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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#L2" title="PCS_0:struct.2">pcs-Str</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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>  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <span class="p1">(<span class="default"> 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#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Q</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a>  the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font></span>)</span> #)</span><br/>

<a NAME="E1:132"/><span class="lab"><font color="Green" title="E46">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#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> <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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#T14" target="_self" title="PCS_0:th.14">Th14</a></span>;<br/>
<a NAME="E2:132"/>
 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> <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="pcs_0.html#K2" title="PCS_0:func.2">\/</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#T14" target="_self" title="PCS_0:th.14">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:132"/>
 <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>  <a href="pcs_0.html#G2" title="PCS_0:aggr.2">pcs-Str</a>(# <span class="p1">(<span class="default"> 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#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Q</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a>  the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font></span>)</span> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:132"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="pcs_0.html#T14" target="_self" title="PCS_0:th.14">Th14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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