Theorems · Theorem · convex and discrete geometry

Convex.quasiconvexOn_of_convex_le

∀ {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 : LE β] [inst_4 : SMul 𝕜 E] {s : Set E} {f : E → β},
  Convex 𝕜 s → (∀ (r : β), Convex 𝕜 {x | f x ≤ r}) → QuasiconvexOn 𝕜 s f

Defined in: Mathlib.Analysis.Convex.Quasiconvex
Cited by: 1 results in Mathlib
Foundations: Depth 15 from the axioms · uses no axioms
Assumes: Semiring PartialOrder AddCommMonoid LE SMul

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
PartialOrderstatement and proof · cited by 6,410
Set.ofPredstatement and proof · cited by 6,101
Convexstatement and proof · cited by 551
QuasiconvexOnstatement · cited by 25
Convex.interproof · cited by 22

Cited by1

Results whose statement or proof uses this declaration.

Convex.quasiconcaveOn_of_convex_geproof · cited by 0