<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c2">I</font> =  <a href="waybel_4.html#K2" title="WAYBEL_4:func.2">IntRel</a> <font color="Maroon" title="c1">L</font>;<br/>
<a NAME="E1:20_1_1"/>
 <a href="waybel_4.html#K2" title="WAYBEL_4:func.2">IntRel</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="waybel_4.html#D9" target="_self" title="WAYBEL_4:def.9">Def9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">I</font> =  <a href="waybel_4.html#K2" title="WAYBEL_4:func.2">IntRel</a> <font color="Maroon" title="c1">L</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1" title="YELLOW_1:th.1">YELLOW_1:1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">I</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" title="YELLOW_0:def.5">YELLOW_0:def 5</a><br/>

<a NAME="E3:20_1_1"/>
<font color="Maroon" title="c3">I</font> <a href="lattice3.html#NR4" title="LATTICE3:NR.4">is_&gt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D9" title="LATTICE3:def.9">LATTICE3:def 9</a><br/>

<b>assume </b><a NAME="E1:20_1_1_1"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:20_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1" title="YELLOW_1:th.1">YELLOW_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">b'</font> = <font color="Maroon" title="c4">b</font> as  <a href="waybel_4.html#V5" title="WAYBEL_4:attr.5">auxiliary</a> <a href="alg_1.html#NM1" title="ALG_1:NM.1">Relation</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="waybel_4.html#D9" target="_self" title="WAYBEL_4:def.9">Def9</a></i>;<br/>
<a NAME="E4:20_1_1_1"/>
<font color="Maroon" title="c5">b'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="ref" href="waybel_4.html#T2" target="_self" title="WAYBEL_4:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_4.html#K3" title="WAYBEL_4:func.3">Aux</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a> <font color="Maroon" title="c3">I</font>
 ;<br/>


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