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<b>let </b><font color="Maroon">L</font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>given </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">S</font> being  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font><b> such that </b><a NAME="E1:32"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">S</font> is <a href="yellow_0.html#V7">infs-inheriting</a>
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">S</font> is <a href="waybel_0.html#V4">directed-sups-inheriting</a>
 <b>and </b><br/><a NAME="E3:32"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">L</font>,<font color="Maroon">S</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 ;<br/>

<b>take </b>
<font color="Maroon">X</font>
;<br/>

<b>reconsider </b><font color="Maroon">S'</font> = <font color="Maroon">S</font> as  <a href="yellow_0.html#V7">closure</a> <a href="waybel10.html#NM1">System</a> of  <a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">c</font> =  <a href="waybel10.html#K7">closure_op</a> <font color="Maroon">S'</font> as  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon">c</font>
;<br/>

<b>thus </b><a NAME="E6:32"/>
<font color="Maroon">c</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 <b>by </b><i>, <a class="ref" href="waybel10.html#T25">WAYBEL10:25</a></i>;<br/>

<a NAME="E7:32"/>
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> #)
 
<b>by </b><i><a class="ref" href="waybel10.html#T19">WAYBEL10:19</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
<font color="Maroon">S</font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:32"/>
<font color="Maroon">L</font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i>, <a class="ref" href="waybel_1.html#T8">WAYBEL_1:8</a></i>;<br/>


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