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

<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c1">x</font> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> )</span><br/>

<b>assume </b><a NAME="E1:8_1_1"/><i><font color="Green" title="E3">A1</font></i>: 
<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"> not <font color="Maroon" title="c1">x</font> is <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a></span><br/>

<b>let </b><font color="Maroon" title="c2">a</font> be  <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self" title="FACIRC_1:def.2">FACIRC_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x</font></span><br/>

<b>thus </b><a NAME="E2:8_1_1"/>
not <font color="Maroon" title="c2">a</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="#E1:8_1_1"><i><font color="Green" title="E3">A1</font></i></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>
