X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FInvTrigonom.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FInvTrigonom.ma;h=73a386b025cbdac4eb516739284fc0e5e40b6629;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma b/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma new file mode 100644 index 000000000..73a386b02 --- /dev/null +++ b/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma @@ -0,0 +1,296 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *********************) + +set "baseuri" "cic:/matita/CoRN-Decl/transc/InvTrigonom". + +include "CoRN.ma". + +(* $Id: InvTrigonom.v,v 1.9 2004/04/23 10:01:07 lcf Exp $ *) + +include "transc/RealPowers.ma". + +include "transc/TrigMon.ma". + +include "ftc/StrongIVT.ma". + +(*#* printing ArcSin %\ensuremath{\arcsin}% *) + +(*#* printing ArcCos %\ensuremath{\arccos}% *) + +(*#* printing ArcTan %\ensuremath{\arctan}% *) + +(*#* *Inverse Trigonometric Functions + +**Definitions + +We will now define arcsine, arccosine and arctangent as indefinite +integrals and prove their main properties. We begin by proving that +the appropriate indefinite integrals can be defined, then prove the +main properties of the function. + +Arccosine is defined in terms of arcsine by the relation +[ArcCos(x)=Pi[/]Two-ArcSin(x)]. + +***Arcsine +*) + +(* UNEXPORTED +Opaque Sine Cosine Expon Logarithm. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con". + +inline "cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con". + +inline "cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con". + +(* UNEXPORTED +Hint Resolve Derivative_ArcSin: derivate. +*) + +(* UNEXPORTED +Hint Resolve Continuous_ArcSin: continuous. +*) + +(*#* ***Arccosine +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcCos.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con". + +inline "cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con". + +inline "cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con". + +(*#* ***Arctangent +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcTang.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan.con". + +inline "cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con". + +inline "cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con". + +(* UNEXPORTED +Hint Resolve Derivative_ArcCos Derivative_ArcTan: derivate. +*) + +(* UNEXPORTED +Hint Resolve Continuous_ArcCos Continuous_ArcTan: continuous. +*) + +(* UNEXPORTED +Section Inverses +*) + +(*#* **Composition properties + +We now prove that this functions are in fact inverses to the corresponding trigonometric functions. + +***Sine and Arcsine +*) + +inline "cic:/CoRN/transc/InvTrigonom/maps_Sin.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con". + +(* UNEXPORTED +Opaque ArcSin. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con". + +(* UNEXPORTED +Transparent ArcSin. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con". + +(* UNEXPORTED +Transparent ArcSin. +*) + +inline "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con". + +inline "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con". + +(*#* ***Cosine and Arcosine +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con". + +inline "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con". + +inline "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con". + +inline "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con". + +(* UNEXPORTED +Opaque ArcSin. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con". + +(*#* ***Tangent and Arctangent +*) + +inline "cic:/CoRN/transc/InvTrigonom/maps_Tan.con". + +(* UNEXPORTED +Opaque Tang. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con". + +(* UNEXPORTED +Transparent Tang. +*) + +(* UNEXPORTED +Opaque ArcTang. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con". + +(* UNEXPORTED +Opaque iprop. +*) + +(* UNEXPORTED +Transparent iprop. +*) + +(* UNEXPORTED +Opaque Cos. +*) + +inline "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con". + +(* UNEXPORTED +Opaque Min. +*) + +(* UNEXPORTED +Transparent Cos. +*) + +(* UNEXPORTED +Section ArcTan_Range +*) + +alias id "x" = "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var". + +(* begin hide *) + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__". + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con". + +(* end hide *) + +(* UNEXPORTED +Transparent ArcTang. +*) + +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con". + +(* UNEXPORTED +End ArcTan_Range +*) + +(* UNEXPORTED +Transparent ArcTang. +*) + +inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con". + +(* UNEXPORTED +Opaque ArcTang. +*) + +inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con". + +(* UNEXPORTED +End Inverses +*) +