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

<b>set </b><font color="Maroon" title="c5">R</font> = <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</font>;<br/>
<b>set </b><font color="Maroon" title="c6">TR</font> = the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">D1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font>;<br/>
<b>set </b><font color="Maroon" title="c8">D2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Q</font>;<br/>
<b>let </b><font color="Maroon" title="c9">p</font>, <font color="Maroon" title="c10">p'</font>, <font color="Maroon" title="c11">q</font>, <font color="Maroon" title="c12">q'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</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="E1:181_1_1"/><i><font color="Green" title="E64">A1</font></i>: 
<font color="Maroon" title="c9">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c11">q</font>
 <b>and </b><br/><a NAME="E2:181_1_1"/><i><font color="Green" title="E65">A2</font></i>: 
<font color="Maroon" title="c10">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">p</font>
 <b>and </b><br/><a NAME="E3:181_1_1"/><i><font color="Green" title="E66">A3</font></i>: 
<font color="Maroon" title="c12">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c11">q</font>
 ;<br/>

<a NAME="E4:181_1_1"/><i><font color="Green" title="E67">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c11">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"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E1:181_1_1"><i><font color="Green" title="E64">A1</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c14">b</font>, <font color="Maroon" title="c15">c</font>, <font color="Maroon" title="c16">d</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:181_1_1"/><i><font color="Green" title="E68">A5</font></i>: 
( <font color="Maroon" title="c9">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c14">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c11">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">c</font>,<font color="Maroon" title="c16">d</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>and </b><br/><a NAME="E7:181_1_1"/><i><font color="Green" title="E69">A6</font></i>: 
( <font color="Maroon" title="c13">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> &amp; <font color="Maroon" title="c14">b</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="c4">Q</font> &amp; <font color="Maroon" title="c15">c</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> &amp; <font color="Maroon" title="c16">d</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="c4">Q</font> )
 <b>and </b><br/><a NAME="E8:181_1_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c15">c</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> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c16">d</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="c4">Q</font> )
 <b>by </b><i><a class="ref" href="pcs_0.html#D2" target="_self" title="PCS_0:def.2">Def2</a></i>;<br/>
<a NAME="E9:181_1_1"/><i><font color="Green" title="E70">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">p'</font>,<font color="Maroon" title="c9">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"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E2:181_1_1"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E10:181_1_1"/><b>then </b>
<font color="Maroon" title="c10">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"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</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>then consider </b><font color="Maroon" title="c17">e</font>, <font color="Maroon" title="c18">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E12:181_1_1"/><i><font color="Green" title="E71">A8</font></i>: 
( <font color="Maroon" title="c17">e</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> &amp; <font color="Maroon" title="c18">f</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="c4">Q</font> )
 <b>and </b><br/><a NAME="E13:181_1_1"/><i><font color="Green" title="E72">A9</font></i>: 
<font color="Maroon" title="c10">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">e</font>,<font color="Maroon" title="c18">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E14:181_1_1"/><i><font color="Green" title="E73">A10</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">q'</font>,<font color="Maroon" title="c11">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"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E3:181_1_1"><i><font color="Green" title="E66">A3</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E15:181_1_1"/><b>then </b>
<font color="Maroon" title="c12">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"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</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>then consider </b><font color="Maroon" title="c19">g</font>, <font color="Maroon" title="c20">h</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E17:181_1_1"/><i><font color="Green" title="E74">A11</font></i>: 
( <font color="Maroon" title="c19">g</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> &amp; <font color="Maroon" title="c20">h</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="c4">Q</font> )
 <b>and </b><br/><a NAME="E18:181_1_1"/><i><font color="Green" title="E75">A12</font></i>: 
<font color="Maroon" title="c12">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">g</font>,<font color="Maroon" title="c20">h</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">P</font> = <font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c22">Q</font> = <font color="Maroon" title="c4">Q</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a>  <a href="pcs_0.html#L2" title="PCS_0:struct.2">pcs-Str</a>  <b>by </b><i><a class="txt" href="pcs_0.html#E7:181_1_1"><i><font color="Green" title="E69">A6</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c23">a</font> = <font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c24">c</font> = <font color="Maroon" title="c15">c</font>, <font color="Maroon" title="c25">e</font> = <font color="Maroon" title="c17">e</font>, <font color="Maroon" title="c26">g</font> = <font color="Maroon" title="c19">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c21">P</font> <b>by </b><i><a class="txt" href="pcs_0.html#E7:181_1_1"><i><font color="Green" title="E69">A6</font></i></a>, <a class="txt" href="pcs_0.html#E12:181_1_1"><i><font color="Green" title="E71">A8</font></i></a>, <a class="txt" href="pcs_0.html#E17:181_1_1"><i><font color="Green" title="E74">A11</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c27">b</font> = <font color="Maroon" title="c14">b</font>, <font color="Maroon" title="c28">d</font> = <font color="Maroon" title="c16">d</font>, <font color="Maroon" title="c29">f</font> = <font color="Maroon" title="c18">f</font>, <font color="Maroon" title="c30">h</font> = <font color="Maroon" title="c20">h</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c22">Q</font> <b>by </b><i><a class="txt" href="pcs_0.html#E7:181_1_1"><i><font color="Green" title="E69">A6</font></i></a>, <a class="txt" href="pcs_0.html#E12:181_1_1"><i><font color="Green" title="E71">A8</font></i></a>, <a class="txt" href="pcs_0.html#E17:181_1_1"><i><font color="Green" title="E74">A11</font></i></a></i>;<br/>
<a NAME="E22:181_1_1"/>
<span class="p1"><a href="pcs_0.html#K9" title="PCS_0:func.9">[^</a><span class="default"><font color="Maroon" title="c23">a</font>,<font color="Maroon" title="c27">b</font></span><a href="pcs_0.html#K9" title="PCS_0:func.9">^]</a></span> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <span class="p1"><a href="pcs_0.html#K9" title="PCS_0:func.9">[^</a><span class="default"><font color="Maroon" title="c24">c</font>,<font color="Maroon" title="c28">d</font></span><a href="pcs_0.html#K9" title="PCS_0:func.9">^]</a></span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E4:181_1_1"><i><font color="Green" title="E67">A4</font></i></a>, <a class="txt" href="pcs_0.html#E6:181_1_1"><i><font color="Green" title="E68">A5</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/>
<a NAME="E23:181_1_1"/><b>then </b><i><font color="Green" title="E76">A13</font></i>: 
( <font color="Maroon" title="c23">a</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c24">c</font> or <font color="Maroon" title="c27">b</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c28">d</font> )
 
<b>by </b><i><a class="ref" href="pcs_0.html#T6" target="_self" title="PCS_0:th.6">Th6</a></i>;<br/>
<a NAME="E24:181_1_1"/><i><font color="Green" title="E77">A14</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c21">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c22">Q</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c21">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c22">Q</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c21">P</font>,<font color="Maroon" title="c22">Q</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#D2" title="YELLOW_3:def.2">YELLOW_3:def 2</a></i>;<br/>
<a NAME="E25:181_1_1"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c25">e</font>,<font color="Maroon" title="c29">f</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c23">a</font>,<font color="Maroon" title="c27">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E6:181_1_1"><i><font color="Green" title="E68">A5</font></i></a>, <a class="txt" href="pcs_0.html#E9:181_1_1"><i><font color="Green" title="E70">A7</font></i></a>, <a class="txt" href="pcs_0.html#E13:181_1_1"><i><font color="Green" title="E72">A9</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E26:181_1_1"/><b>then </b><i><font color="Green" title="E78">A15</font></i>: 
( <font color="Maroon" title="c25">e</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c23">a</font> &amp; <font color="Maroon" title="c29">f</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c27">b</font> )
 
<b>by </b><i><a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></i>;<br/>
<a NAME="E27:181_1_1"/>
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c26">g</font>,<font color="Maroon" title="c30">h</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c24">c</font>,<font color="Maroon" title="c28">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 
<b>by </b><i><a class="txt" href="pcs_0.html#E6:181_1_1"><i><font color="Green" title="E68">A5</font></i></a>, <a class="txt" href="pcs_0.html#E14:181_1_1"><i><font color="Green" title="E73">A10</font></i></a>, <a class="txt" href="pcs_0.html#E18:181_1_1"><i><font color="Green" title="E75">A12</font></i></a>, <a class="txt" href="pcs_0.html#E24:181_1_1"><i><font color="Green" title="E77">A14</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E28:181_1_1"/><b>then </b>
( <font color="Maroon" title="c26">g</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c24">c</font> &amp; <font color="Maroon" title="c30">h</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c28">d</font> )
 
<b>by </b><i><a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></i>;<br/>
<a NAME="E29:181_1_1"/><b>then </b>
( <font color="Maroon" title="c25">e</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c26">g</font> or <font color="Maroon" title="c29">f</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c30">h</font> )
 
<b>by </b><i><a class="txt" href="pcs_0.html#E23:181_1_1"><i><font color="Green" title="E76">A13</font></i></a>, <a class="txt" href="pcs_0.html#E26:181_1_1"><i><font color="Green" title="E78">A15</font></i></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></i>;<br/>
<a NAME="E30:181_1_1"/><b>then </b><i><font color="Green" title="E79">A16</font></i>: 
( <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c25">e</font>,<font color="Maroon" title="c26">g</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</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="c21">P</font> or <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c29">f</font>,<font color="Maroon" title="c30">h</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</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="c22">Q</font> )
 
<b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/>
<a NAME="E31:181_1_1"/>
( <font color="Maroon" title="c10">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c25">e</font>,<font color="Maroon" title="c29">f</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> &amp; <font color="Maroon" title="c12">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c26">g</font>,<font color="Maroon" title="c30">h</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> )
 
<b>by </b><i><a class="txt" href="pcs_0.html#E13:181_1_1"><i><font color="Green" title="E72">A9</font></i></a>, <a class="txt" href="pcs_0.html#E18:181_1_1"><i><font color="Green" title="E75">A12</font></i></a></i>;<br/>
<b>hence </b><a NAME="E32:181_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">p'</font>,<font color="Maroon" title="c12">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"><font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K22" title="PCS_0:func.22">pcs-times</a> <font color="Maroon" title="c4">Q</font></span>)</span>
 <b>by </b><i><a class="txt" href="pcs_0.html#E30:181_1_1"><i><font color="Green" title="E79">A16</font></i></a>, <a class="ref" href="pcs_0.html#D3" target="_self" title="PCS_0:def.3">Def3</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/>


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