X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fftc%2FTaylorLemma.ma;h=29affb739515d7d80cd8e5b025bb50021df82984;hb=5e01cba364607e7937aec2e359c34f049bb0f108;hp=0fc55435693aa1bf35bf4473bf809ce3efd82d03;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma index 0fc554356..29affb739 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma @@ -16,18 +16,18 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/TaylorLemma". +include "CoRN.ma". + (* $Id: TaylorLemma.v,v 1.8 2004/04/23 10:01:01 lcf Exp $ *) -(* INCLUDE -Rolle -*) +include "ftc/Rolle.ma". (* UNEXPORTED Opaque Min. *) (* UNEXPORTED -Section Taylor_Defs. +Section Taylor_Defs *) (*#* *Taylor's Theorem @@ -44,31 +44,31 @@ define the nth order derivative of [F] in the interval [[Min(a,b),Max(a,b)]]. *) -inline cic:/CoRN/ftc/TaylorLemma/a.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/b.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/Hap.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var" "Taylor_Defs__". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/Hab'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/Hab.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/I.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__". (* end hide *) -inline cic:/CoRN/ftc/TaylorLemma/F.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/Ha.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/Hb.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var" "Taylor_Defs__". (* begin show *) -inline cic:/CoRN/ftc/TaylorLemma/fi.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__". (* end show *) @@ -79,7 +79,7 @@ $f_i=f^{(i)}$#fi=f(i)#. (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con". (* end hide *) @@ -94,41 +94,49 @@ corresponding to [a] and [b]. (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/TL_compact_a.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__". + +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/TL_compact_b.con. +(* NOTATION +Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a). +*) + +(* NOTATION +Notation B := (Build_subcsetoid_crr IR _ _ TL_compact_b). +*) (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/TaylorLemma/funct_i.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__". (* end show *) (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/funct_i'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/TL_a_i.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con". -inline cic:/CoRN/ftc/TaylorLemma/TL_b_i.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con". -inline cic:/CoRN/ftc/TaylorLemma/TL_x_i.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con". -inline cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con". -inline cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con". -inline cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con". -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con". -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con". -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con". -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con". (* end hide *) @@ -137,13 +145,13 @@ Adding the previous expressions up to a given bound [n] gives us the Taylor sum of order [n]. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'_aux.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con". (* end hide *) @@ -151,21 +159,21 @@ inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con. It is easy to show that [b] is in the domain of this series, which allows us to write down the Taylor remainder around [b]. *) -inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con". -inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con". (* end hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/g.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__". (* UNEXPORTED Opaque Taylor_seq'_aux Taylor_rem. @@ -191,7 +199,7 @@ Opaque funct_i'. Opaque funct_i. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con". (* UNEXPORTED Transparent funct_i funct_i'. @@ -213,15 +221,15 @@ Opaque FSumx. Opaque funct_i'. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con". (* UNEXPORTED Transparent funct_i' FSumx. *) -inline cic:/CoRN/ftc/TaylorLemma/funct_aux.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con". (* UNEXPORTED Ltac Lazy_Included := @@ -245,9 +253,9 @@ Ltac Lazy_Eq := | apply csf_wd_unfolded ]; Algebra. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con". -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con". (* UNEXPORTED Opaque funct_aux. @@ -257,15 +265,15 @@ Opaque funct_aux. Transparent funct_aux. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con". -inline cic:/CoRN/ftc/TaylorLemma/g'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__". (* UNEXPORTED Opaque Taylor_rem funct_aux. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con". (* UNEXPORTED Transparent Taylor_rem funct_aux. @@ -280,25 +288,25 @@ Now Taylor's theorem. %\end{convention}% *) -inline cic:/CoRN/ftc/TaylorLemma/e.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var" "Taylor_Defs__". -inline cic:/CoRN/ftc/TaylorLemma/He.var. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var" "Taylor_Defs__". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__". (* end show *) (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/TLH.con. +inline "cic:/CoRN/ftc/TaylorLemma/TLH.con". (* end hide *) @@ -314,9 +322,9 @@ Opaque Taylor_rem. Transparent Taylor_rem funct_aux. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con". (* UNEXPORTED -End Taylor_Defs. +End Taylor_Defs *)