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<a NAME="E1:81_1_1"/>
 for <font color="Olive" title="b1">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0: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#K18" title="SIN_COS:func.18">cos</a> &amp;  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</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#K18" title="SIN_COS:func.18">cos</a> holds <br/><a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</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#K18" title="SIN_COS:func.18">cos</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T30" onmouseover="rs('sin_cos/T30')" onmouseout="rh()">SIN_COS:30</a></span>;<br/>
<a NAME="E2:81_1_1"/><span class="kw">then </span>
(  <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a>  is  <a href="funct_8.html#V2" title="FUNCT_8:attr.2">with_symmetrical_domain</a>  &amp;  <a href="sin_cos.html#K18" title="SIN_COS:func.18">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="sin_cos.html#T24" onmouseover="rs('sin_cos/T24')" onmouseout="rh()">SIN_COS:24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:81_1_1"/>
 <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a>  is  <a href="funct_8.html#V4" title="FUNCT_8:attr.4">even</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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