Theorems · Theorem · order theory
monotoneOn_id
∀ {α : Type u} [inst : Preorder α] {s : Set α}, MonotoneOn id s- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Preorder
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 · cited by 311
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzOnWith.locallyBoundedVariationOnproof · cited by 3
- MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_leproof · cited by 2
- Real.monotoneOn_rpowIntegrand₁₂proof · cited by 1