X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FTrigonometric.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FTrigonometric.ma;h=3498c20a84646c654bb8108a9cdb780e2fe423e7;hb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;hp=0000000000000000000000000000000000000000;hpb=438a29376390222b94c1fe9772917c3aad50d42e;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma b/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma new file mode 100644 index 000000000..3498c20a8 --- /dev/null +++ b/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma @@ -0,0 +1,216 @@ +(**************************************************************************) +(* ___ *) +(* ||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/Trigonometric". + +(* $Id: Trigonometric.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *) + +(* INCLUDE +TaylorSeries +*) + +(*#* *The Trigonometric Functions + +In this section, we explore the properties of the trigonometric functions which we previously defined. +*) + +(* UNEXPORTED +Section Lemmas. +*) + +(*#* First, we need a lemma on mappings. *) + +inline cic:/CoRN/transc/Trigonometric/maps_translation.con. + +(* UNEXPORTED +End Lemmas. +*) + +(* UNEXPORTED +Section Sine_and_Cosine. +*) + +(*#* Sine, cosine and tangent at [Zero]. *) + +inline cic:/CoRN/transc/Trigonometric/Sin_zero.con. + +inline cic:/CoRN/transc/Trigonometric/Cos_zero.con. + +(* UNEXPORTED +Hint Resolve Sin_zero Cos_zero: algebra. +*) + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +inline cic:/CoRN/transc/Trigonometric/Tan_zero.con. + +(* UNEXPORTED +Transparent Sine Cosine. +*) + +(*#* +Continuity of sine and cosine are trivial. +*) + +inline cic:/CoRN/transc/Trigonometric/Continuous_Sin.con. + +inline cic:/CoRN/transc/Trigonometric/Continuous_Cos.con. + +(*#* +The rules for the derivative of the sine and cosine function; we begin by proving that their defining sequences can be expressed in terms of one another. +*) + +inline cic:/CoRN/transc/Trigonometric/cos_sin_seq.con. + +inline cic:/CoRN/transc/Trigonometric/sin_cos_seq.con. + +inline cic:/CoRN/transc/Trigonometric/Derivative_Sin.con. + +inline cic:/CoRN/transc/Trigonometric/Derivative_Cos.con. + +(* UNEXPORTED +Hint Resolve Derivative_Sin Derivative_Cos: derivate. +*) + +(* UNEXPORTED +Hint Resolve Continuous_Sin Continuous_Cos: continuous. +*) + +(* UNEXPORTED +Section Sine_of_Sum. +*) + +(*#* +We now prove the rule for the sine and cosine of the sum. These rules +have to be proved first as functional equalities, which is why we also +state the results in a function form (which we won't do in other +situations). + +%\begin{convention}% Let: + - [F := fun y => Sine[o] (FId{+} [-C-]y)]; + - [G := fun y => (Sine{*} [-C-] (Cos y)) {+} (Cosine{*} [-C-] (Sin y))]. + +%\end{convention}% +*) + +(* begin hide *) + +inline cic:/CoRN/transc/Trigonometric/F.con. + +inline cic:/CoRN/transc/Trigonometric/G.con. + +inline cic:/CoRN/transc/Trigonometric/F'.con. + +inline cic:/CoRN/transc/Trigonometric/G'.con. + +(* end hide *) + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +inline cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con. + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +(* UNEXPORTED +Opaque FAbs. +*) + +(* UNEXPORTED +Transparent FAbs. +*) + +inline cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con. + +inline cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con. + +inline cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con. + +inline cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con. + +inline cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con. + +(* UNEXPORTED +End Sine_of_Sum. +*) + +(* UNEXPORTED +Opaque Sine Cosine. +*) + +inline cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con. + +(* UNEXPORTED +End Sine_and_Cosine. +*) +