Theorems · Theorem · order theory
MonotoneOn.image_Icc_subset
∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : Preorder α] [inst_1 : Preorder β] {a b : α},
MonotoneOn f (Set.Icc a b) → f '' Set.Icc a b ⊆ Set.Icc (f a) (f b)- Defined in
- Mathlib.Order.Interval.Set.Image
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.imagestatement · cited by 5,609
- Set.Iccstatement and proof · cited by 1,702
- MonotoneOnstatement and proof · cited by 311
- Set.MapsTo.image_subsetproof · cited by 49
- MonotoneOn.mapsTo_Iccproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousOn.image_Icc_of_monotoneOnproof · cited by 5
- Monotone.image_Icc_subsetproof · cited by 0