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<a NAME="E1:19_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> is   <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dualsp01.html#T9" target="_self" onmouseover="rs('dualsp01/T9')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:19_1_1"/>
 not  <a href="dualsp01.html#K7" title="DUALSP01:func.7">LinearFunctionals</a> <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="dualsp01.html#D6" target="_self" onmouseover="rs('dualsp01/D6')" onmouseout="rh()">Def7</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">  <a href="dualsp01.html#K7" title="DUALSP01:func.7">LinearFunctionals</a> <font color="Maroon" title="c1">X</font> is  <a href="funct_1.html#V4" title="FUNCT_1:attr.4">functional</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_1.html#D13" onmouseover="rs('funct_1/D13')" onmouseout="rh()">FUNCT_1:def 13</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"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dualsp01.html#K7" title="DUALSP01:func.7">LinearFunctionals</a> <font color="Maroon" title="c1">X</font> or <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:19_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dualsp01.html#K7" title="DUALSP01:func.7">LinearFunctionals</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"> <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> </span><br/>

<span class="kw">hence </span><a NAME="E4:19_1_1"/>
<font color="Maroon" title="c2">x</font> is    <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"> verum</span><br/>


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