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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="realset2.html#V3">trivial</a> <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">T</font> be  non <a href="realset2.html#V3">trivial</a> <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>







<b>assume </b><a NAME="E1:65"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">f</font> <a href="ndiff_1.html#R2" target="_self">is_differentiable_on</a> <font color="Maroon">X</font>
 ;<br/>

<b>hence </b><a NAME="E2:65"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="nfcont_1.html#D11">NFCONT_1:def 11</a><br/>

<b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E3:65"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E4:65"/><b>then </b>
<font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="ndiff_1.html#R1" target="_self">is_differentiable_in</a> <font color="Maroon">x</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:65"/>
<font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="nfcont_1.html#R1">is_continuous_in</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="ndiff_1.html#E1:65"><i><font color="Green">E43</font></i></a></i>;<br/>


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