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<span class="kw">let </span><font color="Maroon" title="c1">X</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="dualsp01.html#V1" title="DUALSP01:attr.1">Lipschitzian</a>  <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <font color="Maroon" title="c1">X</font> holds   <a href="dualsp01.html#K14" title="DUALSP01:func.14">Bound2Lipschitz</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">X</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="dualsp01.html#V1" title="DUALSP01:attr.1">Lipschitzian</a>  <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <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="dualsp01.html#K14" title="DUALSP01:func.14">Bound2Lipschitz</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font></span><br/>



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<font color="Maroon" title="c2">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dualsp01.html#K11" title="DUALSP01:func.11">BoundedLinearFunctionals</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dualsp01.html#D10" target="_self" onmouseover="rs('dualsp01/D10')" onmouseout="rh()">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:50"/>
 <a href="dualsp01.html#K14" title="DUALSP01:func.14">Bound2Lipschitz</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D8" onmouseover="rs('subset_1/D8')" onmouseout="rh()">SUBSET_1:def 8</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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