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

<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">E</font> is  <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a>  implies  not <font color="Maroon" title="c1">E</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:8"/>
<font color="Maroon" title="c1">E</font> is  <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c1">E</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<a NAME="E2:8"/><span class="kw">then </span>
<font color="Maroon" title="c1">E</font> is  <a href="intpro_1.html#V1" title="INTPRO_1:attr.1">with_FALSUM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#D7" target="_self" title="INTPRO_1:def.7">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:8"/>
 not <font color="Maroon" title="c1">E</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#D1" target="_self" title="INTPRO_1:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
