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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">s2</font> holds <br/> <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Olive" title="b2">s2</font></span><br/><b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">s2</font> implies  <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Maroon" title="c2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Maroon" title="c3">s2</font> )</span><br/>



<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c2">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">s2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Maroon" title="c2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Maroon" title="c3">s2</font></span><br/>

<a NAME="E2:20"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">s2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="osalg_4.html#K1" title="OSALG_4:func.1">Path_Rel</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="osalg_4.html#T2" target="_self" title="OSALG_4:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
 <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Maroon" title="c2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_4.html#K3" title="OSALG_4:func.3">CComp</a> <font color="Maroon" title="c3">s2</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T44" title="EQREL_1:th.44">EQREL_1:44</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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