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<b>set </b><font color="Maroon" title="c4">PR</font> =  <a href="osalg_4.html#K1" title="OSALG_4:func.1">Path_Rel</a> <font color="Maroon" title="c1">R</font>;<br/>
<a NAME="E1:14_1_2"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="osalg_4.html#K1" title="OSALG_4:func.1">Path_Rel</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></i>;<br/>
<a NAME="E2:14_1_2"/><b>then </b>
 <a href="osalg_4.html#K1" title="OSALG_4:func.1">Path_Rel</a> <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R3" title="RELAT_2:pred.3">is_symmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D11" title="RELAT_2:def.11">RELAT_2:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:14_1_2"/>
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 <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">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> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">s2</font>,<font color="Olive" title="b1">s1</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="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</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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