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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:139"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V3">empty-yielding</a>
 <b>and </b><br/><a NAME="E2:139"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D15" target="_self">PBOOLE:def 15</a><br/>

<b>assume </b><a NAME="E3:139"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E4:139"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="pboole.html#E2:139"><i><font color="Green">E75</font></i></a>, <a class="ref" href="pboole.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:139"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="txt" href="pboole.html#E1:139"><i><font color="Green">E74</font></i></a>, <a class="txt" href="pboole.html#E3:139"><i><font color="Green">E76</font></i></a>, <a class="ref" href="pboole.html#D15" target="_self">Def15</a></i>;<br/>
<b>hence </b><a NAME="E6:139"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="pboole.html#E4:139"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>


</div>
