Hint Rewrite
Pphi0
Pphi1
mkPinj_ok
mkPX_ok
(morph0 CRmorph)
(morph1 CRmorph)
(morph0 CRmorph)
(morph_add CRmorph)
(morph_mul CRmorph)
(morph_sub CRmorph)
(morph_opp CRmorph)
: Esimpl.
(* Quicker than autorewrite with Esimpl :-) *)
Ltac Esimpl := try rewrite_db Esimpl; rsimpl; simpl.

Lemma Pmul_ok P P' l : (P**P')@l == P@l * P'@l.