Theorems · Theorem · functional analysis
convex_RCLike_iff_convex_real
∀ {K : Type u_1} {E : Type u_2} [inst : RCLike K] [inst_1 : AddCommMonoid E] [inst_2 : Module K E] [inst_3 : Module ℝ E]
[IsScalarTower ℝ K E] {s : Set E}, Convex K s ↔ Convex ℝ s- Defined in
- Mathlib.Analysis.RCLike.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- IsScalarTowerstatement and proof · cited by 3,896
- RCLikestatement and proof · cited by 2,829
- Convexstatement and proof · cited by 551
- RCLike.toPartialOrderstatement · cited by 106
- RCLike.nonneg_iff_exists_ofRealproof · cited by 4
- Convex.liftproof · cited by 4
- convex_of_nonneg_surjective_algebraMapproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.polar_AbsConvexproof · cited by 0