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<b>set </b><font color="Maroon">cL</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E1:44_1_1"/><i><font color="Green">E30</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E3:44_1_1"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="waybel20.html#K1" target="_self">[:</a><span class="default"><font color="Maroon">k</font>,<font color="Maroon">k</font></span><a href="waybel20.html#K1" target="_self">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">k</font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">k</font></span>)</span></span><a href="yellow_3.html#K6">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/>
<a NAME="E4:44_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="waybel20.html#K1" target="_self">[:</a><span class="default"><font color="Maroon">k</font>,<font color="Maroon">k</font></span><a href="waybel20.html#K1" target="_self">:]</a></span>
 
<b>by </b><i><a class="txt" href="waybel20.html#E1:44_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E5:44_1_1"/><i><font color="Green">E37</font></i>: 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>
<a NAME="E6:44_1_1"/>
<span class="p1"><a href="waybel20.html#K1" target="_self">[:</a><span class="default"><font color="Maroon">k</font>,<font color="Maroon">k</font></span><a href="waybel20.html#K1" target="_self">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="waybel20.html#E1:44_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/>
<b>hence </b><a NAME="E7:44_1_1"/>
<span class="p1"><a href="waybel20.html#K1" target="_self">[:</a><span class="default"><font color="Maroon">k</font>,<font color="Maroon">k</font></span><a href="waybel20.html#K1" target="_self">:]</a></span> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font></span>)</span> is  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">L</font>,<font color="Maroon">L</font></span><a href="yellow_3.html#K3">:]</a></span>
 <b>by </b><i><a class="txt" href="waybel20.html#E4:44_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="waybel20.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>


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