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<b>set </b><font color="Maroon" title="c4">P</font> =  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font>;<br/>
<b>thus </b><a NAME="E1:87_1_1"/>
(  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> )
 ; <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"> (  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="pcs_0.html#V4" title="PCS_0:attr.4">pcs-tol-reflexive</a> &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a> )</span><br/>

<b>thus </b><a NAME="E2:87_1_1"/>
(  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="pcs_0.html#V4" title="PCS_0:attr.4">pcs-tol-reflexive</a> &amp;  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="pcs_0.html#V6" title="PCS_0:attr.6">pcs-tol-symmetric</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font> is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a></span><br/>

<b>let </b><font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">p'</font>, <font color="Maroon" title="c7">q</font>, <font color="Maroon" title="c8">q'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">PCS_0:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c6">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font> &amp; <font color="Maroon" title="c8">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">q</font> implies <font color="Maroon" title="c6">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c8">q'</font> )</span><br/>

<b>assume </b><a NAME="E3:87_1_1"/>
<font color="Maroon" title="c5">p</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c7">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font> or  not <font color="Maroon" title="c8">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">q</font> or <font color="Maroon" title="c6">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c8">q'</font> )</span><br/>

<b>assume </b><a NAME="E4:87_1_1"/>
( <font color="Maroon" title="c6">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font> &amp; <font color="Maroon" title="c8">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c8">q'</font></span><br/>

<a NAME="E5:87_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">p'</font>,<font color="Maroon" title="c5">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">q'</font>,<font color="Maroon" title="c7">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c3">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E6:87_1_1"/><b>then </b>
( <font color="Maroon" title="c6">p'</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 <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> &amp; <font color="Maroon" title="c8">q'</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 <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E7:87_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">p'</font>,<font color="Maroon" title="c8">q'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K12" title="PCS_0:func.12">pcs-total</a> <font color="Maroon" title="c3">D</font></span>)</span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">PCS_0:def 7</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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