<?xml version="1.0"?>
<div class="add">

<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">RNS</font> being  <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/> for <font color="Olive" title="b2">CNS</font> being  <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a><br/> for <font color="Olive" title="b3">f</font> being  <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Olive" title="b2">CNS</font>,<font color="Olive" title="b1">RNS</font>  st <font color="Olive" title="b3">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Olive" title="b3">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><br/><b>let </b><font color="Maroon" title="c2">RNS</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</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">CNS</font> being  <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a><br/> for <font color="Olive" title="b2">f</font> being  <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Olive" title="b1">CNS</font>,<font color="Maroon" title="c2">RNS</font>  st <font color="Olive" title="b2">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Olive" title="b2">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><br/><b>let </b><font color="Maroon" title="c3">CNS</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</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="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c3">CNS</font>,<font color="Maroon" title="c2">RNS</font>  st <font color="Olive" title="b1">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Olive" title="b1">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c3">CNS</font>,<font color="Maroon" title="c2">RNS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> implies  <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> )</span><br/>







<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">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="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E2:20"/>
 <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">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="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="ref" href="vfunct_1.html#T29" title="VFUNCT_1:th.29">VFUNCT_1:29</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
 <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font> <a href="ncfcont2.html#R2" title="NCFCONT2:pred.2">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="ncfcont2.html#T11" target="_self" title="NCFCONT2:th.11">Th11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
