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<b>let </b><font color="Maroon">X</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"><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_0.html#D39">WAYBEL_0:def 39</a><br/>

<b>reconsider </b><font color="Maroon">X1</font> =  <a href="yellow_3.html#K4">proj1</a> <font color="Maroon">X</font> as  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 <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="yellow_3.html#T21">YELLOW_3:21</a>, <a class="ref" href="yellow_3.html#T22">YELLOW_3:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">X2</font> =  <a href="yellow_3.html#K5">proj2</a> <font color="Maroon">X</font> as  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 <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="yellow_3.html#T21">YELLOW_3:21</a>, <a class="ref" href="yellow_3.html#T22">YELLOW_3:22</a></i>;<br/>
<b>consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E4:14_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X1</font>
 <b>and </b><br/><a NAME="E5:14_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">z</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X1</font> holds <br/><font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">z</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#D39">WAYBEL_0:def 39</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E7:14_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">y</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X2</font>
 <b>and </b><br/><a NAME="E8:14_1_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>  st <font color="Olive">z</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X2</font> holds <br/><font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">z</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#D39">WAYBEL_0:def 39</a></i>;<br/>
<b>take </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="yellow_3.html#K7">]</a></span>
;<br/>

<b>thus </b><a NAME="E9:14_1_1"/>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X</font>
 <b>by </b><i>, , <a class="ref" href="yellow_3.html#T31">YELLOW_3:31</a></i>;<br/>

<b>let </b><font color="Maroon">z</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>;<br/>

<b>assume </b><a NAME="E10:14_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">z</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E11:14_1_1"/>
the <a href="struct_0.html#U1">carrier</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> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#D2">YELLOW_3:def 2</a></i>;<br/>
<a NAME="E12:14_1_1"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">z</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">z</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">z</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="E13:14_1_1"/><b>then </b>
( <font color="Maroon">z</font> <a href="yellow_3.html#K8">`1</a>  <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">z</font> <a href="yellow_3.html#K9">`2</a>  <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X2</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T31">YELLOW_3:31</a></i>;<br/>
<a NAME="E14:14_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="yellow_3.html#K8">`1</a>  &amp; <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="yellow_3.html#K9">`2</a>  )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E15:14_1_1"/>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="yellow_3.html#K7">]</a></span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font>
 <b>by </b><i>, <a class="ref" href="yellow_3.html#T11">YELLOW_3:11</a></i>;<br/>


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