apply sum_congr rfl
s : Sieve
⊢ (∑ d ∈ A, if P.Coprime d then s.weights d else 0) = ∑ d ∈ A, s.weights d * δ (P.gcd d)
s : Sieve
⊢ ∀ x ∈ A, (if P.Coprime x then s.weights x else 0) = s.weights x * δ (P.gcd x)