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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel27.html#K2" target="_self">UPS</a> <font color="Maroon">S</font>,<font color="Maroon">T</font></span>)</span>, <font color="Maroon">g</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel27.html#K2" target="_self">UPS</a> <font color="Maroon">S</font>,<font color="Maroon">T</font></span>)</span>;<br/>





<a NAME="E1:39"/><i><font color="Green">E36</font></i>: 
 <a href="waybel27.html#K2" target="_self">UPS</a> <font color="Maroon">S</font>,<font color="Maroon">T</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">T</font> <a href="yellow_1.html#K6">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">f</font>, <font color="Maroon">b</font> = <font color="Maroon">g</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="yellow_1.html#K6">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/>
<a NAME="E3:39"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">f</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">g</font> iff <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
( <font color="Maroon">f</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">g</font> implies for <font color="Olive">s</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Maroon">f</font> <a href="waybel27.html#K3" target="_self">.</a> <font color="Olive">s</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">g</font> <a href="waybel27.html#K3" target="_self">.</a> <font color="Olive">s</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E5:39"/>
for <font color="Olive">s</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Maroon">f</font> <a href="waybel27.html#K3" target="_self">.</a> <font color="Olive">s</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">g</font> <a href="waybel27.html#K3" target="_self">.</a> <font color="Olive">s</font>
 ;<br/>

<b>hence </b><a NAME="E6:39"/>
<font color="Maroon">f</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">g</font>
 <b>by </b><i>, </i>;<br/>


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