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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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="waybel_0.html#V24">up-complete</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>;<br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D2">WAYBEL_3:def 2</a><br/>

<b>hence </b><a NAME="E2:25"/>
<font color="Maroon">c<sub>3</sub></font> <a href="yellow_3.html#K8">`1</a>  <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_3.html#K8">`1</a> 
 <b>by </b><i><a class="ref" href="yellow10.html#T20" target="_self">Th20</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D2">WAYBEL_3:def 2</a><br/>

<b>thus </b><a NAME="E3:25"/>
<font color="Maroon">c<sub>3</sub></font> <a href="yellow_3.html#K9">`2</a>  <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_3.html#K9">`2</a> 
 <b>by </b><i><a class="txt" href="yellow10.html#E1:25"><i><font color="Green">E14</font></i></a>, <a class="ref" href="yellow10.html#T20" target="_self">Th20</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D2">WAYBEL_3:def 2</a><br/>


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