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<b>let </b><font color="Maroon">V</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">K</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>, <font color="Maroon">L</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>, <font color="Maroon">M</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:33_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">c</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:33_1"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c</font> )
 <b>by </b><i/>;<br/><a NAME="E4:33_1"/>
<font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> <b>by </b><i><a class="ref" href="substlat.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E6:33_1"/>
( <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> &amp; <font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> )
 <b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">c'</font> = <font color="Maroon">c</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> <b>by </b><i><a class="ref" href="substlat.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E8:33_1"/>
( <font color="Maroon">b'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">c'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a'</font> )
 <b>by </b><i><a class="ref" href="substlat.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E9:33_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">b'</font> <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">c'</font>
 <b>by </b><i><a class="ref" href="partfun1.html#T139">PARTFUN1:139</a></i>;<br/><a NAME="E10:33_1"/>
( <font color="Maroon">c'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> or <font color="Maroon">c'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 <b>by </b><i><a class="ref" href="substlat.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E11:33_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">L</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">M</font> )
 <b>by </b><i><a class="ref" href="substlat.html#T2" target="_self">Th2</a>, </i>;<br/><b>hence </b><a NAME="E12:33_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:33"/>
<font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E3:33"/>
( <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font> &amp; <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:33"/><b>then </b>
( <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font></span>)</span> &amp; <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:33"/>
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">L</font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">M</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="substlat.html#K4" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="finsub_1.html#K1">\/</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>


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