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

<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">let </span><font color="Maroon" title="c9">p</font>, <font color="Maroon" title="c10">p9</font>, <font color="Maroon" title="c11">q</font>, <font color="Maroon" title="c12">q9</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>; <span class="comment"><font color="firebrick">:: according to </font></span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <font color="Maroon" title="c10">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">p</font> &amp; <font color="Maroon" title="c12">q9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c11">q</font> implies <font color="Maroon" title="c10">p9</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c12">q9</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:180_1_1"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:180_1_1"/><span class="lab"><font color="Green" title="E65">A2</font></span>: 
<font color="Maroon" title="c10">p9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">p</font>
 <span class="kw">and </span><br/><a NAME="E3:180_1_1"/><span class="lab"><font color="Green" title="E66">A3</font></span>: 
<font color="Maroon" title="c12">q9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c11">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">p9</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c12">q9</font></span><br/>

<a NAME="E4:180_1_1"/><span class="lab"><font color="Green" title="E67">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:180_1_1"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E6:180_1_1"/><span class="lab"><font color="Green" title="E68">A5</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E7:180_1_1"/><span class="lab"><font color="Green" title="E69">A6</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E8:180_1_1"/><span class="lab"><font color="Green" title="E70">A7</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E9:180_1_1"/><span class="lab"><font color="Green" title="E71">A8</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E10:180_1_1"/><span class="lab"><font color="Green" title="E72">A9</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E11:180_1_1"/><span class="lab"><font color="Green" title="E73">A10</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E12:180_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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D2" target="_self" title="PCS_0:def.2">Def2</a></span>;<br/>
<a NAME="E13:180_1_1"/><span class="lab"><font color="Green" title="E74">A11</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">p9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:180_1_1"><span class="lab"><font color="Green" title="E65">A2</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E14:180_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">p9</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E16:180_1_1"/><span class="lab"><font color="Green" title="E75">A12</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E17:180_1_1"/><span class="lab"><font color="Green" title="E76">A13</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E18:180_1_1"/><span class="lab"><font color="Green" title="E77">A14</font></span>: 
<font color="Maroon" title="c10">p9</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E19:180_1_1"/><span class="lab"><font color="Green" title="E78">A15</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">q9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:180_1_1"><span class="lab"><font color="Green" title="E66">A3</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E20:180_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">q9</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E22:180_1_1"/><span class="lab"><font color="Green" title="E79">A16</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E23:180_1_1"/><span class="lab"><font color="Green" title="E80">A17</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E24:180_1_1"/><span class="lab"><font color="Green" title="E81">A18</font></span>: 
<font color="Maroon" title="c12">q9</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:180_1_1"><span class="lab"><font color="Green" title="E70">A7</font></span></a>, <a class="txt" href="#E9:180_1_1"><span class="lab"><font color="Green" title="E71">A8</font></span></a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:180_1_1"><span class="lab"><font color="Green" title="E70">A7</font></span></a>, <a class="txt" href="#E10:180_1_1"><span class="lab"><font color="Green" title="E72">A9</font></span></a>, <a class="txt" href="#E16:180_1_1"><span class="lab"><font color="Green" title="E75">A12</font></span></a>, <a class="txt" href="#E22:180_1_1"><span class="lab"><font color="Green" title="E79">A16</font></span></a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:180_1_1"><span class="lab"><font color="Green" title="E71">A8</font></span></a>, <a class="txt" href="#E11:180_1_1"><span class="lab"><font color="Green" title="E73">A10</font></span></a>, <a class="txt" href="#E17:180_1_1"><span class="lab"><font color="Green" title="E76">A13</font></span></a>, <a class="txt" href="#E23:180_1_1"><span class="lab"><font color="Green" title="E80">A17</font></span></a></span>;<br/>
<a NAME="E28:180_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:180_1_1"><span class="lab"><font color="Green" title="E67">A4</font></span></a>, <a class="txt" href="#E6:180_1_1"><span class="lab"><font color="Green" title="E68">A5</font></span></a>, <a class="txt" href="#E7:180_1_1"><span class="lab"><font color="Green" title="E69">A6</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/>
<a NAME="E29:180_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A19</font></span>: 
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#T6" target="_self" title="PCS_0:th.6">Th6</a></span>;<br/>
<a NAME="E30:180_1_1"/><span class="lab"><font color="Green" title="E83">A20</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_3.html#D2" title="YELLOW_3:def.2">YELLOW_3:def 2</a></span>;<br/>
<a NAME="E31:180_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A21</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:180_1_1"><span class="lab"><font color="Green" title="E68">A5</font></span></a>, <a class="txt" href="#E13:180_1_1"><span class="lab"><font color="Green" title="E74">A11</font></span></a>, <a class="txt" href="#E18:180_1_1"><span class="lab"><font color="Green" title="E77">A14</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E32:180_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A22</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></span>;<br/>
<a NAME="E33:180_1_1"/><span class="lab"><font color="Green" title="E86">A23</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:180_1_1"><span class="lab"><font color="Green" title="E84">A21</font></span></a>, <a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></span>;<br/>
<a NAME="E34:180_1_1"/><span class="lab"><font color="Green" title="E87">A24</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:180_1_1"><span class="lab"><font color="Green" title="E69">A6</font></span></a>, <a class="txt" href="#E19:180_1_1"><span class="lab"><font color="Green" title="E78">A15</font></span></a>, <a class="txt" href="#E24:180_1_1"><span class="lab"><font color="Green" title="E81">A18</font></span></a>, <a class="txt" href="#E30:180_1_1"><span class="lab"><font color="Green" title="E83">A20</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E35:180_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A25</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></span>;<br/>
<a NAME="E36:180_1_1"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:180_1_1"><span class="lab"><font color="Green" title="E87">A24</font></span></a>, <a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></span>;<br/>
<a NAME="E37:180_1_1"/><span class="kw">then </span>
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:180_1_1"><span class="lab"><font color="Green" title="E82">A19</font></span></a>, <a class="txt" href="#E32:180_1_1"><span class="lab"><font color="Green" title="E85">A22</font></span></a>, <a class="txt" href="#E33:180_1_1"><span class="lab"><font color="Green" title="E86">A23</font></span></a>, <a class="txt" href="#E35:180_1_1"><span class="lab"><font color="Green" title="E88">A25</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/>
<a NAME="E38:180_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A26</font></span>: 
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/>
<a NAME="E39:180_1_1"/><span class="lab"><font color="Green" title="E90">A27</font></span>: 
<font color="Maroon" title="c10">p9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:180_1_1"><span class="lab"><font color="Green" title="E77">A14</font></span></a></span>;<br/>
<a NAME="E40:180_1_1"/>
<font color="Maroon" title="c12">q9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:180_1_1"><span class="lab"><font color="Green" title="E81">A18</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E41:180_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">p9</font>,<font color="Maroon" title="c12">q9</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:180_1_1"><span class="lab"><font color="Green" title="E89">A26</font></span></a>, <a class="txt" href="#E39:180_1_1"><span class="lab"><font color="Green" title="E90">A27</font></span></a>, <a class="ref" href="pcs_0.html#D3" target="_self" title="PCS_0:def.3">Def3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
