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<a NAME="E1:30"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:30"/>
(  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp; ( 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="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds <br/> <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <span class="p1">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> </span>)</span>,<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">sin</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="integra8.html#T23" target="_self" title="INTEGRA8:th.23">Th23</a>, <a class="ref" href="integra8.html#T25" target="_self" title="INTEGRA8:th.25">Th25</a>, <a class="ref" href="sin_cos.html#T72" title="SIN_COS:th.72">SIN_COS:72</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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