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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="yellow_4.html#R1" title="YELLOW_4:pred.1">is_finer_than</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c3">B</font> <a href="yellow_4.html#R1" title="YELLOW_4:pred.1">is_finer_than</a> <font color="Maroon" title="c4">C</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_4.html#D1" target="_self" title="YELLOW_4:def.1">YELLOW_4:def 1</a><br/>

<b>assume </b><a NAME="E2:6"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E4:6"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">b</font> )
 <b>by </b><i><a class="txt" href="yellow_4.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="yellow_4.html#D1" target="_self" title="YELLOW_4:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E6:6"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp; <font color="Maroon" title="c6">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font> )
 <b>by </b><i><a class="txt" href="yellow_4.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="yellow_4.html#E4:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="yellow_4.html#D1" target="_self" title="YELLOW_4:def.1">Def1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c7">c</font>
;<br/>

<b>thus </b><a NAME="E7:6"/>
( <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp; <font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font> )
 <b>by </b><i><a class="txt" href="yellow_4.html#E4:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="yellow_4.html#E6:6"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/>


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