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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">R</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">L</font>,<font color="Maroon">L</font></span><a href="yellow_3.html#K3">:]</a></span>;<br/>



<b>assume </b><a NAME="E1:47"/>
<font color="Maroon">R</font> is <a href="waybel20.html#V1" target="_self">CLCongruence</a>
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel20.html#K5" target="_self">./.</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" target="_self">EqRel</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel20.html#T2" target="_self">Th2</a></i>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:47_1"/>
<font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel20.html#K5" target="_self">./.</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><a NAME="E2:47_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" target="_self">EqRel</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:47_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" target="_self">EqRel</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/><b>take </b><font color="Maroon">y</font> = <font color="Maroon">y</font>;<br/><b>thus </b><a NAME="E6:47_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" target="_self">EqRel</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E4:47"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" target="_self">EqRel</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">y</font>
 ;<br/>

<b>thus </b><a NAME="E5:47"/>
<font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="waybel20.html#K5" target="_self">./.</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>


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