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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM2">D_Lattice</a>;<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="E1:23_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K9" target="_self">StoneS</a> <font color="Maroon">L</font>
 ;<br/><a NAME="E2:23_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span>
 ;<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="E4:23_1"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_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><a class="ref" href="openlatt.html#T2" target="_self">Th2</a>, </i>;<br/><b>take </b><font color="Maroon">y</font> = <font color="Maroon">y</font>;<br/><b>thus </b><a NAME="E6:23_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="openlatt.html#T2" target="_self">Th2</a></i>;<br/></div>
<b>end;</b></div>

<b>given </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><a NAME="E2:23"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E3:23"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
;<br/>
<a NAME="E4:23"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:23"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="openlatt.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:23"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K9" target="_self">StoneS</a> <font color="Maroon">L</font>
 ;<br/>


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