Set.smul

{α : Type u_2} → {β : Type u_3} → [SMul α β] → SMul (Set α) (Set β)

The pointwise scalar multiplication of sets s • t is defined as {x • y | x ∈ s, y ∈ t} in scope Pointwise.

Defined in: Mathlib.Algebra.Group.Pointwise.Set.Scalar
Cited by: 110 results in Mathlib
Foundations: Depth 5 from the axioms, rests on 17 definitions · uses no axioms
Assumes: SMul

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.