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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font>  st <font color="Olive" title="b3">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Olive" title="b3">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c3">T</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>  st <font color="Olive" title="b1">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Olive" title="b1">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">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#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> implies  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c4">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font> )</span><br/>







<a NAME="E1:7"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</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#T23" onmouseover="rs('vfunct_1/T23')" onmouseout="rh()">VFUNCT_1:23</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:7"/>
<font color="Maroon" title="c4">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c4">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">hence </span><a NAME="E3:7"/>
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c4">f</font> <a href="nfcont_2.html#R1" title="NFCONT_2:pred.1">is_uniformly_continuous_on</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="nfcont_2.html#T4" target="_self" onmouseover="rs('nfcont_2/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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