--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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 *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/algebra/Expon".
+
+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
+*)
+
+alias id "R" = "cic:/CoRN/algebra/Expon/More_Nexp/R.var".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con".
+
+(* UNEXPORTED
+Hint Resolve nexp_resp_ap_zero: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/nexp_distr_div.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_distr_div'.con".
+
+inline "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con".
+
+inline "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con".
+
+inline "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con".
+
+inline "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_distr_recip.con".
+
+(* UNEXPORTED
+Hint Resolve nexp_distr_recip: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_le'.con".
+
+inline "cic:/CoRN/algebra/Expon/nexp_resp_le.con".
+
+inline "cic:/CoRN/algebra/Expon/bin_less_un.con".
+
+(* 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
+*)
+
+alias id "R" = "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 "cic:/CoRN/algebra/Expon/zexp.con".
+
+(* 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
+*)
+
+alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_properties/R.var".
+
+inline "cic:/CoRN/algebra/Expon/zexp_zero.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_zero: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_nexp.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_nexp: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_inv_nexp: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_inv_nexp': algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_strext.con".
+
+inline "cic:/CoRN/algebra/Expon/zexp_wd.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_wd: algebra_c.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_plus1.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_plus1: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_resp_ap_zero: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_inv.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_inv: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_inv1.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_inv1: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_plus.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_plus: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_minus.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_minus: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/one_zexp.con".
+
+(* UNEXPORTED
+Hint Resolve one_zexp: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/mult_zexp.con".
+
+(* UNEXPORTED
+Hint Resolve mult_zexp: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_mult.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_mult: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_two.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_two: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/inv_zexp_even.con".
+
+(* UNEXPORTED
+Hint Resolve inv_zexp_even: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/inv_zexp_two.con".
+
+(* UNEXPORTED
+Hint Resolve inv_zexp_two: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/inv_zexp_odd.con".
+
+inline "cic:/CoRN/algebra/Expon/zexp_one.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_one: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_funny.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_funny: algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_funny'.con".
+
+(* UNEXPORTED
+Hint Resolve zexp_funny': algebra.
+*)
+
+inline "cic:/CoRN/algebra/Expon/zexp_pos.con".
+
+(* 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
+*)
+
+alias id "R" = "cic:/CoRN/algebra/Expon/Root_Unique/R.var".
+
+inline "cic:/CoRN/algebra/Expon/root_unique.con".
+
+inline "cic:/CoRN/algebra/Expon/root_one.con".
+
+(* UNEXPORTED
+End Root_Unique
+*)
+
projects / helm.git / blobdiff