X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FSinCos.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FSinCos.ma;h=314d0f5fa686496b7232784a91871434ce2fd2eb;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/transc/SinCos.ma b/matita/contribs/CoRN-Decl/transc/SinCos.ma new file mode 100644 index 000000000..314d0f5fa --- /dev/null +++ b/matita/contribs/CoRN-Decl/transc/SinCos.ma @@ -0,0 +1,176 @@ +(**************************************************************************) +(* ___ *) +(* ||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/SinCos". + +include "CoRN.ma". + +(* $Id: SinCos.v,v 1.6 2004/04/23 10:01:08 lcf Exp $ *) + +include "transc/Trigonometric.ma". + +(* UNEXPORTED +Section Sum_and_so_on +*) + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +(* begin hide *) + +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__". + +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__". + +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__". + +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__". + +(* end hide *) + +inline "cic:/CoRN/transc/SinCos/Sin_plus.con". + +inline "cic:/CoRN/transc/SinCos/Cos_plus.con". + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +(* UNEXPORTED +Hint Resolve Cos_plus Sin_plus: algebra. +*) + +(*#* As a corollary we get the rule for the tangent of the sum. *) + +inline "cic:/CoRN/transc/SinCos/Tan_plus.con". + +(* UNEXPORTED +Transparent Sine Cosine. +*) + +(*#* Sine, cosine and tangent of [[--]x]. *) + +inline "cic:/CoRN/transc/SinCos/Cos_inv.con". + +inline "cic:/CoRN/transc/SinCos/Sin_inv.con". + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +(* UNEXPORTED +Hint Resolve Cos_inv Sin_inv: algebra. +*) + +inline "cic:/CoRN/transc/SinCos/Tan_inv.con". + +(* UNEXPORTED +Transparent Sine Cosine. +*) + +(*#* +The fundamental formulas of trigonometry: $\cos(x)^2+\sin(x)^2=1$#cos(x)2+sin(x)2=1# and, equivalently, $1+\tan(x)^2=\frac1{\cos(x)^2}$#1+tan(x)2=1/(cos(x)2)#. +*) + +(* UNEXPORTED +Hint Resolve Cos_zero: algebra. +*) + +inline "cic:/CoRN/transc/SinCos/FFT.con". + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +(* UNEXPORTED +Hint Resolve FFT: algebra. +*) + +inline "cic:/CoRN/transc/SinCos/FFT'.con". + +(* UNEXPORTED +End Sum_and_so_on +*) + +(* UNEXPORTED +Hint Resolve Derivative_Sin Derivative_Cos: derivate. +*) + +(* UNEXPORTED +Hint Resolve Continuous_Sin Continuous_Cos: continuous. +*) + +(* UNEXPORTED +Hint Resolve Sin_zero Cos_zero Tan_zero Sin_plus Cos_plus Tan_plus Sin_inv + Cos_inv Tan_inv FFT FFT': algebra. +*) + +(* UNEXPORTED +Opaque Min Sine Cosine. +*) + +(* UNEXPORTED +Section Basic_Properties +*) + +(*#* **Basic properties + +We now prove most of the usual trigonometric (in)equalities. + +Sine, cosine and tangent are strongly extensional and well defined. +*) + +inline "cic:/CoRN/transc/SinCos/Sin_strext.con". + +inline "cic:/CoRN/transc/SinCos/Cos_strext.con". + +inline "cic:/CoRN/transc/SinCos/Tan_strext.con". + +inline "cic:/CoRN/transc/SinCos/Sin_wd.con". + +inline "cic:/CoRN/transc/SinCos/Cos_wd.con". + +inline "cic:/CoRN/transc/SinCos/Tan_wd.con". + +(*#* +The sine and cosine produce values in [[-1,1]]. +*) + +inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con". + +inline "cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con". + +inline "cic:/CoRN/transc/SinCos/Sin_leEq_One.con". + +inline "cic:/CoRN/transc/SinCos/Cos_leEq_One.con". + +(*#* +If the cosine is positive then the sine is in [(-1,1)]. +*) + +inline "cic:/CoRN/transc/SinCos/Sin_less_One.con". + +inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con". + +(* UNEXPORTED +End Basic_Properties +*) + +(* UNEXPORTED +Hint Resolve Sin_wd Cos_wd Tan_wd: algebra. +*) +