X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Freals%2FCReals1.ma;h=21dc9e6e4c79dd7ba4e77e624eaa7ab9722d457a;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=c87c3e978978d3532db7aa63b151c6c785c6c38a;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma b/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma index c87c3e978..21dc9e6e4 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals1". +include "CoRN.ma". + (* $Id: CReals1.v,v 1.4 2004/04/23 10:01:04 lcf Exp $ *) -(* INCLUDE -Max_AbsIR -*) +include "reals/Max_AbsIR.ma". -(* INCLUDE -Expon -*) +include "algebra/Expon.ma". -(* INCLUDE -CPoly_ApZero -*) +include "algebra/CPoly_ApZero.ma". (* UNEXPORTED Section More_Cauchy_Props. @@ -42,20 +38,20 @@ more useful properties about them. The sequence defined by $x_n=\frac2{n+1}$#x(n)=2/(n+1)#. *) -inline cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con. +inline "cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con". -inline cic:/CoRN/reals/CReals1/twice_inv_seq.con. +inline "cic:/CoRN/reals/CReals1/twice_inv_seq.con". (*#* Next, we prove that the sequence of absolute values of a Cauchy sequence is also Cauchy. *) -inline cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con. +inline "cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con". -inline cic:/CoRN/reals/CReals1/Cauchy_abs.con. +inline "cic:/CoRN/reals/CReals1/Cauchy_abs.con". -inline cic:/CoRN/reals/CReals1/Lim_abs.con. +inline "cic:/CoRN/reals/CReals1/Lim_abs.con". (* UNEXPORTED End More_Cauchy_Props. @@ -81,35 +77,35 @@ Finally, for some of our results it is important to assume that [seq2] is monotonous. *) -inline cic:/CoRN/reals/CReals1/seq1.var. +inline "cic:/CoRN/reals/CReals1/seq1.var". -inline cic:/CoRN/reals/CReals1/seq2.var. +inline "cic:/CoRN/reals/CReals1/seq2.var". -inline cic:/CoRN/reals/CReals1/f.var. +inline "cic:/CoRN/reals/CReals1/f.var". -inline cic:/CoRN/reals/CReals1/monF.var. +inline "cic:/CoRN/reals/CReals1/monF.var". -inline cic:/CoRN/reals/CReals1/crescF.var. +inline "cic:/CoRN/reals/CReals1/crescF.var". -inline cic:/CoRN/reals/CReals1/subseq.var. +inline "cic:/CoRN/reals/CReals1/subseq.var". -inline cic:/CoRN/reals/CReals1/mon_seq2.var. +inline "cic:/CoRN/reals/CReals1/mon_seq2.var". -inline cic:/CoRN/reals/CReals1/unbnd_f.con. +inline "cic:/CoRN/reals/CReals1/unbnd_f.con". (* begin hide *) -inline cic:/CoRN/reals/CReals1/mon_F'.con. +inline "cic:/CoRN/reals/CReals1/mon_F'.con". (* end hide *) -inline cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con. +inline "cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con". -inline cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con. +inline "cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con". -inline cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con. +inline "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con". -inline cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con. +inline "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con". (* UNEXPORTED End Subsequences. @@ -119,23 +115,23 @@ End Subsequences. Section Cauchy_Subsequences. *) -inline cic:/CoRN/reals/CReals1/seq1.var. +inline "cic:/CoRN/reals/CReals1/seq1.var". -inline cic:/CoRN/reals/CReals1/seq2.var. +inline "cic:/CoRN/reals/CReals1/seq2.var". -inline cic:/CoRN/reals/CReals1/f.var. +inline "cic:/CoRN/reals/CReals1/f.var". -inline cic:/CoRN/reals/CReals1/monF.var. +inline "cic:/CoRN/reals/CReals1/monF.var". -inline cic:/CoRN/reals/CReals1/crescF.var. +inline "cic:/CoRN/reals/CReals1/crescF.var". -inline cic:/CoRN/reals/CReals1/subseq.var. +inline "cic:/CoRN/reals/CReals1/subseq.var". -inline cic:/CoRN/reals/CReals1/mon_seq2.var. +inline "cic:/CoRN/reals/CReals1/mon_seq2.var". -inline cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con. +inline "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con". -inline cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con. +inline "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con". (* UNEXPORTED End Cauchy_Subsequences. @@ -150,13 +146,13 @@ Section Properties_of_Exponentiation. Finally, we prove that [x[^]n] grows to infinity if [x [>] One]. *) -inline cic:/CoRN/reals/CReals1/power_big'.con. +inline "cic:/CoRN/reals/CReals1/power_big'.con". -inline cic:/CoRN/reals/CReals1/power_big.con. +inline "cic:/CoRN/reals/CReals1/power_big.con". -inline cic:/CoRN/reals/CReals1/qi_yields_zero.con. +inline "cic:/CoRN/reals/CReals1/qi_yields_zero.con". -inline cic:/CoRN/reals/CReals1/qi_lim_zero.con. +inline "cic:/CoRN/reals/CReals1/qi_lim_zero.con". (* UNEXPORTED End Properties_of_Exponentiation. @@ -164,9 +160,9 @@ End Properties_of_Exponentiation. (*#* *** [IR] has characteristic zero *) -inline cic:/CoRN/reals/CReals1/char0_IR.con. +inline "cic:/CoRN/reals/CReals1/char0_IR.con". -inline cic:/CoRN/reals/CReals1/poly_apzero_IR.con. +inline "cic:/CoRN/reals/CReals1/poly_apzero_IR.con". -inline cic:/CoRN/reals/CReals1/poly_IR_extensional.con. +inline "cic:/CoRN/reals/CReals1/poly_IR_extensional.con".