<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">B</font> be  <a href="waybel23.html#V6" title="WAYBEL23:attr.6">with_bottom</a>  <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:93"/><i><font color="Green" title="E51">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="waybel23.html#K5" title="WAYBEL23:func.5">baseMap</a> <font color="Maroon" title="c2">B</font></span>)</span>
 ;<br/>

<a NAME="E2:93"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="waybel23.html#K5" title="WAYBEL23:func.5">baseMap</a> <font color="Maroon" title="c2">B</font></span>)</span> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1" title="YELLOW_1:th.1">YELLOW_1:1</a></i>;<br/>
<a NAME="E3:93"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel23.html#E1:93"><i><font color="Green" title="E51">A1</font></i></a></i>;<br/>
<a NAME="E4:93"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X</font> where <font color="Olive" title="b1">X</font> is   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_0.html#D23" title="WAYBEL_0:def.23">WAYBEL_0:def 23</a></i>;<br/>
<a NAME="E5:93"/><b>then </b>
 ex <font color="Olive" title="b1">I</font> being  <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font>
 
;<br/>
<b>hence </b><a NAME="E6:93"/>
<font color="Maroon" title="c3">x</font> is   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span>
 ;<br/>


</div>
