X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Freals%2FSeries.ma;h=40315e1179aa41364aec8a9ea0f5f45ebaae0d26;hb=a5bfa65b18a876fca982270f673c686a7d124f65;hp=3a90759c09c73655d15423e99e149743620d6848;hpb=62596f4e0a109e43c9df5da20571827c8b905ce4;p=helm.git diff --git a/matita/contribs/CoRN-Decl/reals/Series.ma b/matita/contribs/CoRN-Decl/reals/Series.ma index 3a90759c0..40315e117 100644 --- a/matita/contribs/CoRN-Decl/reals/Series.ma +++ b/matita/contribs/CoRN-Decl/reals/Series.ma @@ -45,7 +45,7 @@ To each such sequence we can assign a sequence of partial sums. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/Definitions/x.var" "Definitions__". +alias id "x" = "cic:/CoRN/reals/Series/Definitions/x.var". inline "cic:/CoRN/reals/Series/seq_part_sum.con". @@ -99,7 +99,7 @@ End Definitions Section More_Definitions *) -inline "cic:/CoRN/reals/Series/More_Definitions/x.var" "More_Definitions__". +alias id "x" = "cic:/CoRN/reals/Series/More_Definitions/x.var". (*#* We also define absolute convergence. *) @@ -129,11 +129,11 @@ we can also compute its sum. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/Power_Series/c.var" "Power_Series__". +alias id "c" = "cic:/CoRN/reals/Series/Power_Series/c.var". -inline "cic:/CoRN/reals/Series/Power_Series/H0c.var" "Power_Series__". +alias id "H0c" = "cic:/CoRN/reals/Series/Power_Series/H0c.var". -inline "cic:/CoRN/reals/Series/Power_Series/Hc1.var" "Power_Series__". +alias id "Hc1" = "cic:/CoRN/reals/Series/Power_Series/Hc1.var". inline "cic:/CoRN/reals/Series/c_exp_Lim.con". @@ -168,13 +168,13 @@ of two convergent series. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/Operations/x.var" "Operations__". +alias id "x" = "cic:/CoRN/reals/Series/Operations/x.var". -inline "cic:/CoRN/reals/Series/Operations/y.var" "Operations__". +alias id "y" = "cic:/CoRN/reals/Series/Operations/y.var". -inline "cic:/CoRN/reals/Series/Operations/convX.var" "Operations__". +alias id "convX" = "cic:/CoRN/reals/Series/Operations/convX.var". -inline "cic:/CoRN/reals/Series/Operations/convY.var" "Operations__". +alias id "convY" = "cic:/CoRN/reals/Series/Operations/convY.var". inline "cic:/CoRN/reals/Series/convergent_wd.con". @@ -190,7 +190,7 @@ inline "cic:/CoRN/reals/Series/series_sum_minus.con". (*#* Multiplication by a scalar [c] is also permitted. *) -inline "cic:/CoRN/reals/Series/Operations/c.var" "Operations__". +alias id "c" = "cic:/CoRN/reals/Series/Operations/c.var". inline "cic:/CoRN/reals/Series/conv_series_mult_scal.con". @@ -204,9 +204,9 @@ End Operations Section More_Operations *) -inline "cic:/CoRN/reals/Series/More_Operations/x.var" "More_Operations__". +alias id "x" = "cic:/CoRN/reals/Series/More_Operations/x.var". -inline "cic:/CoRN/reals/Series/More_Operations/convX.var" "More_Operations__". +alias id "convX" = "cic:/CoRN/reals/Series/More_Operations/convX.var". (*#* As a corollary, we get the series of the inverses. *) @@ -230,13 +230,13 @@ and derive an important corollary for series. Let [x,y : nat->IR] be equal after some natural number. *) -inline "cic:/CoRN/reals/Series/Almost_Everywhere/x.var" "Almost_Everywhere__". +alias id "x" = "cic:/CoRN/reals/Series/Almost_Everywhere/x.var". -inline "cic:/CoRN/reals/Series/Almost_Everywhere/y.var" "Almost_Everywhere__". +alias id "y" = "cic:/CoRN/reals/Series/Almost_Everywhere/y.var". inline "cic:/CoRN/reals/Series/aew_eq.con". -inline "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var" "Almost_Everywhere__". +alias id "aew_equal" = "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var". inline "cic:/CoRN/reals/Series/aew_Cauchy.con". @@ -254,11 +254,11 @@ Section Cauchy_Almost_Everywhere (*#* Suppose furthermore that [x,y] are Cauchy sequences. *) -inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var" "Cauchy_Almost_Everywhere__". +alias id "x" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var". -inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var" "Cauchy_Almost_Everywhere__". +alias id "y" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var". -inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var" "Cauchy_Almost_Everywhere__". +alias id "aew_equal" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var". inline "cic:/CoRN/reals/Series/aew_Lim.con". @@ -276,7 +276,7 @@ Section Convergence_Criteria %\end{convention}% *) -inline "cic:/CoRN/reals/Series/Convergence_Criteria/x.var" "Convergence_Criteria__". +alias id "x" = "cic:/CoRN/reals/Series/Convergence_Criteria/x.var". (*#* We include the comparison test for series, both in a strong and in a less general (but simpler) form. @@ -306,7 +306,7 @@ End Convergence_Criteria Section More_CC *) -inline "cic:/CoRN/reals/Series/More_CC/x.var" "More_CC__". +alias id "x" = "cic:/CoRN/reals/Series/More_CC/x.var". inline "cic:/CoRN/reals/Series/ratio_test_conv.con". @@ -326,13 +326,13 @@ Alternate series are a special case. Suppose that [x] is nonnegative and decreasing convergent to 0. *) -inline "cic:/CoRN/reals/Series/Alternate_Series/x.var" "Alternate_Series__". +alias id "x" = "cic:/CoRN/reals/Series/Alternate_Series/x.var". -inline "cic:/CoRN/reals/Series/Alternate_Series/pos_x.var" "Alternate_Series__". +alias id "pos_x" = "cic:/CoRN/reals/Series/Alternate_Series/pos_x.var". -inline "cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var" "Alternate_Series__". +alias id "Lim_x" = "cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var". -inline "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var" "Alternate_Series__". +alias id "mon_x" = "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var". (* begin hide *)