Theorems · Theorem · order theory
MonotoneOn.mono
∀ {α : Type u_1} {β : Type u_2} {s s₂ : Set α} {f : α → β} [inst : Preorder α] [inst_1 : Preorder β],
MonotoneOn f s → s₂ ⊆ s → MonotoneOn f s₂- Defined in
- Mathlib.Data.Set.Monotone
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- MonotoneOnstatement and proof · cited by 311
Cited by16
Results whose statement or proof uses this declaration.
- eVariationOn.sum_le_of_monotoneOn_Iicproof · cited by 5
- MeasurableSet.image_of_monotoneOnproof · cited by 4
- MonotoneOn.ae_differentiableWithinAt_of_memproof · cited by 3
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interiorproof · cited by 2
- ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interiorproof · cited by 2
- MonotoneOn.exists_monotone_extensionproof · cited by 2
- Unitary.norm_sub_one_sq_eqproof · cited by 2
- eVariationOn.comp_inter_Icc_eq_of_monotoneOnproof · cited by 2
- MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonnegproof · cited by 1
- ConvexOn.monotoneOn_slope_gtproof · cited by 1
- ConvexOn.monotoneOn_slope_ltproof · cited by 1