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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a> <a href="osalg_4.html#V2" target="_self">locally_directed</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E33</font></i>: 
 ex <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Olive">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font>, <font color="Maroon">y1</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> ;<br/>
<b>consider </b><font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E4:39"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> )
 <b>by </b><i/>;<br/>
<a NAME="E5:39"/>
(  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">x</font> &amp;  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:39"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">z</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E7:39"/><b>then </b>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">u</font> <a href="hidden.html#R2">in</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">z</font> &amp; <font color="Maroon">x1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">u</font> &amp; <font color="Maroon">y1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">u</font> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E8:39"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">u</font> &amp; <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">u</font> )
 ;<br/>


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