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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">R1</font> be   <a href="alg_1.html#NM1">Relation</a> of <font color="Maroon">L</font>, <font color="Maroon">R2</font> be   <a href="alg_1.html#NM1">Relation</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">R1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R2</font>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:65"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E3:65"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">z</font> where <font color="Olive">z</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">z</font>,<font color="Maroon">x</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E5:65"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">x</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> )
 ;<br/>
<a NAME="E6:65"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">z</font> where <font color="Olive">z</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">z</font>,<font color="Maroon">x</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> </span>}</span> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:65"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/>


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