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 for <font color="Olive" title="b1">x</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> holds <br/>( <font color="Olive" title="b1">x</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> &amp; <font color="Olive" title="b1">x</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> &amp; <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T24" title="SIN_COS:th.24">SIN_COS:24</a>, <a class="ref" href="sin_cos.html#T78" title="SIN_COS:th.78">SIN_COS:78</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:29"/>
 <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a>  is 2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="funct_9.html#V1" title="FUNCT_9:attr.1">-periodic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_9.html#T1" target="_self" title="FUNCT_9:th.1">Th1</a></span>; <a class="txt" 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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