proposition: Fact dio_fun_rem p x : 𝔻F p -> 𝔻F x -> 𝔻F (fun ν => rem (x ν) (p ν)).
proof: Proof. dio by lemma (fun v => rem_equiv (p v⭳) (x v⭳) (v 0)). Defined.
imports: Arith Nat ZArith Lia Undecidability.Shared.Libs.DLW.Utils(utils_tac gcd sums bounded_quantification)