<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c2">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">e</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:12_1_1_1"/>
( <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1_1"><b>suppose </b></a><a NAME="E1:12_1_1_1_1"/>
<font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">e</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a></span><br/><div class="add"><b>hence </b><a NAME="E2:12_1_1_1_1"/>
<font color="Maroon" title="c2">e</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>
 <b>by </b><i><a class="ref" href="subset_1.html#D2" title="SUBSET_1:def.2">SUBSET_1:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1_2"><b>suppose </b></a><a NAME="E1:12_1_1_1_2"/>
not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">e</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a></span><br/><div class="add"><b>hence </b><a NAME="E2:12_1_1_1_2"/>
<font color="Maroon" title="c2">e</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>
 <b>by </b><i><a class="ref" href="membered.html#D1" target="_self" title="MEMBERED:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
