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

<b>set </b><font color="Maroon" title="c4">R</font> =  <a href="pcs_0.html#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font>;<br/>
<a NAME="E1:169_1_1"/><i><font color="Green" title="E63">a1</font></i>: 
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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</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>
 
<b>by </b><i><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Defa1</a></i>;<br/>
<a NAME="E2:169_1_1"/><i><font color="Green" title="E64">a3</font></i>: 
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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</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="relset_1.html#K6" title="RELSET_1:func.6">~</a> 
 
<b>by </b><i><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Defa1</a></i>;<br/>
<a NAME="E3:169_1_1"/><i><font color="Green" title="E65">a2</font></i>: 
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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Defa1</a></i>;<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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</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><br/>

<b>assume </b><b>that </b><br/><a NAME="E4:169_1_1"/><i><font color="Green" title="E66">b1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">p</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> 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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>
 <b>and </b><br/><a NAME="E5:169_1_1"/><i><font color="Green" title="E67">b2</font></i>: 
<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> 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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>
 <b>and </b><br/><a NAME="E6:169_1_1"/><i><font color="Green" title="E68">b3</font></i>: 
<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> 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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a>,<a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">PCS_0:def 7</a><br/>

<a NAME="E7:169_1_1"/><i><font color="Green" title="E69">a4</font></i>: 
( <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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="pcs_0.html#E5:169_1_1"><i><font color="Green" title="E67">b2</font></i></a>, <a class="txt" href="pcs_0.html#E6:169_1_1"><i><font color="Green" title="E68">b3</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">p'0</font> = <font color="Maroon" title="c6">p'</font>, <font color="Maroon" title="c10">q'0</font> = <font color="Maroon" title="c8">q'</font>, <font color="Maroon" title="c11">p0</font> = <font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c12">q0</font> = <font color="Maroon" title="c7">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> <b>by </b><i><a class="ref" href="pcs_0.html#D40" target="_self" title="PCS_0:def.40">Defa1</a></i>;<br/>
<a NAME="E9:169_1_1"/>
not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">p0</font>,<font color="Maroon" title="c12">q0</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 <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E3:169_1_1"><i><font color="Green" title="E65">a2</font></i></a>, <a class="txt" href="pcs_0.html#E4:169_1_1"><i><font color="Green" title="E66">b1</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E10:169_1_1"/><b>then </b><i><font color="Green" title="E70">c1</font></i>: 
not <font color="Maroon" title="c11">p0</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c12">q0</font>
 
<b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def3</a></i>;<br/>
<a NAME="E11:169_1_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">p0</font>,<font color="Maroon" title="c9">p'0</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="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">q0</font>,<font color="Maroon" title="c10">q'0</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="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> )
 
<b>by </b><i><a class="txt" href="pcs_0.html#E2:169_1_1"><i><font color="Green" title="E64">a3</font></i></a>, <a class="txt" href="pcs_0.html#E5:169_1_1"><i><font color="Green" title="E67">b2</font></i></a>, <a class="txt" href="pcs_0.html#E6:169_1_1"><i><font color="Green" title="E68">b3</font></i></a>, <a class="ref" href="relat_1.html#D7" title="RELAT_1:def.7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E12:169_1_1"/><b>then </b>
( <font color="Maroon" title="c11">p0</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">p'0</font> &amp; <font color="Maroon" title="c12">q0</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c10">q'0</font> )
 
<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="E13:169_1_1"/><b>then </b>
not <font color="Maroon" title="c9">p'0</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c10">q'0</font>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E10:169_1_1"><i><font color="Green" title="E70">c1</font></i></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def4</a></i>;<br/>
<a NAME="E14:169_1_1"/><b>then </b><i><font color="Green" title="E71">b4</font></i>: 
not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p'0</font>,<font color="Maroon" title="c10">q'0</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 <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def3</a></i>;<br/>
<a NAME="E15:169_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> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><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>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E1:169_1_1"><i><font color="Green" title="E63">a1</font></i></a>, <a class="txt" href="pcs_0.html#E7:169_1_1"><i><font color="Green" title="E69">a4</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E16:169_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#K21" title="PCS_0:func.21">pcs-reverse</a> <font color="Maroon" title="c3">P</font></span>)</span>
 <b>by </b><i><a class="txt" href="pcs_0.html#E3:169_1_1"><i><font color="Green" title="E65">a2</font></i></a>, <a class="txt" href="pcs_0.html#E14:169_1_1"><i><font color="Green" title="E71">b4</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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><br/>


</div>
