Theorems · Theorem · convex and discrete geometry

ConcaveOn.subset

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : AddCommMonoid β] [inst_4 : PartialOrder β] [inst_5 : SMul 𝕜 E] [inst_6 : SMul 𝕜 β] {s : Set E} {f : E → β}
  {t : Set E}, ConcaveOn 𝕜 t f → s ⊆ t → Convex 𝕜 s → ConcaveOn 𝕜 s f

Defined in

Mathlib.Analysis.Convex.Function

Cited by

4 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidPartialOrderSMulSMul