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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 *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/algebra/Expon".
19 (* $Id: Expon.v,v 1.5 2004/04/23 10:00:54 lcf Exp $ *)
21 (*#* printing [^^] %\ensuremath{\hat{\ }}% #^# *)
36 **More properties about [nexp]
37 %\begin{convention}% Let [R] be an ordered field.
45 inline cic:/CoRN/algebra/Expon/R.var.
47 inline cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con.
50 Hint Resolve nexp_resp_ap_zero: algebra.
53 inline cic:/CoRN/algebra/Expon/nexp_distr_div.con.
55 inline cic:/CoRN/algebra/Expon/nexp_distr_div'.con.
57 inline cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con.
59 inline cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con.
61 inline cic:/CoRN/algebra/Expon/small_nexp_resp_le.con.
63 inline cic:/CoRN/algebra/Expon/great_nexp_resp_le.con.
65 inline cic:/CoRN/algebra/Expon/nexp_resp_leEq.con.
67 inline cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con.
69 inline cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con.
71 inline cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con.
73 inline cic:/CoRN/algebra/Expon/nexp_distr_recip.con.
76 Hint Resolve nexp_distr_recip: algebra.
79 inline cic:/CoRN/algebra/Expon/nexp_even_nonneg.con.
81 inline cic:/CoRN/algebra/Expon/nexp_resp_le'.con.
83 inline cic:/CoRN/algebra/Expon/nexp_resp_le.con.
85 inline cic:/CoRN/algebra/Expon/bin_less_un.con.
92 Hint Resolve nexp_distr_div nexp_distr_recip: algebra.
96 Implicit Arguments nexp_resp_ap_zero [R x].
99 (*#* **Definition of [zexp]: integer exponentiation
100 %\begin{convention}% Let [R] be an ordered field.
108 inline cic:/CoRN/algebra/Expon/R.var.
111 It would be nicer to define [zexp] using [caseZdiff], but we already
112 have most properties now.
115 inline cic:/CoRN/algebra/Expon/zexp.con.
122 Implicit Arguments zexp [R].
125 (*#* **Properties of [zexp]
126 %\begin{convention}% Let [R] be an ordered field.
131 Section Zexp_properties.
134 inline cic:/CoRN/algebra/Expon/R.var.
136 inline cic:/CoRN/algebra/Expon/zexp_zero.con.
139 Hint Resolve zexp_zero: algebra.
142 inline cic:/CoRN/algebra/Expon/zexp_nexp.con.
145 Hint Resolve zexp_nexp: algebra.
148 inline cic:/CoRN/algebra/Expon/zexp_inv_nexp.con.
151 Hint Resolve zexp_inv_nexp: algebra.
154 inline cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con.
157 Hint Resolve zexp_inv_nexp': algebra.
160 inline cic:/CoRN/algebra/Expon/zexp_strext.con.
162 inline cic:/CoRN/algebra/Expon/zexp_wd.con.
165 Hint Resolve zexp_wd: algebra_c.
168 inline cic:/CoRN/algebra/Expon/zexp_plus1.con.
171 Hint Resolve zexp_plus1: algebra.
174 inline cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con.
177 Hint Resolve zexp_resp_ap_zero: algebra.
180 inline cic:/CoRN/algebra/Expon/zexp_inv.con.
183 Hint Resolve zexp_inv: algebra.
186 inline cic:/CoRN/algebra/Expon/zexp_inv1.con.
189 Hint Resolve zexp_inv1: algebra.
192 inline cic:/CoRN/algebra/Expon/zexp_plus.con.
195 Hint Resolve zexp_plus: algebra.
198 inline cic:/CoRN/algebra/Expon/zexp_minus.con.
201 Hint Resolve zexp_minus: algebra.
204 inline cic:/CoRN/algebra/Expon/one_zexp.con.
207 Hint Resolve one_zexp: algebra.
210 inline cic:/CoRN/algebra/Expon/mult_zexp.con.
213 Hint Resolve mult_zexp: algebra.
216 inline cic:/CoRN/algebra/Expon/zexp_mult.con.
219 Hint Resolve zexp_mult: algebra.
222 inline cic:/CoRN/algebra/Expon/zexp_two.con.
225 Hint Resolve zexp_two: algebra.
228 inline cic:/CoRN/algebra/Expon/inv_zexp_even.con.
231 Hint Resolve inv_zexp_even: algebra.
234 inline cic:/CoRN/algebra/Expon/inv_zexp_two.con.
237 Hint Resolve inv_zexp_two: algebra.
240 inline cic:/CoRN/algebra/Expon/inv_zexp_odd.con.
242 inline cic:/CoRN/algebra/Expon/zexp_one.con.
245 Hint Resolve zexp_one: algebra.
248 inline cic:/CoRN/algebra/Expon/zexp_funny.con.
251 Hint Resolve zexp_funny: algebra.
254 inline cic:/CoRN/algebra/Expon/zexp_funny'.con.
257 Hint Resolve zexp_funny': algebra.
260 inline cic:/CoRN/algebra/Expon/zexp_pos.con.
267 Hint Resolve nexp_resp_ap_zero zexp_zero zexp_nexp zexp_inv_nexp
268 zexp_inv_nexp' zexp_plus1 zexp_resp_ap_zero zexp_inv zexp_inv1 zexp_plus
269 zexp_minus one_zexp mult_zexp zexp_mult zexp_two inv_zexp_even inv_zexp_two
270 zexp_one zexp_funny zexp_funny': algebra.
274 Hint Resolve zexp_wd: algebra_c.
281 inline cic:/CoRN/algebra/Expon/R.var.
283 inline cic:/CoRN/algebra/Expon/root_unique.con.
285 inline cic:/CoRN/algebra/Expon/root_one.con.