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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c3">T</font> be  non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="nfcont_1.html#NM1" title="NFCONT_1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>;<br/>







<b>assume </b><a NAME="E1:65"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="ndiff_1.html#R2" title="NDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>hence </b><a NAME="E2:65"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="ref" href="ndiff_1.html#D8" target="_self" title="NDIFF_1:def.8">Def8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nfcont_1.html#D11" title="NFCONT_1:def.11">NFCONT_1:def 11</a><br/>

<b>let </b><font color="Maroon" title="c5">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font>;<br/>

<b>assume </b><a NAME="E3:65"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E4:65"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c1">X</font> <a href="ndiff_1.html#R1" title="NDIFF_1:pred.1">is_differentiable_in</a> <font color="Maroon" title="c5">x</font>
 
<b>by </b><i><a class="txt" href="ndiff_1.html#E1:65"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="ndiff_1.html#D8" target="_self" title="NDIFF_1:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E5:65"/>
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c1">X</font> <a href="nfcont_1.html#R1" title="NFCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="ref" href="ndiff_1.html#T49" target="_self" title="NDIFF_1:th.49">Th49</a></i>;<br/>


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