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<b>set </b><font color="Maroon" title="c3">cL</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>;<br/>
<a NAME="E1:44_1_1"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>;<br/>
<a NAME="E3:44_1_1"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="waybel20.html#K1" title="WAYBEL20:func.1">[:</a><span class="default"><font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c2">k</font></span><a href="waybel20.html#K1" title="WAYBEL20:func.1">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K6" title="YELLOW_3:func.6">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">k</font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">k</font></span>)</span></span><a href="yellow_3.html#K6" title="YELLOW_3:func.6">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D9" title="FUNCT_3:def.9">FUNCT_3:def 9</a></i>;<br/>
<a NAME="E4:44_1_1"/><b>then </b><i><font color="Green" title="E31">A2</font></i>: 
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c4">x</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="waybel20.html#K1" title="WAYBEL20:func.1">[:</a><span class="default"><font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c2">k</font></span><a href="waybel20.html#K1" title="WAYBEL20:func.1">:]</a></span>
 
<b>by </b><i><a class="txt" href="waybel20.html#E1:44_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E5:44_1_1"/><i><font color="Green" title="E32">A3</font></i>: 
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#D10" title="RELAT_1:def.10">RELAT_1:def 10</a></i>;<br/>
<a NAME="E6:44_1_1"/>
<span class="p1"><a href="waybel20.html#K1" title="WAYBEL20:func.1">[:</a><span class="default"><font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c2">k</font></span><a href="waybel20.html#K1" title="WAYBEL20:func.1">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 
<b>by </b><i><a class="txt" href="waybel20.html#E1:44_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="funct_3.html#D9" title="FUNCT_3:def.9">FUNCT_3:def 9</a></i>;<br/>
<b>hence </b><a NAME="E7:44_1_1"/>
<span class="p1"><a href="waybel20.html#K1" title="WAYBEL20:func.1">[:</a><span class="default"><font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c2">k</font></span><a href="waybel20.html#K1" title="WAYBEL20:func.1">:]</a></span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span>)</span> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>
 <b>by </b><i><a class="txt" href="waybel20.html#E4:44_1_1"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="waybel20.html#E5:44_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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