<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">P</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"> for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st not <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font> holds <br/> <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Olive" title="b1">a</font> is   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font> implies  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a> )</span><br/>



<span class="kw">assume </span><a NAME="E1:157"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">R</font> =  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font>;<br/>
<a NAME="E2:157"/>
(  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  &amp;  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  &amp;  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is  <a href="pcs_0.html#V4" title="PCS_0:attr.4">pcs-tol-reflexive</a>  &amp;  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is  <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a>  &amp;  <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is  <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:157"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="ref" href="pcs_0.html#T30" target="_self" title="PCS_0:th.30">Th30</a>, <a class="ref" href="pcs_0.html#T31" target="_self" title="PCS_0:th.31">Th31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:157"/>
 <a href="pcs_0.html#K20" title="PCS_0:func.20">pcs-extension</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">a</font> is   <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"> verum</span><br/>


</div>
