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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_3.html#V3">continuous</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">B</font> be  <a href="waybel23.html#V6" target="_self">with_bottom</a>  <a href="waybel23.html#M1" target="_self">CLbasis</a> of <font color="Maroon">L</font>;<br/>



<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <a href="zfmisc_1.html#K1">K10</a>(the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span>) =  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E1:109"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>) is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="109_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span>;<br/>

<a NAME="E1:109_1"/>
 <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> : verum </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E2:109_1"/>
 <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:109"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S9">FUNCT_2:sch 9</a>();<br/></i>
<a NAME="E4:109"/>
<font color="Maroon">f</font> is <a href="waybel_0.html#V23">isomorphic</a>
 
<b>by </b><i>, <a class="ref" href="waybel13.html#T13">WAYBEL13:13</a></i>;<br/>
<a NAME="E5:109"/><b>then </b>
 <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font>, <a href="waybel_8.html#K1">CompactSublatt</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span> <a href="waybel_1.html#R5">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E6:109"/>
 <a href="waybel_8.html#K1">CompactSublatt</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span>, <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">B</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="ref" href="waybel_1.html#T7">WAYBEL_1:7</a></i>;<br/>


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