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

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D39">WAYBEL_0:def 39</a><br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="waybel30.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E2:5_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E4:5_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/>(  not <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="waybel30.html#E3"><i><font color="Green">Lemma3</font></i></a>, <a class="txt" href="waybel30.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/>


</div>
