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<b>consider </b><font color="Maroon">x</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:46_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<b>thus </b><a NAME="E3:46_1_1"/>
not  <a href="pscomp_1.html#K5" target="_self">Inv</a> <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, <a class="ref" href="pscomp_1.html#T1" target="_self">Th1</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_1_1_1"/><i><font color="Green">E31</font></i>: 
0 <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K5" target="_self">Inv</a> <font color="Maroon">X</font>
 ;<br/><b>consider </b><font color="Maroon">r3</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:46_1_1_1"/><i><font color="Green">E32</font></i>: 
0 <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K6">/</a> <font color="Maroon">r3</font>
 <b>and </b><br/><a NAME="E4:46_1_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">r3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:46_1_1"><i><font color="Green">E30</font></i></a></i>;<br/><a NAME="E5:46_1_1_1"/>
<font color="Maroon">r3</font> <a href="real_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:46_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/><b>hence </b><a NAME="E6:46_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T203">XCMPLX_1:203</a>, <a class="txt" href="pscomp_1.html#E3:46_1_1_1"><i><font color="Green">E32</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:46_1_1"/>
 <a href="pscomp_1.html#K5" target="_self">Inv</a> <font color="Maroon">X</font> is <a href="setfam_1.html#V1">without_zero</a>
 <b>by </b><i/>;<br/>


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