Theorems · Theorem · convex and discrete geometry

ConvexOn.comp

∀ {𝕜 : Type u_1} {E : Type u_2} {α : Type u_4} {β : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜]
  [inst_2 : AddCommMonoid E] [inst_3 : AddCommMonoid α] [inst_4 : PartialOrder α] [inst_5 : AddCommMonoid β]
  [inst_6 : PartialOrder β] [inst_7 : SMul 𝕜 E] [inst_8 : SMul 𝕜 α] [inst_9 : SMul 𝕜 β] {s : Set E} {f : E → β}
  {g : β → α}, ConvexOn 𝕜 (f '' s) g → ConvexOn 𝕜 s f → MonotoneOn g (f '' s) → ConvexOn 𝕜 s (g ∘ f)

Defined in

Mathlib.Analysis.Convex.Function

Cited by

2 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidPartialOrderAddCommMonoidPartialOrderSMulSMulSMul