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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="rcomp_1.html#V1">compact</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="fcont_2.html#R1" target="_self">is_uniformly_continuous_on</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="fcont_1.html#R2">is_continuous_on</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="fcont_2.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
<font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>1</sub></font> is <a href="rcomp_1.html#V1">compact</a>
 <b>by </b><i><a class="txt" href="fcont_2.html#E1:12"><i><font color="Green">E7</font></i></a>, <a class="ref" href="fcont_1.html#T30">FCONT_1:30</a></i>;<br/>


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