Theorems · Definition · group theory
Set.vadd
{α : Type u_2} → {β : Type u_3} → [VAdd α β] → VAdd (Set α) (Set β)The pointwise scalar addition of sets s +ᵥ t is defined as {x +ᵥ y | x ∈ s, y ∈ t} in locale
Pointwise.
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- VAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- HVAdd.hVAddproof · cited by 1,820
- VAddstatement and proof · cited by 616
- Set.image2proof · cited by 311
Cited by72
Results whose statement or proof uses this declaration.
- Set.iUnion_vadd_setstatement · cited by 10
- IsClosed.vadd_left_of_isCompactstatement · cited by 5
- Set.vadd_set_subset_vaddstatement · cited by 5
- Set.singleton_vaddstatement · cited by 5
- Set.vadd_subset_vadd_rightstatement · cited by 4
- Finset.support_vaddAntidiagonal_subset_vaddstatement · cited by 3
- Set.IsPWO.vaddstatement · cited by 3
- Set.vadd_mem_vaddstatement · cited by 3
- IsOpen.vadd_leftstatement · cited by 3
- Set.vadd_subset_iffstatement · cited by 3
- Finset.coe_vaddstatement · cited by 3
- Set.vadd_image_prodstatement · cited by 2