Fact congr_equiv x y p : rem x p = rem y p <-> (exists r, r = rem x p /\ r = rem y p).

Lemma dio_rel_congruence x y p : 𝔻P x -> 𝔻P y -> 𝔻P p -> 𝔻R (fun ν => rem (x ν) (p ν) = rem (y ν) (p ν)).