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<a NAME="E1:115"/>
(  <a href="numbers.html#K1">REAL</a>  is  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  &amp;  <a href="numbers.html#K1">REAL</a>  <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <a href="sin_cos.html#K22" target="_self">cos</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  holds <br/> <a href="sin_cos.html#K22" target="_self">cos</a>  <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="ref" href="sin_cos.html#D22" target="_self">Def22</a>, <a class="ref" href="sin_cos.html#T68" target="_self">Th68</a>, <a class="ref" href="fcont_3.html#T4">FCONT_3:4</a>, <a class="ref" href="subset_1.html#D4">SUBSET_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E2:115"/>
(  <a href="sin_cos.html#K22" target="_self">cos</a>  <a href="fdiff_1.html#R2">is_differentiable_on</a>  <a href="numbers.html#K1">REAL</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  holds <br/> <a href="fdiff_1.html#K1">diff</a> <a href="sin_cos.html#K22" target="_self">cos</a> ,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="sin_cos.html#T68" target="_self">Th68</a>, <a class="ref" href="fdiff_1.html#T16">FDIFF_1:16</a></i>;<br/>


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