1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: CPoly_Rev.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
21 include "algebra/CPoly_Degree.ma".
23 (*#* * Reverse of polynomials
31 %\begin{convention}% Let [R] be a ring, and let [RX] be the
32 polynomials over this ring.
37 cic:/CoRN/fta/CPoly_Rev/Monomials/R.var
42 inline procedural "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__" as definition.
46 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom.con" as definition.
48 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff.con" as lemma.
50 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con" as lemma.
53 Hint Resolve monom_coeff monom_coeff': algebra.
56 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_degree.con" as lemma.
58 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_S.con" as lemma.
61 Hint Resolve monom_S: algebra.
64 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con" as lemma.
67 Hint Resolve monom_wd_lft: algebra_c.
70 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con" as lemma.
73 Hint Resolve monom_mult': algebra.
76 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult.con" as lemma.
78 inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_sum.con" as lemma.
85 Hint Resolve monom_coeff monom_coeff' monom_mult monom_sum: algebra.
89 Implicit Arguments monom [R].
97 cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var
102 inline procedural "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__" as definition.
106 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev.con" as definition.
108 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con" as lemma.
110 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con" as lemma.
113 Hint Resolve Rev_coeff Rev_coeff': algebra.
116 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_wd.con" as lemma.
119 Hint Resolve Rev_wd: algebra_c.
122 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con" as lemma.
125 Hint Resolve Rev_rev: algebra.
128 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con" as lemma.
130 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree.con" as lemma.
132 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_monom.con" as lemma.
135 Hint Resolve Rev_monom: algebra.
138 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con" as lemma.
141 Hint Resolve Rev_zero: algebra.
144 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_plus.con" as lemma.
147 Hint Resolve Rev_plus: algebra.
150 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con" as lemma.
153 Hint Resolve Rev_minus: algebra.
156 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con" as lemma.
159 Hint Resolve Rev_sum0: algebra.
162 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con" as lemma.
164 inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con" as lemma.
171 Hint Resolve Rev_wd: algebra_c.
175 Hint Resolve Rev_rev Rev_mult: algebra.
179 Implicit Arguments Rev [R].