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<span class="kw">let </span><font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c4">Q</font> be   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">P</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">Q</font> implies 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#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font></span>)</span> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:138"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Q</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tsep_1.html#D3" title="TSEP_1:def.3">TSEP_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 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#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font></span>)</span> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a> </span><br/>

<a NAME="E2:138"/>
 <a href="pcs_0.html#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#T15" target="_self" title="PCS_0:th.15">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:138"/>
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#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font></span>)</span> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:138"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="pcs_0.html#T1" target="_self" title="PCS_0:th.1">Th1</a></span>; <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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