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

<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c4">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D5" title="PBOOLE:def.5">PBOOLE:def 5</a><br/>







<b>assume </b><a NAME="E1:24"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
<span class="p1"><a href="pboole.html#K10" title="PBOOLE:func.10">[|</a><span class="default"><font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c3">Y</font></span><a href="pboole.html#K10" title="PBOOLE:func.10">|]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D21" title="PBOOLE:def.21">PBOOLE:def 21</a></i>;<br/>
<span class="p1">(<span class="default"><a href="mboolean.html#K1" title="MBOOLEAN:func.1">bool</a> <span class="p2">(<span class="default"><a href="mboolean.html#K1" title="MBOOLEAN:func.1">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c3">Y</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> = 
 <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mboolean.html#K1" title="MBOOLEAN:func.1">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span>
<b>by </b><i><a class="txt" href="mboolean.html#E1:24"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="mboolean.html#D1" target="_self" title="MBOOLEAN:def.1">Def1</a></i>
<br/>.= 
 <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="mboolean.html#E1:24"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="mboolean.html#E3"><i><font color="Green" title="E3">Lm2</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:24"/>
<span class="p1"><a href="pboole.html#K10" title="PBOOLE:func.10">[|</a><span class="default"><font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c3">Y</font></span><a href="pboole.html#K10" title="PBOOLE:func.10">|]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="mboolean.html#K1" title="MBOOLEAN:func.1">bool</a> <span class="p2">(<span class="default"><a href="mboolean.html#K1" title="MBOOLEAN:func.1">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c3">Y</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="mboolean.html#E2:24"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T105" title="ZFMISC_1:th.105">ZFMISC_1:105</a></i>;<br/>


</div>
