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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <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>   st <font color="Olive" title="b1">f</font> <a href="fcont_2.html#R1" title="FCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Olive" title="b1">f</font> <a href="fcont_2.html#R1" title="FCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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">X</font> implies  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <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">X</font> )</span><br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E4">A1</font></i>: 
<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">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <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">X</font></span><br/>

<a NAME="E2:6"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c2">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c2">f</font>
 
;<br/>
<b>hence </b><a NAME="E3:6"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <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">X</font>
 <b>by </b><i><a class="txt" href="fcont_2.html#E1:6"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="fcont_2.html#T5" target="_self" title="FCONT_2:th.5">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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