proposition: Lemma eval_eqb' : forall P Q : Pol, P =? Q = true -> forall vs : Vars V, eval vs P = eval vs Q.
proof: Proof. induction P as [c|P1 IHP1 v P2 IHP2];destruct Q as [d|Q1 w Q2];intros E vs; change eqb with Peqb in E;simpl in E. - simpl. apply ap. apply decide_eqb_ok;trivial. - destruct (false_ne_true E). - destruct (false_ne_true E). - apply andb_true in E. destruct E as [E1 E2]. apply andb_true in E2. destruct E2 as [E2 E3]. simpl. apply compare_eqb_eq,tricho_compare_eq in E1. apply ap011;auto. apply ap011;auto. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.theory.additional_operations HoTT.Classes.tactics.ring_quote HoTT.Classes.theory.rings