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<span class="kw">let </span><font color="Maroon" title="c1">BL</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="lopclset.html#K13" title="LOPCLSET:func.13">UFilter</a> <font color="Maroon" title="c1">BL</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<a NAME="E1:48"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 <a href="lopclset.html#K13" title="LOPCLSET:func.13">UFilter</a> <font color="Maroon" title="c1">BL</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopclset.html#T29" target="_self" title="LOPCLSET:th.29">Th29</a></span>;<br/>
<a NAME="E2:48"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="lopclset.html#K13" title="LOPCLSET:func.13">UFilter</a> <font color="Maroon" title="c1">BL</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="lopclset.html#K12" title="LOPCLSET:func.12">StoneBLattice</a> <font color="Maroon" title="c1">BL</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopclset.html#T41" target="_self" title="LOPCLSET:th.41">Th41</a></span>;<br/>
<a NAME="E3:48"/><span class="kw">then </span>
 <a href="lopclset.html#K13" title="LOPCLSET:func.13">UFilter</a> <font color="Maroon" title="c1">BL</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:48"/>
 <a href="lopclset.html#K13" title="LOPCLSET:func.13">UFilter</a> <font color="Maroon" title="c1">BL</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E30">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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