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<b>consider </b><font color="Maroon" title="c2">x</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E2:46_1_1"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<b>thus </b><a NAME="E3:46_1_1"/>
not  <a href="pscomp_1.html#K5" title="PSCOMP_1:func.5">Inv</a> <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:46_1_1"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="pscomp_1.html#T28" target="_self" title="PSCOMP_1:th.28">Th28</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" title="E30">A2</font></i>: 
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K5" title="PSCOMP_1:func.5">Inv</a> <font color="Maroon" title="c1">X</font>
 ;<br/><b>consider </b><font color="Maroon" title="c3">r3</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E3:46_1_1_1"/><i><font color="Green" title="E31">A3</font></i>: 
0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c3">r3</font>
 <b>and </b><br/><a NAME="E4:46_1_1_1"/><i><font color="Green" title="E32">A4</font></i>: 
<font color="Maroon" title="c3">r3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:46_1_1_1"><i><font color="Green" title="E30">A2</font></i></a></i>;<br/><a NAME="E5:46_1_1_1"/>
<font color="Maroon" title="c3">r3</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:46_1_1_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">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="pscomp_1.html#D1" target="_self" title="PSCOMP_1:def.1">Def1</a>, <a class="ref" href="xcmplx_1.html#T203" title="XCMPLX_1:th.203">XCMPLX_1:203</a>, <a class="txt" href="pscomp_1.html#E4:46_1_1_1"><i><font color="Green" title="E32">A4</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" title="PSCOMP_1:func.5">Inv</a> <font color="Maroon" title="c1">X</font> is <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">without_zero</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#D1" target="_self" title="PSCOMP_1:def.1">Def1</a></i>;<br/>


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