Theorems · Theorem · convex and discrete geometry

Convex.prod

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : AddCommMonoid F] [inst_4 : SMul 𝕜 E] [inst_5 : SMul 𝕜 F] {s : Set E} {t : Set F},
  Convex 𝕜 s → Convex 𝕜 t → Convex 𝕜 (s ×ˢ t)

Defined in

Mathlib.Analysis.Convex.Basic

Cited by

4 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidSMulSMul