Section ALMOST_RING.
Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req.
Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext3.

Lemma ARgen_phiPOS_add : forall x y,
gen_phiPOS1 (x + y) == (gen_phiPOS1 x) + (gen_phiPOS1 y).