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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">A</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">B</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>let </b><font color="Maroon" title="c5">C</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c2">J</font>;<br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>
 ;<br/>

<a NAME="E2:17"/><i><font color="Green" title="E13">A2</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">J</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:17"/><b>then </b><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow20.html#E1:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="yellow20.html#D2" target="_self" title="YELLOW20:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
<font color="Maroon" title="c2">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D2" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a><br/>

<b>let </b><font color="Maroon" title="c6">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E5:17"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">J</font>
 ;<br/>

<a NAME="E6:17"/><b>then </b>
<font color="Maroon" title="c5">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow20.html#E1:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow20.html#E2:17"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="yellow20.html#E3:17"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="yellow20.html#D2" target="_self" title="YELLOW20:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E7:17"/>
<font color="Maroon" title="c5">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>


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