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<b>let </b><font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c2">S</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">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="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c4">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c4">Y</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="c3">f</font> &amp; <font color="Maroon" title="c4">Y</font> is <a href="nfcont_1.html#V1" title="NFCONT_1:attr.1">compact</a> &amp; <font color="Maroon" title="c3">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c4">Y</font> )
 ;<br/>

<a NAME="E2:13"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Maroon" title="c4">Y</font>
 
<b>by </b><i><a class="ref" href="nfcont_2.html#T7" target="_self" title="NFCONT_2:th.7">Th7</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">Y</font> is <a href="nfcont_1.html#V1" title="NFCONT_1:attr.1">compact</a>
 <b>by </b><i><a class="txt" href="nfcont_2.html#E1:13"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="nfcont_1.html#T39" title="NFCONT_1:th.39">NFCONT_1:39</a></i>;<br/>


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