End ALMOST_RING.
Variable Rth : ring_theory 0 1 radd rmul rsub ropp req.
Let ARth := Rth_ARth Rsth Reqe Rth.
Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext4.

(** N is a semi-ring and a setoid*)
Lemma Nsth : Setoid_Theory N (@eq N).
Proof (Eqsth N).