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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E8">A1</font></i>: 
not  <a href="margrel1.html#K4" title="MARGREL1:func.4">empty_rel</a> <font color="Maroon" title="c1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K4" title="MARGREL1:func.4">empty_rel</a> <font color="Maroon" title="c1">D</font>;<br/>
<a NAME="E3:26"/>
 <a href="margrel1.html#K4" title="MARGREL1:func.4">empty_rel</a> <font color="Maroon" title="c1">D</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="margrel1.html#D8" target="_self" title="MARGREL1:def.8">Def8</a></i>;<br/>
<a NAME="E4:26"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 
<b>by </b><i><a class="txt" href="margrel1.html#E1:26"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">x</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> <b>by </b><i><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E6:26"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="margrel1.html#K4" title="MARGREL1:func.4">empty_rel</a> <font color="Maroon" title="c1">D</font>
 
<b>by </b><i><a class="txt" href="margrel1.html#E1:26"><i><font color="Green" title="E8">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
contradiction
 <b>by </b><i><a class="ref" href="margrel1.html#D10" target="_self" title="MARGREL1:def.10">Def10</a></i>;<br/>


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