Ltac destr_factor := match goal with
  | H : context [CFactor ?P _] |- context [CFactor ?P ?c] =>
    destruct (CFactor P c); destr_factor; rewrite H; clear H
  | H : context [MFactor ?P _ _] |- context [MFactor ?P ?c ?M] =>
    specialize (H M); destruct (MFactor P c M); destr_factor; rewrite H; clear H
  | _ => idtac
 end.

Lemma Mcphi_ok P c l : let (Q,R) := CFactor P c in P@l == Q@l + [c] * R@l.