Theorems · Theorem · convex and discrete geometry
convex_univ
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : SMul 𝕜 E], Convex 𝕜 Set.univ- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Set.univstatement and proof · cited by 3,945
- Convexstatement · cited by 551
- starConvex_univproof · cited by 1
Cited by53
Results whose statement or proof uses this declaration.
- lipschitzWith_of_nnnorm_deriv_leproof · cited by 4
- IsExposed.isExtremeproof · cited by 3
- NNReal.strictConcaveOn_rpowproof · cited by 3
- convexOn_univ_distproof · cited by 2
- convexOn_univ_normproof · cited by 2
- strictMono_of_deriv_posproof · cited by 2
- convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Iciproof · cited by 2
- strictConvexOn_expproof · cited by 2
- taylor_isLittleO_univproof · cited by 1
- Antitone.quasiconcaveOnproof · cited by 1
- Antitone.quasiconvexOnproof · cited by 1
- ContDiff.dimH_range_leproof · cited by 1