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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_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><a NAME="E1:16"/>
<font color="Maroon">L</font> <a href="lattice8.html#R2" target="_self">has_a_representation_of_type&lt;=</a> 2
 ;<br/>

<b>then consider </b><font color="Maroon">A</font> being  non <a href="realset1.html#V1">trivial</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">f</font> being   <a href="lattice5.html#NM1">Homomorphism</a> of <font color="Maroon">L</font>,<span class="p1">(<span class="default"><a href="lattice5.html#K1">EqRelLATT</a> <font color="Maroon">A</font></span>)</span><b> such that </b><br/><a NAME="E3:16"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font> is <a href="lattice8.html#V1" target="_self">finitely_typed</a> &amp;  ex <font color="Olive">e</font> being  <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">A</font> st <br/>( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font></span>)</span> &amp; <font color="Olive">e</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">A</font> ) &amp;  <a href="lattice5.html#K3">type_of</a> <span class="p1">(<span class="default"><a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 2 )
 <b>by </b><i/>;<br/>
<a NAME="E4:16"/><i><font color="Green">E42</font></i>: 
 <a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font> is <a href="yellow11.html#V1">modular</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:16"/><i><font color="Green">E58</font></i>: 
(  <a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font> is  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM8">LATTICE</a> &amp;  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i>, , <a class="ref" href="waybel_1.html#T32">WAYBEL_1:32</a></i>;<br/>
<a NAME="E6:16"/><i><font color="Green">E59</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E7:16"/><i><font color="Green">E60</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">y</font> holds <br/><span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font>
 
<b>by </b><i><a class="ref" href="waybel_1.html#D2">WAYBEL_1:def 2</a></i>;<br/>
<a NAME="E8:16"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> holds <br/><font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">y</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:16"/><b>then </b>
 <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">f</font> is <a href="waybel_0.html#V23">isomorphic</a>
 
<b>by </b><i>, , , <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E10:16"/><b>then </b>
<font color="Maroon">L</font>, <a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font> <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/>
<a NAME="E11:16"/><b>then </b>
 <a href="lattice5.html#K2">Image</a> <font color="Maroon">f</font>,<font color="Maroon">L</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/>
<b>hence </b><a NAME="E12:16"/>
<font color="Maroon">L</font> is <a href="yellow11.html#V1">modular</a>
 <b>by </b><i>, , </i>;<br/>


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