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<span class="kw">set </span><font color="Maroon" title="c4">R</font> =  <a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font>;<br/>
<a NAME="E1:164_1_1"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</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="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Def40</a></span>;<br/>
<a NAME="E2:164_1_1"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Def40</a></span>;<br/>
<a NAME="E3:164_1_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:164_1_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:164_1_1"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="txt" href="#E2:164_1_1"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="ref" href="orders_1.html#T190" title="ORDERS_1:th.190">ORDERS_1:190</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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