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<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">A</font>, <font color="Maroon" title="c3">B</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="E1:19"/><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/>

<b>then </b><i><font color="Green" title="E9">A2</font></i>: <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">A</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</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="c3">B</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</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> = 
<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">A</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c3">B</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="c3">B</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</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="ref" href="pboole.html#D7" title="PBOOLE:def.7">PBOOLE:def 7</a></i>
<br/>.= 
<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">A</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#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">B</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="c3">B</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</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#E1:19"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="mboolean.html#E5"><i><font color="Green" title="E5">Lm4</font></i></a></i>
<br/>.= 
<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">A</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#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">B</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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="c3">B</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#K4" title="XBOOLE_0:func.4">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">A</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#E1:19"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="mboolean.html#E5"><i><font color="Green" title="E5">Lm4</font></i></a></i>
;<br/>
<a NAME="E3:19"/>
<span class="p1">(<span class="default"><a href="mboolean.html#K1" title="MBOOLEAN:func.1">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="pboole.html#K5" title="PBOOLE:func.5">\+\</a> <font color="Maroon" title="c3">B</font></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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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"><font color="Maroon" title="c2">A</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#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="mboolean.html#E1:19"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="mboolean.html#E6"><i><font color="Green" title="E6">Lm5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:19"/>
<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">A</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</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="c3">B</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</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="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"><font color="Maroon" title="c2">A</font> <a href="pboole.html#K5" title="PBOOLE:func.5">\+\</a> <font color="Maroon" title="c3">B</font></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#E2:19"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T86" title="ZFMISC_1:th.86">ZFMISC_1:86</a></i>;<br/>


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