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<b>let </b><font color="Maroon">T</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><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">T</font>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:13"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">Y</font> is <a href="nfcont_1.html#V1">compact</a> &amp; <font color="Maroon">f</font> <a href="nfcont_2.html#R1" target="_self">is_uniformly_continuous_on</a> <font color="Maroon">Y</font> )
 ;<br/>

<a NAME="E2:13"/><b>then </b>
<font color="Maroon">f</font> <a href="nfcont_1.html#R3">is_continuous_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:13"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="nfcont_1.html#V1">compact</a>
 <b>by </b><i>, <a class="ref" href="nfcont_1.html#T39">NFCONT_1:39</a></i>;<br/>


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