<?xml version="1.0"?>
<div class="add">

<a NAME="E1:82_1_1"/>
for <font color="Olive" title="b1">x</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  &amp;  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  holds <br/><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T33" title="SIN_COS:th.33">SIN_COS:33</a></span>;<br/>
<a NAME="E2:82_1_1"/><span class="kw">then </span>
(  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  is  <a href="funct_8.html#V2" title="FUNCT_8:attr.2">with_symmetrical_domain</a>  &amp;  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  is  <a href="funct_8.html#V3" title="FUNCT_8:attr.3">quasi_even</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_8.html#D2" target="_self" title="FUNCT_8:def.2">Def2</a>, <a class="ref" href="funct_8.html#D3" target="_self" title="FUNCT_8:def.3">Def3</a>, <a class="ref" href="sin_cos.html#T27" title="SIN_COS:th.27">SIN_COS:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:82_1_1"/>
 <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  is  <a href="funct_8.html#V4" title="FUNCT_8:attr.4">even</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
