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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="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substlat.html#K1">SubstitutionSet</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>;<br/>





<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">A</font> <a href="substlat.html#K4">^</a> <span class="p1">(<span class="default"><a href="heyting2.html#K2" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="substlat.html#K4">^</a> <span class="p1">(<span class="default"><a href="heyting2.html#K2" target="_self">-</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E4:20"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">s</font> is    <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>, <font color="Olive">t</font> is    <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> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="heyting2.html#K2" target="_self">-</a> <font color="Maroon">A</font> &amp; <font color="Olive">s</font> <a href="partfun1.html#R1">tolerates</a> <font color="Olive">t</font> ) </span>}</span> 
 
<b>by </b><i>, <a class="ref" href="substlat.html#D3">SUBSTLAT:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">s1</font> being    <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>, <font color="Maroon">t1</font> being    <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> such that </b><br/><a NAME="E6:20"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">t1</font> &amp; <font color="Maroon">s1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">t1</font> <a href="hidden.html#R2">in</a>  <a href="heyting2.html#K2" target="_self">-</a> <font color="Maroon">A</font> &amp; <font color="Maroon">s1</font> <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">t1</font> )
 ;<br/>
<a NAME="E7:20"/>
<font color="Maroon">t1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <span class="p1">(<span class="default"><a href="heyting2.html#K1" target="_self">Involved</a> <font color="Maroon">A</font></span>)</span>,<font color="Maroon">C</font> : for <font color="Olive">g</font> being   <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>  st <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/> not <font color="Olive">f</font> <a href="partfun1.html#R1">tolerates</a> <font color="Olive">g</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">f1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <span class="p1">(<span class="default"><a href="heyting2.html#K1" target="_self">Involved</a> <font color="Maroon">A</font></span>)</span>,<font color="Maroon">C</font><b> such that </b><br/><a NAME="E9:20"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t1</font> &amp; ( for <font color="Olive">g</font> being   <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>  st <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/> not <font color="Maroon">f1</font> <a href="partfun1.html#R1">tolerates</a> <font color="Olive">g</font> ) )
 ;<br/>
<b>thus </b><a NAME="E10:20"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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