Theorems · Theorem · convex and discrete geometry
AntitoneOn.quasilinearOn
∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : LinearOrder E] [IsOrderedAddMonoid E] [inst_5 : PartialOrder β] [inst_6 : Module 𝕜 E] [PosSMulMono 𝕜 E]
{s : Set E} {f : E → β}, AntitoneOn f s → Convex 𝕜 s → QuasilinearOn 𝕜 s f- Defined in
- Mathlib.Analysis.Convex.Quasiconvex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Convexstatement and proof · cited by 551
- AntitoneOnstatement and proof · cited by 266
- PosSMulMonostatement and proof · cited by 188
- QuasilinearOnstatement · cited by 11
- AntitoneOn.quasiconvexOnproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- quasilinearOn_iff_monotoneOn_or_antitoneOnproof · cited by 0