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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>







<a NAME="E1:20"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vfunct_1.html#T29" title="VFUNCT_1:th.29">VFUNCT_1:29</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:20"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="ncfcont2.html#T11" target="_self" title="NCFCONT2:th.11">Th11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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