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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="waybel_1.html#V8">kernel</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:50"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T42">WAYBEL_1:42</a></i>;<br/>
<a NAME="E2:50"/><b>then </b>
(  <a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_1.html#V5">lower_adjoint</a> &amp;  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_1.html#V4">upper_adjoint</a> )
 
<b>by </b><i><a class="ref" href="waybel_1.html#D11">WAYBEL_1:def 11</a>, <a class="ref" href="waybel_1.html#D12">WAYBEL_1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E3:50"/>
(  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V17">infs-preserving</a> &amp;  <a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a> )
 <b>by </b><i><a class="ref" href="waybel_1.html#T13">WAYBEL_1:13</a>, <a class="ref" href="waybel_1.html#T14">WAYBEL_1:14</a></i>;<br/>

<b>hence </b><a NAME="E4:50"/>
(  <a href="waybel34.html#K1" target="_self">LowerAdj</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="waybel34.html#E1:50"><i><font color="Green">E35</font></i></a>, <a class="ref" href="waybel34.html#D1" target="_self">Def1</a>, <a class="ref" href="waybel34.html#D2" target="_self">Def2</a></i>;<br/>


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