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<b>let </b><font color="Maroon" title="c1">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E7">A1</font></i>: 
( <font color="Maroon" title="c1">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="c2">f</font> &amp; <font color="Maroon" title="c1">Y</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> &amp; <font color="Maroon" title="c2">f</font> <a href="fcont_2.html#R1" title="FCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">Y</font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="fcont_2.html#T9" target="_self" title="FCONT_2:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
<font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">Y</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>
 <b>by </b><i><a class="txt" href="fcont_2.html#E1:12"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="fcont_1.html#T30" title="FCONT_1:th.30">FCONT_1:30</a></i>;<br/>


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