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[helm.git] / matita / contribs / CoRN-Decl / complex / AbsCC.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/complex/AbsCC".
+
+include "CoRN.ma".
+
+(* $Id: AbsCC.v,v 1.2 2004/04/23 10:00:54 lcf Exp $ *)
+
+include "complex/CComplex.ma".
+
+(*#* * Absolute value on [CC]
+** Properties of [AbsCC] *)
+
+(* UNEXPORTED
+Section AbsCC_properties
+*)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_wd.con".
+
+(* UNEXPORTED
+Hint Resolve AbsCC_wd: algebra_c.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/cc_inv_abs.con".
+
+(* UNEXPORTED
+Hint Resolve cc_inv_abs: algebra.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/cc_minus_abs.con".
+
+inline "cic:/CoRN/complex/AbsCC/cc_mult_abs.con".
+
+(* UNEXPORTED
+Hint Resolve cc_mult_abs: algebra.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_IR.con".
+
+(* UNEXPORTED
+Hint Resolve AbsCC_IR: algebra.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/cc_div_abs.con".
+
+inline "cic:/CoRN/complex/AbsCC/cc_div_abs'.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_zero.con".
+
+(* UNEXPORTED
+Hint Resolve AbsCC_zero: algebra.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_one.con".
+
+inline "cic:/CoRN/complex/AbsCC/cc_pow_abs.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_pos.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con".
+
+(* begin hide *)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__".
+
+(* end hide *)
+
+(* UNEXPORTED
+Hint Resolve l_1_1_2: algebra.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con".
+
+(* UNEXPORTED
+Hint Resolve AbsCC_square_Re_Im: algebra.
+*)
+
+(* begin hide *)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__".
+
+(* end hide *)
+
+(* UNEXPORTED
+Hint Resolve l_1_2_3_CC: algebra.
+*)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con".
+
+(* UNEXPORTED
+Hint Resolve CC_conj_mult: algebra.
+*)
+
+(* begin hide *)
+
+inline "cic:/CoRN/complex/AbsCC/l_2_1_2.con".
+
+(* UNEXPORTED
+Hint Resolve l_2_1_2: algebra.
+*)
+
+(* end hide *)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con".
+
+inline "cic:/CoRN/complex/AbsCC/cc_recip_char.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_strext.con".
+
+inline "cic:/CoRN/complex/AbsCC/AbsSmallCC.con".
+
+inline "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con".
+
+(* The following lemmas are just auxiliary results *)
+
+(* begin hide *)
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__".
+
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__".
+
+(* end hide *)
+
+(* UNEXPORTED
+End AbsCC_properties
+*)
+
+(* UNEXPORTED
+Hint Resolve AbsCC_wd: algebra_c.
+*)
+
+(* UNEXPORTED
+Hint Resolve cc_inv_abs cc_mult_abs cc_div_abs cc_div_abs' cc_pow_abs
+  AbsCC_zero AbsCC_one AbsCC_IR AbsCC_mult_conj AbsCC_mult_square
+  cc_recip_char: algebra.
+*)
+
+(*#* ** The triangle inequality *)
+
+inline "cic:/CoRN/complex/AbsCC/triangle.con".
+
+inline "cic:/CoRN/complex/AbsCC/triangle_Sum.con".
+