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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  <span class="p1">(<span class="default"><a href="dualsp01.html#K16" title="DUALSP01:func.16">BoundedLinearFunctionalsNorm</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <span class="p1">(<span class="default"><a href="dualsp01.html#K15" title="DUALSP01:func.15">PreNorms</a> <font color="Olive" title="b1">f</font></span>)</span></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"> <span class="p1">(<span class="default"><a href="dualsp01.html#K16" title="DUALSP01:func.16">BoundedLinearFunctionalsNorm</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <span class="p1">(<span class="default"><a href="dualsp01.html#K15" title="DUALSP01:func.15">PreNorms</a> <font color="Maroon" title="c2">f</font></span>)</span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">f9</font> = <font color="Maroon" title="c2">f</font> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
<a NAME="E2:51"/>
<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><span class="p1">(<span class="default"><a href="dualsp01.html#K16" title="DUALSP01:func.16">BoundedLinearFunctionalsNorm</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">f</font> = 
 <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <span class="p1">(<span class="default"><a href="dualsp01.html#K15" title="DUALSP01:func.15">PreNorms</a> <span class="p2">(<span class="default"><a href="dualsp01.html#K14" title="DUALSP01:func.14">Bound2Lipschitz</a> (<font color="Maroon" title="c3">f9</font>,<font color="Maroon" title="c1">X</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="dualsp01.html#D14" target="_self" onmouseover="rs('dualsp01/D14')" onmouseout="rh()">Def13</a></span>
<br/>.= 
 <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <span class="p1">(<span class="default"><a href="dualsp01.html#K15" title="DUALSP01:func.15">PreNorms</a> <font color="Maroon" title="c2">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="dualsp01.html#T23" target="_self" onmouseover="rs('dualsp01/T23')" onmouseout="rh()">Th29</a></span>
;<br/> <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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