X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fftc%2FCalculusTheorems.ma;h=37510497572b983fe86912bdbc592fd981b6d3f7;hb=0a9ed4329c069d2e06902934b6d1d58d3690959c;hp=57fcf425c0f42fcc59e3f3640b4998437b1a5001;hpb=0e0d5c57eb154bf20d101f09e560401434156c1d;p=helm.git diff --git a/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma b/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma index 57fcf425c..375104975 100644 --- a/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma +++ b/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma @@ -16,22 +16,20 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/CalculusTheorems". +include "CoRN.ma". + (* $Id: CalculusTheorems.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *) -(* INCLUDE -Rolle -*) +include "ftc/Rolle.ma". -(* INCLUDE -DiffTactics3 -*) +include "tactics/DiffTactics3.ma". (* UNEXPORTED Opaque Min Max. *) (* UNEXPORTED -Section Various_Theorems. +Section Various_Theorems *) (*#* *Calculus Theorems @@ -45,52 +43,52 @@ continuous function commutes with the limit of a numerical sequence (sometimes called Heine continuity). *) -inline cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con". (*#* This is a tricky result: if [F] is continuous and positive in both [[a,b]] and [(b,c]], then it is positive in [[a,c]]. *) -inline cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con". (*#* Similar results for increasing functions: *) -inline cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con. +inline "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con". -inline cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con. +inline "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con". -inline cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con. +inline "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con". -inline cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con. +inline "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con". (*#* More on glueing intervals. *) -inline cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con. +inline "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con". -inline cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con. +inline "cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con". -inline cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con. +inline "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con". (*#* Any function that has the null function as its derivative must be constant. *) -inline cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con. +inline "cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con". (*#* As a corollary, two functions with the same derivative must differ by a constant. *) -inline cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con". (*#* This yields the following known result: any differential equation of the form [f'=g] with initial condition [f(a) [=] b] has a unique solution. *) -inline cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con". (*#* Finally, a well known result: any function with a (strictly) positive @@ -99,11 +97,11 @@ quite similar the proofs are completely different, both from the formalization and from the mathematical point of view. *) -inline cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con". -inline cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con". -inline cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con". (*#* From these results we can finally prove that exponentiation to a real power preserves the less or equal than relation! @@ -117,9 +115,9 @@ Opaque nring. Transparent nring. *) -inline cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con. +inline "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con". (* UNEXPORTED -End Various_Theorems. +End Various_Theorems *)