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.
+Section More_Cauchy_Props
*)
(*#* **Miscellaneous
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.
+End More_Cauchy_Props
*)
(* UNEXPORTED
-Section Subsequences.
+Section Subsequences
*)
(*#* *** Subsequences
[seq2] is monotonous.
*)
-inline cic:/CoRN/reals/CReals1/seq1.var.
+alias id "seq1" = "cic:/CoRN/reals/CReals1/Subsequences/seq1.var".
-inline cic:/CoRN/reals/CReals1/seq2.var.
+alias id "seq2" = "cic:/CoRN/reals/CReals1/Subsequences/seq2.var".
-inline cic:/CoRN/reals/CReals1/f.var.
+alias id "f" = "cic:/CoRN/reals/CReals1/Subsequences/f.var".
-inline cic:/CoRN/reals/CReals1/monF.var.
+alias id "monF" = "cic:/CoRN/reals/CReals1/Subsequences/monF.var".
-inline cic:/CoRN/reals/CReals1/crescF.var.
+alias id "crescF" = "cic:/CoRN/reals/CReals1/Subsequences/crescF.var".
-inline cic:/CoRN/reals/CReals1/subseq.var.
+alias id "subseq" = "cic:/CoRN/reals/CReals1/Subsequences/subseq.var".
-inline cic:/CoRN/reals/CReals1/mon_seq2.var.
+alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Subsequences/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/Subsequences/mon_F'.con" "Subsequences__".
(* 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.
+End Subsequences
*)
(* UNEXPORTED
-Section Cauchy_Subsequences.
+Section Cauchy_Subsequences
*)
-inline cic:/CoRN/reals/CReals1/seq1.var.
+alias id "seq1" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var".
-inline cic:/CoRN/reals/CReals1/seq2.var.
+alias id "seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var".
-inline cic:/CoRN/reals/CReals1/f.var.
+alias id "f" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var".
-inline cic:/CoRN/reals/CReals1/monF.var.
+alias id "monF" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var".
-inline cic:/CoRN/reals/CReals1/crescF.var.
+alias id "crescF" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var".
-inline cic:/CoRN/reals/CReals1/subseq.var.
+alias id "subseq" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var".
-inline cic:/CoRN/reals/CReals1/mon_seq2.var.
+alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/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.
+End Cauchy_Subsequences
*)
(* UNEXPORTED
-Section Properties_of_Exponentiation.
+Section Properties_of_Exponentiation
*)
(*#* *** More 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.
+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".