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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c2">Z</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c2">Z</font>
 ;<br/>

<a NAME="E2:19"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c2">Z</font> is  <a href="rcomp_1.html#V3" title="RCOMP_1:attr.3">open</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<b>by </b><i><a class="txt" href="taylor_2.html#E1:19"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="fdiff_1.html#T17" title="FDIFF_1:th.17">FDIFF_1:17</a></i>;<br/>
<span class="p1">(<span class="default"><a href="seq_1.html#K16" title="SEQ_1:func.16">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c2">Z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c2">Z</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T38" title="RFUNCT_1:th.38">RFUNCT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="seq_1.html#K13" title="SEQ_1:func.13">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c2">Z</font></span>)</span>
<b>by </b><i><a class="txt" href="taylor_2.html#E1:19"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="taylor_2.html#E2:19"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="fdiff_2.html#T19" title="FDIFF_2:th.19">FDIFF_2:19</a></i>
<br/>.= 
 <a href="seq_1.html#K16" title="SEQ_1:func.16">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c2">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T38" title="RFUNCT_1:th.38">RFUNCT_1:38</a></i>
;<br/>
<b>hence </b><a NAME="E4:19"/>
<span class="p1">(<span class="default"><a href="seq_1.html#K16" title="SEQ_1:func.16">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_1.html#K16" title="SEQ_1:func.16">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c2">Z</font></span>)</span>
 ;<br/>


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