English
Restriction of a locally finite function to a closed ball defines a monoid homomorphism to the restricted domain, i.e., toClosedBall r : locallyFinsuppWithin(univ) ℤ →+ locallyFinsuppWithin(closedBall(0,|r|)) ℤ.
Русский
Ограничение локально ограниченной функции до замкнутого шара задаёт моноидный гомоморфизм: toClosedBall r : локально ограниченная ≤ ℤ →+ локально ограниченная на замкнутом шаре.
LaTeX
$$$\text{toClosedBall}(r) : \text{locallyFinsuppWithin}(\!\text{univ})\mathbb{Z} \to+ \text{locallyFinsuppWithin}(\text{closedBall}(0,|r|))\mathbb{Z}$$$
Lean4
/-- Shorthand notation for the restriction of a function with locally finite support within `Set.univ`
to the closed unit ball of radius `r`.
-/
noncomputable def toClosedBall {E : Type*} [NormedAddCommGroup E] (r : ℝ) :
locallyFinsuppWithin (univ : Set E) ℤ →+ locallyFinsuppWithin (closedBall (0 : E) |r|) ℤ :=
by
apply restrictMonoidHom
tauto
