Theorems · Theorem · convex and discrete geometry
convexJoin_mono
∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] {s₁ s₂ t₁ t₂ : Set E}, s₁ ⊆ s₂ → t₁ ⊆ t₂ → convexJoin 𝕜 s₁ t₁ ⊆ convexJoin 𝕜 s₂ t₂- Defined in
- Mathlib.Analysis.Convex.Join
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- convexJoinstatement · cited by 31
- Set.biUnion_subset_biUnion_leftproof · cited by 18
- Set.biUnion_monoproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- convexJoin_mono_leftproof · cited by 0
- convexJoin_mono_rightproof · cited by 0