Theorems · Theorem · order theory
StrictMono.strictMonoOn_IccExtend
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : Preorder β] {a b : α} (h : a ≤ b)
{f : ↑(Set.Icc a b) → β}, StrictMono f → StrictMonoOn (Set.IccExtend h f) (Set.Icc a b)- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- LinearOrderPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- Set.Elemstatement and proof · cited by 7,166
- Set.Iccstatement and proof · cited by 1,702
- StrictMonostatement and proof · cited by 706
- StrictMonoOnstatement · cited by 194
- Set.IccExtendstatement · cited by 26
- StrictMono.comp_strictMonoOnproof · cited by 4
- Set.strictMonoOn_projIccproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Real.strictMonoOn_arcsinproof · cited by 4