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<b>let </b><font color="Maroon">S</font> be   <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">S</font>;<br/>



<b>assume </b><a NAME="E1:72"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="partfun2.html#K1">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x0</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>assume </b><a NAME="E1:72_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x0</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 ;<br/><b>thus </b><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x0</font> = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x0</font>
<b>by </b><i><a class="ref" href="nfcont_1.html#D3" target="_self">Def3</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">x0</font>
<b>by </b><i>, <a class="ref" href="nfcont_1.html#D3" target="_self">Def3</a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:72"/>
<font color="Maroon">f</font> <a href="nfcont_1.html#R3" target="_self">is_continuous_on</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>


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