(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Require Export List.
Require Export Morphisms Setoid Bool.
Require Export Algebra_syntax.
Require Export Ncring.
Require Export Ncring_initial.
Require Export Ncring_tac.
Class Cring {R:Type}`{Rr:Ring R} :=
cring_mul_comm: forall x y:R, x * y == y * x.
Ltac reify_goal lvar lexpr lterm:=
(*idtac lvar; idtac lexpr; idtac lterm;*)
match lexpr with
nil => idtac
| ?e1::?e2::_ =>
match goal with
|- (?op ?u1 ?u2) =>
change (op
(@Ring_polynom.PEeval
_ zero one _+_ _*_ _-_ -_ Z Ncring_initial.gen_phiZ N (fun n:N => n)
(@Ring_theory.pow_N _ 1 multiplication) lvar e1)
(@Ring_polynom.PEeval
_ zero one _+_ _*_ _-_ -_ Z Ncring_initial.gen_phiZ N (fun n:N => n)
(@Ring_theory.pow_N _ 1 multiplication) lvar e2))
end
end.
Section cring.
Context {R:Type}`{Rr:Cring R}.

Lemma cring_eq_ext: ring_eq_ext _+_ _*_ -_ _==_.