proposition: Fact E_it x n : Normal R (it n rho x) -> E (S n) x = Some (it n rho x).
proof: Proof. Proof using red. revert x. induction n as [|n IH]; intros x. - cbn. destruct (delta x) as [H|H]; tauto. - cbn [it]. rewrite it_commute. intros H1 % IH. rewrite E_S. destruct (delta x) as [H|H]; [|exact H1]. rewrite red_fun_fp; [|exact H]. rewrite red_fun_fp_it; [|exact H]. reflexivity. Qed.
imports: Morphisms FinFun ConstructiveEpsilon Undecidability.HOU(std.tactics std.decidable std.misc std.ars.basic std.ars.confluence)