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<b>let </b><font color="Maroon" title="c1">CNS1</font>, <font color="Maroon" title="c2">CNS2</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c1">CNS1</font>,<font color="Maroon" title="c2">CNS2</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="c1">CNS1</font>;<br/>







<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E20">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="ncfcont1.html#V1" title="NCFCONT1:attr.1">compact</a> &amp; <font color="Maroon" title="c3">f</font> <a href="ncfcont2.html#R1" title="NCFCONT2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c4">Y</font> )
 ;<br/>

<a NAME="E2:37"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R7" title="NCFCONT1:pred.7">is_continuous_on</a> <font color="Maroon" title="c4">Y</font>
 
<b>by </b><i><a class="ref" href="ncfcont2.html#T19" target="_self" title="NCFCONT2:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
<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="ncfcont1.html#V1" title="NCFCONT1:attr.1">compact</a>
 <b>by </b><i><a class="txt" href="ncfcont2.html#E1:37"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="ncfcont1.html#T104" title="NCFCONT1:th.104">NCFCONT1:104</a></i>;<br/>


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