Instance Join_nat_rmap': Join (nat * rmap') := Join_prod _ (Join_equiv nat) _ _.

Lemma fmap_p2p'_inj: forall p q, @fmap SM.preds f_preds K.predicate (@pred rmap ag_rmap) p2p' p = @fmap SM.preds f_preds K.predicate (@pred rmap ag_rmap) p2p' q -> p=q.