X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2Fprocedural%2FCoRN%2Freals%2FIVT.mma;fp=matitaB%2Fmatita%2Fcontribs%2Fprocedural%2FCoRN%2Freals%2FIVT.mma;h=b44cbcc441f524dc800d53e2fd57b81df5869d46;hb=cacbe3c6493ddce76c4c13379ade271d8dd172e8;hp=0000000000000000000000000000000000000000;hpb=f04a064bb34aabaf91dc0c48e3b08b37ecd7b0a2;p=helm.git diff --git a/matitaB/matita/contribs/procedural/CoRN/reals/IVT.mma b/matitaB/matita/contribs/procedural/CoRN/reals/IVT.mma new file mode 100644 index 000000000..b44cbcc44 --- /dev/null +++ b/matitaB/matita/contribs/procedural/CoRN/reals/IVT.mma @@ -0,0 +1,288 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *********************) + +include "CoRN.ma". + +(* $Id: IVT.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *) + +include "reals/CPoly_Contin.ma". + +(* UNEXPORTED +Section Nested_Intervals +*) + +(*#* * Intermediate Value Theorem + +** Nested intervals + +%\begin{convention}% Let [a,b:nat->IR] be sequences such that: +- [a] is increasing; +- [b] is decreasing; +- [forall (i:nat), (a i) [<] (b i)]; +- for every positive real number [eps], there is an [i] such that [(b i) [<] (a i) [+]eps]. + +%\end{convention}% +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/a.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/b.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var +*) + +inline procedural "cic:/CoRN/reals/IVT/a_mon'.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/b_mon'.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/a_b'.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/intervals_cauchy.con" as lemma. + +(* begin hide *) + +inline procedural "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__" as definition. + +(* end hide *) + +inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con" as lemma. + +(*#* %\begin{convention}% Let [f] be a continuous real function. +%\end{convention}% +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var +*) + +inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/f_contin_neg.con" as lemma. + +(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var +*) + +inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con" as lemma. + +(* UNEXPORTED +End Nested_Intervals +*) + +(* UNEXPORTED +Section Bisection +*) + +(*#* ** Bissections *) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/a.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/b.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/a_b.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f_a.var +*) + +(* UNEXPORTED +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]. +%\end{convention}% +*) + +(* begin hide *) + +inline procedural "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__" as definition. + +inline procedural "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__" as definition. + +inline procedural "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__" as definition. + +(* end hide *) + +inline procedural "cic:/CoRN/reals/IVT/a_lft.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/rht_b.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/lft_rht.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/smaller_lft.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/smaller_rht.con" as lemma. + +(* UNEXPORTED +Hint Resolve smaller_lft smaller_rht: algebra. +*) + +inline procedural "cic:/CoRN/reals/IVT/Cbisect'.con" as lemma. + +(* UNEXPORTED +End Bisection +*) + +(* UNEXPORTED +Section Bisect_Interval +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisect_Interval/f.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var +*) + +(* begin hide *) + +inline procedural "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__" as definition. + +(* end hide *) + +inline procedural "cic:/CoRN/reals/IVT/bisect_interval.ind". + +inline procedural "cic:/CoRN/reals/IVT/Cbisect_exists.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/bisect.con" as definition. + +inline procedural "cic:/CoRN/reals/IVT/bisect_prop.con" as lemma. + +(* UNEXPORTED +End Bisect_Interval +*) + +(* UNEXPORTED +Section IVT_Op +*) + +(*#* ** IVT for operations +Same conventions as before. +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_contin.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/a.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/b.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/a_b.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_a.var +*) + +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_b.var +*) + +(* begin hide *) + +inline procedural "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__" as definition. + +(* end hide *) + +inline procedural "cic:/CoRN/reals/IVT/interval_sequence.con" as definition. + +inline procedural "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__" as definition. + +inline procedural "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__" as definition. + +inline procedural "cic:/CoRN/reals/IVT/intervals_smaller.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/intervals_small''.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/intervals_small'.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/intervals_small.con" as lemma. + +inline procedural "cic:/CoRN/reals/IVT/Civt_op.con" as lemma. + +(* UNEXPORTED +End IVT_Op +*) + +(* UNEXPORTED +Section IVT_Poly +*) + +(*#* ** IVT for polynomials *) + +inline procedural "cic:/CoRN/reals/IVT/Civt_poly.con" as lemma. + +(* UNEXPORTED +End IVT_Poly +*) +