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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>assume </b><a NAME="E1:158"/><i><font color="Green" title="E59">A1</font></i>: 
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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>set </b><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="E2:158"/>
 <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#V14" title="PCS_0:attr.14">pcs-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:158_1"/>
(  <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> )
 <b>by </b><i><a class="txt" href="pcs_0.html#E1:158"><i><font color="Green" title="E59">A1</font></i></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></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D23" target="_self" title="PCS_0:def.23">PCS_0:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:158"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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