Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext3.Ltac norm := gen_srewrite Rsth Reqe ARth.Ltac add_push := gen_add_push radd Rsth Reqe ARth.

(* Specifications: *)
Lemma same_gen : forall x, gen_phiPOS1 x == gen_phiPOS x.
Lemma ARgen_phiPOS_Psucc : forall x, gen_phiPOS1 (Pos.succ x) == 1 + (gen_phiPOS1 x).
Lemma ARgen_phiPOS_add : forall x y, gen_phiPOS1 (x + y) == (gen_phiPOS1 x) + (gen_phiPOS1 y).
Lemma ARgen_phiPOS_mult : forall x y, gen_phiPOS1 (x * y) == gen_phiPOS1 x * gen_phiPOS1 y.