set "baseuri" "cic:/matita/CoRN-Decl/reals/IVT".
+include "CoRN.ma".
+
(* $Id: IVT.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
-(* INCLUDE
-CPoly_Contin
-*)
+include "reals/CPoly_Contin.ma".
(* UNEXPORTED
-Section Nested_Intervals.
+Section Nested_Intervals
*)
(*#* * Intermediate Value Theorem
%\end{convention}%
*)
-inline cic:/CoRN/reals/IVT/a.var.
+alias id "a" = "cic:/CoRN/reals/IVT/Nested_Intervals/a.var".
-inline cic:/CoRN/reals/IVT/b.var.
+alias id "b" = "cic:/CoRN/reals/IVT/Nested_Intervals/b.var".
-inline cic:/CoRN/reals/IVT/a_mon.var.
+alias id "a_mon" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var".
-inline cic:/CoRN/reals/IVT/b_mon.var.
+alias id "b_mon" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var".
-inline cic:/CoRN/reals/IVT/a_b.var.
+alias id "a_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var".
-inline cic:/CoRN/reals/IVT/b_a.var.
+alias id "b_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var".
-inline cic:/CoRN/reals/IVT/a_mon'.con.
+inline "cic:/CoRN/reals/IVT/a_mon'.con".
-inline cic:/CoRN/reals/IVT/b_mon'.con.
+inline "cic:/CoRN/reals/IVT/b_mon'.con".
-inline cic:/CoRN/reals/IVT/a_b'.con.
+inline "cic:/CoRN/reals/IVT/a_b'.con".
-inline cic:/CoRN/reals/IVT/intervals_cauchy.con.
+inline "cic:/CoRN/reals/IVT/intervals_cauchy.con".
(* begin hide *)
-inline cic:/CoRN/reals/IVT/a'.con.
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__".
(* end hide *)
-inline cic:/CoRN/reals/IVT/Cnested_intervals_limit.con.
+inline "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con".
(*#* %\begin{convention}% Let [f] be a continuous real function.
%\end{convention}%
*)
-inline cic:/CoRN/reals/IVT/f.var.
+alias id "f" = "cic:/CoRN/reals/IVT/Nested_Intervals/f.var".
-inline cic:/CoRN/reals/IVT/f_contin.var.
+alias id "f_contin" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var".
-inline cic:/CoRN/reals/IVT/f_contin_pos.con.
+inline "cic:/CoRN/reals/IVT/f_contin_pos.con".
-inline cic:/CoRN/reals/IVT/f_contin_neg.con.
+inline "cic:/CoRN/reals/IVT/f_contin_neg.con".
(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *)
-inline cic:/CoRN/reals/IVT/f_a.var.
+alias id "f_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var".
-inline cic:/CoRN/reals/IVT/f_b.var.
+alias id "f_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var".
-inline cic:/CoRN/reals/IVT/Cnested_intervals_zero.con.
+inline "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con".
(* UNEXPORTED
-End Nested_Intervals.
+End Nested_Intervals
*)
(* UNEXPORTED
-Section Bisection.
+Section Bisection
*)
(*#* ** Bissections *)
-inline cic:/CoRN/reals/IVT/f.var.
+alias id "f" = "cic:/CoRN/reals/IVT/Bisection/f.var".
-inline cic:/CoRN/reals/IVT/f_apzero_interval.var.
+alias id "f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var".
-inline cic:/CoRN/reals/IVT/a.var.
+alias id "a" = "cic:/CoRN/reals/IVT/Bisection/a.var".
-inline cic:/CoRN/reals/IVT/b.var.
+alias id "b" = "cic:/CoRN/reals/IVT/Bisection/b.var".
-inline cic:/CoRN/reals/IVT/a_b.var.
+alias id "a_b" = "cic:/CoRN/reals/IVT/Bisection/a_b.var".
-inline cic:/CoRN/reals/IVT/f_a.var.
+alias id "f_a" = "cic:/CoRN/reals/IVT/Bisection/f_a.var".
-inline cic:/CoRN/reals/IVT/f_b.var.
+alias id "f_b" = "cic:/CoRN/reals/IVT/Bisection/f_b.var".
(*#*
%\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ].
(* begin hide *)
-inline cic:/CoRN/reals/IVT/Small.con.
+inline "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__".
-inline cic:/CoRN/reals/IVT/lft.con.
+inline "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__".
-inline cic:/CoRN/reals/IVT/rht.con.
+inline "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__".
(* end hide *)
-inline cic:/CoRN/reals/IVT/a_lft.con.
+inline "cic:/CoRN/reals/IVT/a_lft.con".
-inline cic:/CoRN/reals/IVT/rht_b.con.
+inline "cic:/CoRN/reals/IVT/rht_b.con".
-inline cic:/CoRN/reals/IVT/lft_rht.con.
+inline "cic:/CoRN/reals/IVT/lft_rht.con".
-inline cic:/CoRN/reals/IVT/smaller_lft.con.
+inline "cic:/CoRN/reals/IVT/smaller_lft.con".
-inline cic:/CoRN/reals/IVT/smaller_rht.con.
+inline "cic:/CoRN/reals/IVT/smaller_rht.con".
(* UNEXPORTED
Hint Resolve smaller_lft smaller_rht: algebra.
*)
-inline cic:/CoRN/reals/IVT/Cbisect'.con.
+inline "cic:/CoRN/reals/IVT/Cbisect'.con".
(* UNEXPORTED
-End Bisection.
+End Bisection
*)
(* UNEXPORTED
-Section Bisect_Interval.
+Section Bisect_Interval
*)
-inline cic:/CoRN/reals/IVT/f.var.
+alias id "f" = "cic:/CoRN/reals/IVT/Bisect_Interval/f.var".
-inline cic:/CoRN/reals/IVT/C_f_apzero_interval.var.
+alias id "C_f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var".
(* begin hide *)
-inline cic:/CoRN/reals/IVT/Small.con.
+inline "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__".
(* end hide *)
-inline cic:/CoRN/reals/IVT/bisect_interval.ind.
+inline "cic:/CoRN/reals/IVT/bisect_interval.ind".
-inline cic:/CoRN/reals/IVT/Cbisect_exists.con.
+inline "cic:/CoRN/reals/IVT/Cbisect_exists.con".
-inline cic:/CoRN/reals/IVT/bisect.con.
+inline "cic:/CoRN/reals/IVT/bisect.con".
-inline cic:/CoRN/reals/IVT/bisect_prop.con.
+inline "cic:/CoRN/reals/IVT/bisect_prop.con".
(* UNEXPORTED
-End Bisect_Interval.
+End Bisect_Interval
*)
(* UNEXPORTED
-Section IVT_Op.
+Section IVT_Op
*)
(*#* ** IVT for operations
Same conventions as before.
*)
-inline cic:/CoRN/reals/IVT/f.var.
+alias id "f" = "cic:/CoRN/reals/IVT/IVT_Op/f.var".
-inline cic:/CoRN/reals/IVT/f_contin.var.
+alias id "f_contin" = "cic:/CoRN/reals/IVT/IVT_Op/f_contin.var".
-inline cic:/CoRN/reals/IVT/f_apzero_interval.var.
+alias id "f_apzero_interval" = "cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var".
-inline cic:/CoRN/reals/IVT/a.var.
+alias id "a" = "cic:/CoRN/reals/IVT/IVT_Op/a.var".
-inline cic:/CoRN/reals/IVT/b.var.
+alias id "b" = "cic:/CoRN/reals/IVT/IVT_Op/b.var".
-inline cic:/CoRN/reals/IVT/a_b.var.
+alias id "a_b" = "cic:/CoRN/reals/IVT/IVT_Op/a_b.var".
-inline cic:/CoRN/reals/IVT/f_a.var.
+alias id "f_a" = "cic:/CoRN/reals/IVT/IVT_Op/f_a.var".
-inline cic:/CoRN/reals/IVT/f_b.var.
+alias id "f_b" = "cic:/CoRN/reals/IVT/IVT_Op/f_b.var".
(* begin hide *)
-inline cic:/CoRN/reals/IVT/Small.con.
+inline "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__".
(* end hide *)
-inline cic:/CoRN/reals/IVT/interval_sequence.con.
+inline "cic:/CoRN/reals/IVT/interval_sequence.con".
-inline cic:/CoRN/reals/IVT/a_.con.
+inline "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__".
-inline cic:/CoRN/reals/IVT/b_.con.
+inline "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__".
-inline cic:/CoRN/reals/IVT/intervals_smaller.con.
+inline "cic:/CoRN/reals/IVT/intervals_smaller.con".
-inline cic:/CoRN/reals/IVT/intervals_small''.con.
+inline "cic:/CoRN/reals/IVT/intervals_small''.con".
-inline cic:/CoRN/reals/IVT/intervals_small'.con.
+inline "cic:/CoRN/reals/IVT/intervals_small'.con".
-inline cic:/CoRN/reals/IVT/intervals_small.con.
+inline "cic:/CoRN/reals/IVT/intervals_small.con".
-inline cic:/CoRN/reals/IVT/Civt_op.con.
+inline "cic:/CoRN/reals/IVT/Civt_op.con".
(* UNEXPORTED
-End IVT_Op.
+End IVT_Op
*)
(* UNEXPORTED
-Section IVT_Poly.
+Section IVT_Poly
*)
(*#* ** IVT for polynomials *)
-inline cic:/CoRN/reals/IVT/Civt_poly.con.
+inline "cic:/CoRN/reals/IVT/Civt_poly.con".
(* UNEXPORTED
-End IVT_Poly.
+End IVT_Poly
*)