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<b>let </b><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">J</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/><b>let </b><font color="Maroon" title="c4">i</font>, <font color="Maroon" title="c5">j</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:10"/>
( <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> &amp; <font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">J</font> )
 ;<br/>

<a NAME="E2:10"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">J</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> <a href="funct_2.html#K4" title="FUNCT_2:func.4">:-&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span>)</span> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T42" title="CQC_LANG:th.42">CQC_LANG:42</a></i>
<br/>.= 
<font color="Maroon" title="c3">M</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="funct_7.html#E2:10"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="funct_7.html#T7" target="_self" title="FUNCT_7:th.7">Th7</a></i>
<br/>.= 
<font color="Maroon" title="c3">M</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">j</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T35" title="ZFMISC_1:th.35">ZFMISC_1:35</a></i>
;<br/>


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