined in
- Mathlib.Order.Interval.Set.SurjOn
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderPartialOrder
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- PartialOrderstatement and proof · cited by 6,410
- Monotonestatement and proof · cited by 1,397
- Set.Iocstatement · cited by 971
- OrderDual.toDualproof · cited by 481
- OrderDual.ofDualproof · cited by 400
- Set.SurjOnstatement and proof · cited by 186
- Monotone.dualproof · cited by 39
- Set.Ico_toDualproof · cited by 11
- surjOn_Ico_of_monotone_surjectiveproof · cited by 1
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