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<b>let </b><font color="Maroon">e</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_1_1_1"/>
( <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1_1"><b>suppose </b></a><a NAME="E1:13_1_1_1_1"/>
<font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:13_1_1_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="subset_1.html#D2">SUBSET_1:def 2</a></i>;<br/><b>hence </b><a NAME="E3:13_1_1_1_1"/>
<font color="Maroon">e</font> is <a href="xreal_0.html#V1">real</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1_2"><b>suppose </b></a><a NAME="E1:13_1_1_1_2"/>
not <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:13_1_1_1_2"/>
<font color="Maroon">e</font> is <a href="xreal_0.html#V1">real</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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