Theorems · Theorem · order theory
StrictMono.strictMonoOn
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
StrictMono f → ∀ (s : Set α), StrictMonoOn f s- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- StrictMonostatement and proof · cited by 706
- StrictMonoOnstatement · cited by 194
- StrictMono.impproof · cited by 4
Cited by24
Results whose statement or proof uses this declaration.
- StrictMono.le_iff_leproof · cited by 104
- StrictMono.lt_iff_ltproof · cited by 86
- StrictMono.cmp_map_eqproof · cited by 7
- strictMonoOn_univproof · cited by 3
- Polynomial.Chebyshev.strictAntiOn_nodeproof · cited by 2
- Real.image_exp_Ioiproof · cited by 2
- StrictMono.comparesproof · cited by 1
- Continuous.image_Ico_of_strictMonoproof · cited by 1
- Continuous.image_Ioc_of_strictMonoproof · cited by 1
- Continuous.image_Ioo_of_strictMonoproof · cited by 1
- AddConstMapClass.strictMono_iff_Iccproof · cited by 1
- StrictMono.strictConvexOn_univ_of_derivproof · cited by 1