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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">u</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:39"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">u</font> holds <br/> ex <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> &amp; <font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">a</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font>, <font color="Maroon">v'</font> = <font color="Maroon">v</font> as    <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> <b>by </b><i><a class="ref" href="substlat.html#D4">SUBSTLAT:def 4</a></i>;<br/>
<font color="Maroon">u</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">v</font> = 
the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="substlat.html#K5">SubstLatt</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">u'</font>,<font color="Maroon">v'</font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
 <a href="substlat.html#K3">mi</a> <span class="p1">(<span class="default"><font color="Maroon">u'</font> <a href="substlat.html#K4">^</a> <font color="Maroon">v'</font></span>)</span>
<b>by </b><i><a class="ref" href="substlat.html#D4">SUBSTLAT:def 4</a></i>
<br/>.= 
<font color="Maroon">u'</font>
<b>by </b><i><a class="ref" href="heyting2.html#T3" target="_self">Th3</a>, </i>
;<br/>
<b>hence </b><a NAME="E4:39"/>
<font color="Maroon">u</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">v</font>
 <b>by </b><i><a class="ref" href="lattices.html#T21">LATTICES:21</a></i>;<br/>


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