Theorems · Theorem · convex and discrete geometry

QuasiconcaveOn.antitone_comp

∀ {𝕜 : Type u_4} {E : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : SMul 𝕜 E] {β : Type u_6} {γ : Type u_7} [inst_4 : LinearOrder β] [inst_5 : Preorder γ] {s : Set E}
  {f : E → β} {g : β → γ}, Antitone g → QuasiconcaveOn 𝕜 s f → QuasiconvexOn 𝕜 s (g ∘ f)

Defined in

Mathlib.Analysis.Convex.Quasiconvex

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidSMulLinearOrderPreorder