(**************************************************************************) (* ___ *) (* ||M|| *) (* ||A|| A project by Andrea Asperti *) (* ||T|| *) (* ||I|| Developers: *) (* ||T|| The HELM team. *) (* ||A|| http://helm.cs.unibo.it *) (* \ / *) (* \ / This file is distributed under the terms of the *) (* v GNU General Public License Version 2 *) (* *) (**************************************************************************) (* This file was automatically generated: do not edit *********************) include "CoRN.ma". (* $Id: Expon.v,v 1.5 2004/04/23 10:00:54 lcf Exp $ *) (*#* printing [^^] %\ensuremath{\hat{\ }}% #^# *) include "algebra/COrdCauchy.ma". include "tactics/Transparent_algebra.ma". (*#* *Exponentiation **More properties about [nexp] %\begin{convention}% Let [R] be an ordered field. %\end{convention}% *) (* UNEXPORTED Section More_Nexp *) (* UNEXPORTED cic:/CoRN/algebra/Expon/More_Nexp/R.var *) inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con" as lemma. (* UNEXPORTED Hint Resolve nexp_resp_ap_zero: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div'.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_recip.con" as lemma. (* UNEXPORTED Hint Resolve nexp_distr_recip: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le'.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/bin_less_un.con" as lemma. (* UNEXPORTED End More_Nexp *) (* UNEXPORTED Hint Resolve nexp_distr_div nexp_distr_recip: algebra. *) (* UNEXPORTED Implicit Arguments nexp_resp_ap_zero [R x]. *) (*#* **Definition of [zexp]: integer exponentiation %\begin{convention}% Let [R] be an ordered field. %\end{convention}% *) (* UNEXPORTED Section Zexp_def *) (* UNEXPORTED cic:/CoRN/algebra/Expon/Zexp_def/R.var *) (*#* It would be nicer to define [zexp] using [caseZdiff], but we already have most properties now. *) inline procedural "cic:/CoRN/algebra/Expon/zexp.con" as definition. (* UNEXPORTED End Zexp_def *) (* UNEXPORTED Implicit Arguments zexp [R]. *) (* NOTATION Notation "( x [//] Hx ) [^^] n" := (zexp x Hx n) (at level 0). *) (*#* **Properties of [zexp] %\begin{convention}% Let [R] be an ordered field. %\end{convention}% *) (* UNEXPORTED Section Zexp_properties *) (* UNEXPORTED cic:/CoRN/algebra/Expon/Zexp_properties/R.var *) inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con" as lemma. (* UNEXPORTED Hint Resolve zexp_zero: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_nexp.con" as lemma. (* UNEXPORTED Hint Resolve zexp_nexp: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv_nexp: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv_nexp': algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_strext.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/zexp_wd.con" as lemma. (* UNEXPORTED Hint Resolve zexp_wd: algebra_c. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_plus1.con" as lemma. (* UNEXPORTED Hint Resolve zexp_plus1: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con" as lemma. (* UNEXPORTED Hint Resolve zexp_resp_ap_zero: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_inv.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_inv1.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv1: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_plus.con" as lemma. (* UNEXPORTED Hint Resolve zexp_plus: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_minus.con" as lemma. (* UNEXPORTED Hint Resolve zexp_minus: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/one_zexp.con" as lemma. (* UNEXPORTED Hint Resolve one_zexp: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/mult_zexp.con" as lemma. (* UNEXPORTED Hint Resolve mult_zexp: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_mult.con" as lemma. (* UNEXPORTED Hint Resolve zexp_mult: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_two.con" as lemma. (* UNEXPORTED Hint Resolve zexp_two: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_even.con" as lemma. (* UNEXPORTED Hint Resolve inv_zexp_even: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_two.con" as lemma. (* UNEXPORTED Hint Resolve inv_zexp_two: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_odd.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/zexp_one.con" as lemma. (* UNEXPORTED Hint Resolve zexp_one: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_funny.con" as lemma. (* UNEXPORTED Hint Resolve zexp_funny: algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_funny'.con" as lemma. (* UNEXPORTED Hint Resolve zexp_funny': algebra. *) inline procedural "cic:/CoRN/algebra/Expon/zexp_pos.con" as lemma. (* UNEXPORTED End Zexp_properties *) (* UNEXPORTED Hint Resolve nexp_resp_ap_zero zexp_zero zexp_nexp zexp_inv_nexp zexp_inv_nexp' zexp_plus1 zexp_resp_ap_zero zexp_inv zexp_inv1 zexp_plus zexp_minus one_zexp mult_zexp zexp_mult zexp_two inv_zexp_even inv_zexp_two zexp_one zexp_funny zexp_funny': algebra. *) (* UNEXPORTED Hint Resolve zexp_wd: algebra_c. *) (* UNEXPORTED Section Root_Unique *) (* UNEXPORTED cic:/CoRN/algebra/Expon/Root_Unique/R.var *) inline procedural "cic:/CoRN/algebra/Expon/root_unique.con" as lemma. inline procedural "cic:/CoRN/algebra/Expon/root_one.con" as lemma. (* UNEXPORTED End Root_Unique *)