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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="lattices.html#NM8">B_Lattice</a>;<br/>

<a NAME="E1:45"/>
 <a href="lopclset.html#K13" target="_self">UFilter</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="lopclset.html#T29" target="_self">Th29</a></i>;<br/>
<a NAME="E2:45"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="lopclset.html#K13" target="_self">UFilter</a> <font color="Maroon">c<sub>1</sub></font> is <a href="lattice4.html#V1">monomorphism</a>
 
<b>by </b><i><a class="ref" href="lattice4.html#D2">LATTICE4:def 2</a></i>;<br/>
<a NAME="E3:45"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="lopclset.html#K13" target="_self">UFilter</a> <font color="Maroon">c<sub>1</sub></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="lopclset.html#K12" target="_self">StoneBLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="lopclset.html#T41" target="_self">Th41</a></i>;<br/>
<a NAME="E4:45"/><b>then </b>
 <a href="lopclset.html#K13" target="_self">UFilter</a> <font color="Maroon">c<sub>1</sub></font> is <a href="lattice4.html#V2">epimorphism</a>
 
<b>by </b><i><a class="ref" href="lattice4.html#D3">LATTICE4:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:45"/>
 <a href="lopclset.html#K13" target="_self">UFilter</a> <font color="Maroon">c<sub>1</sub></font> is <a href="lattice4.html#V3">isomorphism</a>
 <b>by </b><i><a class="txt" href="lopclset.html#E2:45"><i><font color="Green">E38</font></i></a>, <a class="ref" href="lattice4.html#D4">LATTICE4:def 4</a></i>;<br/>


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