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<b>reconsider </b><font color="Maroon" title="c3">f</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</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>take </b>
<font color="Maroon" title="c3">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> is <a href="fdiff_1.html#V4" title="FDIFF_1:attr.4">differentiable</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">Z</font> =  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  as  <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="fdiff_1.html#E48"><i><font color="Green" title="E27">Th4</font></i></a></i>;<br/>
<a NAME="E3:44_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c4">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:44_1_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Z</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="partfun2.html#K1" title="PARTFUN2:func.1">id</a> <font color="Maroon" title="c4">Z</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></i>;<br/>
<a NAME="E5:44_1_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c4">Z</font>
 
<b>by </b><i><a class="txt" href="#E3:44_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="fdiff_1.html#T25" target="_self" title="FDIFF_1:th.25">Th25</a></i>;<br/>
<b>hence </b><a NAME="E6:44_1_1"/>
<font color="Maroon" title="c3">f</font> is <a href="fdiff_1.html#V4" title="FDIFF_1:attr.4">differentiable</a>
 <b>by </b><i><a class="ref" href="fdiff_1.html#D9" target="_self" title="FDIFF_1:def.9">DifDef</a>, <a class="txt" href="#E3:44_1_1"><i><font color="Green" title="E28">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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