proposition: Fact dio_fun_mult r t : 𝔻F r -> 𝔻F t -> 𝔻F (fun ν => r ν * t ν).
proof: Proof. intros H1 H2; red. by dio equiv (fun ν => exists b c, ν 0 = b * c /\ b = r ν⭳ /\ c = t ν⭳). abstract (intros v; split; [ exists (r v⭳), (t v⭳); auto | intros (? & ? & -> & -> & ->); auto ]). Defined.
imports: Arith Nat ZArith Lia Undecidability.Shared.Libs.DLW.Utils(utils_tac gcd sums bounded_quantification)