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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V24">up-complete</a> <a href="orders_2.html#NM1">Poset</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V24">up-complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:59"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> holds <br/> ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">y</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Olive">x</font> )
 <b>and </b><br/><a NAME="E2:59"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> holds <br/> ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Olive">y</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Olive">x</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_6.html#D1">WAYBEL_6:def 1</a><br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_6.html#D1">WAYBEL_6:def 1</a><br/>

<b>assume </b><a NAME="E3:59"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="yellow_3.html#K6">:]</a></span>
 ;<br/>

<a NAME="E4:59"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a> </span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<a NAME="E5:59"/><b>then </b>
<font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon">s</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E7:59"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">s</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a>  )
 <b>by </b><i/>;<br/>
<a NAME="E8:59"/>
<font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="txt" href="yellow10.html#E7:59"><i><font color="Green">E31</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon">t</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E10:59"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">t</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a>  )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">t</font> = <font color="Maroon">t</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> ;<br/>
<b>take </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span>
;<br/>

<b>thus </b><a NAME="E12:59"/>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K6">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="yellow_3.html#K6">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E10:59"><i><font color="Green">E32</font></i></a>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>

<b>thus </b><a NAME="E13:59"/>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E7:59"><i><font color="Green">E31</font></i></a>, <a class="txt" href="yellow10.html#E10:59"><i><font color="Green">E32</font></i></a>, , </i>;<br/>


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