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

<span class="kw">set </span><font color="Maroon" title="c5">P</font> =  <a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">IR</font> = 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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">TR</font> = 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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">CA</font> = 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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>;<br/>
<a NAME="E1:119_1_1"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D36" target="_self" title="PCS_0:def.36">Def36</a></span>;<br/>
<a NAME="E2:119_1_1"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D36" target="_self" title="PCS_0:def.36">Def36</a></span>;<br/>
<a NAME="E3:119_1_1"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">thus </span><a NAME="E4:119_1_1"/>
 <a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font> is  <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="119_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font>, <font color="Maroon" title="c10">y</font>, <font color="Maroon" title="c11">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="relat_2.html#D8" title="RELAT_2:def.8">RELAT_2:def 8</a>,<a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or  not <font color="Maroon" title="c10">y</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or  not <font color="Maroon" title="c11">z</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:119_1_1_1"/>
<font color="Maroon" title="c9">x</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_1"/>
<font color="Maroon" title="c10">y</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:119_1_1_1"/>
<font color="Maroon" title="c11">z</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E4:119_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c10">y</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> or <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">Z1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E6:119_1_1_1"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c10">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Z1</font>
 <span class="kw">and </span><br/><a NAME="E7:119_1_1_1"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
<font color="Maroon" title="c12">Z1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E9:119_1_1_1"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
<font color="Maroon" title="c13">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E10:119_1_1_1"/><span class="lab"><font color="Green" title="E50">A7</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Z1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:119_1_1_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">assume </span><a NAME="E11:119_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">z</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">Z2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E13:119_1_1_1"/><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Z2</font>
 <span class="kw">and </span><br/><a NAME="E14:119_1_1_1"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
<font color="Maroon" title="c14">Z2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">j</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E16:119_1_1_1"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
<font color="Maroon" title="c15">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E17:119_1_1_1"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Z2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:119_1_1_1"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">I</font> = <font color="Maroon" title="c3">I</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:119_1_1_1"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">C</font> = <font color="Maroon" title="c4">C</font> as   <a href="pcs_0.html#NM3" title="PCS_0:NM.3">pcs-Chain</a> of <font color="Maroon" title="c16">I</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">i</font> = <font color="Maroon" title="c13">i</font>, <font color="Maroon" title="c19">j</font> = <font color="Maroon" title="c15">j</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c16">I</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:119_1_1_1"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="txt" href="#E16:119_1_1_1"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E21:119_1_1_1"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c17">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">i</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D6" target="_self" title="PCS_0:def.6">Def6</a></span>;<br/>
<a NAME="E22:119_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A13</font></span>: 
<font color="Maroon" title="c9">x</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E10:119_1_1_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E23:119_1_1_1"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
<font color="Maroon" title="c10">y</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E10:119_1_1_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E21:119_1_1_1"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E24:119_1_1_1"/><span class="lab"><font color="Green" title="E58">A15</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c17">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">j</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D6" target="_self" title="PCS_0:def.6">Def6</a></span>;<br/>
<a NAME="E25:119_1_1_1"/><span class="lab"><font color="Green" title="E59">A16</font></span>: 
<font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c17">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E26:119_1_1_1"/><span class="lab"><font color="Green" title="E60">A17</font></span>: 
<font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c17">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E27:119_1_1_1"/><span class="lab"><font color="Green" title="E61">A18</font></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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E28:119_1_1_1"/><span class="lab"><font color="Green" title="E62">A19</font></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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:119_1_1_1_1"/>
( <font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font> or <font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:119_1_1_1"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="txt" href="#E26:119_1_1_1"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="pcs_0.html#D35" target="_self" title="PCS_0:def.35">Def35</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:119_1_1_1_1_1"/>
<font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span></span><br/><div class="add"><a NAME="E2:119_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A20</font></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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E3:119_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A21</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c10">y</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E10:119_1_1_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E21:119_1_1_1"><span class="lab"><font color="Green" title="E55">A12</font></span></a></span>;<br/><a NAME="E4:119_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A22</font></span>: 
<font color="Maroon" title="c9">x</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E5:119_1_1_1_1_1"/><span class="lab"><font color="Green" title="E66">A23</font></span>: 
<font color="Maroon" title="c10">y</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_1_1_1"><span class="lab"><font color="Green" title="E64">A21</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E6:119_1_1_1_1_1"/>
<font color="Maroon" title="c11">z</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:119_1_1_1"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E17:119_1_1_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E24:119_1_1_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E7:119_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A24</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c11">z</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E10:119_1_1_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E13:119_1_1_1"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E17:119_1_1_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E21:119_1_1_1"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="txt" href="#E24:119_1_1_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E28:119_1_1_1"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="txt" href="#E2:119_1_1_1_1_1"><span class="lab"><font color="Green" title="E63">A20</font></span></a>, <a class="txt" href="#E4:119_1_1_1_1_1"><span class="lab"><font color="Green" title="E65">A22</font></span></a>, <a class="txt" href="#E5:119_1_1_1_1_1"><span class="lab"><font color="Green" title="E66">A23</font></span></a>, <a class="ref" href="relat_2.html#D8" title="RELAT_2:def.8">RELAT_2:def 8</a></span>;<br/><a NAME="E8:119_1_1_1_1_1"/>
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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E14:119_1_1_1"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="txt" href="#E17:119_1_1_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E24:119_1_1_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></span>;<br/><span class="kw">hence </span><a NAME="E9:119_1_1_1_1_1"/>
<span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:119_1_1_1_1_1"><span class="lab"><font color="Green" title="E67">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:119_1_1_1_1_2"/>
<font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span></span><br/><div class="add"><a NAME="E2:119_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A25</font></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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c19">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E3:119_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">z</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:119_1_1_1"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E17:119_1_1_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E24:119_1_1_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a></span>;<br/><a NAME="E4:119_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">z</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E5:119_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A26</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c11">z</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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E10:119_1_1_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E13:119_1_1_1"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E17:119_1_1_1"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="txt" href="#E21:119_1_1_1"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="txt" href="#E22:119_1_1_1"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="txt" href="#E23:119_1_1_1"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="txt" href="#E24:119_1_1_1"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="txt" href="#E27:119_1_1_1"><span class="lab"><font color="Green" title="E61">A18</font></span></a>, <a class="txt" href="#E2:119_1_1_1_1_2"><span class="lab"><font color="Green" title="E63">A25</font></span></a>, <a class="ref" href="relat_2.html#D8" title="RELAT_2:def.8">RELAT_2:def 8</a></span>;<br/><a NAME="E6:119_1_1_1_1_2"/>
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="c17">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c18">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E7:119_1_1_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E10:119_1_1_1"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E21:119_1_1_1"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></span>;<br/><span class="kw">hence </span><a NAME="E7:119_1_1_1_1_2"/>
<span class="p1"><a href="pcs_0.html#NK13" title="PCS_0:NK.13">[^</a><span class="default">,</span><a href="pcs_0.html#NK13" title="PCS_0:NK.13">^]</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:119_1_1_1_1_2"><span class="lab"><font color="Green" title="E64">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>

<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>; <span class="comment"><font color="Red">:: 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="Red">::  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="E5:119_1_1"/><span class="lab"><font color="Green" title="E47">A27</font></span>: 
<font color="Maroon" title="c9">p</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c11">q</font>
 <span class="kw">and </span><br/><a NAME="E6:119_1_1"/><span class="lab"><font color="Green" title="E48">A28</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="E7:119_1_1"/><span class="lab"><font color="Green" title="E49">A29</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="Red">::  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="E8:119_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="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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1"><span class="lab"><font color="Green" title="E48">A28</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">Z1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E10:119_1_1"/><span class="lab"><font color="Green" title="E50">A30</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> <font color="Maroon" title="c13">Z1</font>
 <span class="kw">and </span><br/><a NAME="E11:119_1_1"/><span class="lab"><font color="Green" title="E51">A31</font></span>: 
<font color="Maroon" title="c13">Z1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E13:119_1_1"/><span class="lab"><font color="Green" title="E52">A32</font></span>: 
<font color="Maroon" title="c14">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E14:119_1_1"/><span class="lab"><font color="Green" title="E53">A33</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Z1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:119_1_1"><span class="lab"><font color="Green" title="E51">A31</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">I</font> = <font color="Maroon" title="c3">I</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:119_1_1"><span class="lab"><font color="Green" title="E52">A32</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">C</font> = <font color="Maroon" title="c4">C</font> as   <a href="pcs_0.html#NM3" title="PCS_0:NM.3">pcs-Chain</a> of <font color="Maroon" title="c15">I</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">i</font> = <font color="Maroon" title="c14">i</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c15">I</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:119_1_1"><span class="lab"><font color="Green" title="E52">A32</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E18:119_1_1"/><span class="lab"><font color="Green" title="E54">A34</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">i</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D20" target="_self" title="PCS_0:def.20">Def20</a></span>;<br/>
<a NAME="E19:119_1_1"/><span class="lab"><font color="Green" title="E55">A35</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">i</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D6" target="_self" title="PCS_0:def.6">Def6</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">pi1</font> = <font color="Maroon" title="c9">p</font>, <font color="Maroon" title="c19">p9i</font> = <font color="Maroon" title="c10">p9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E21:119_1_1"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:119_1_1"><span class="lab"><font color="Green" title="E49">A29</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">Z2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E23:119_1_1"/><span class="lab"><font color="Green" title="E56">A36</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> <font color="Maroon" title="c20">Z2</font>
 <span class="kw">and </span><br/><a NAME="E24:119_1_1"/><span class="lab"><font color="Green" title="E57">A37</font></span>: 
<font color="Maroon" title="c20">Z2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c16">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c21">j</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E26:119_1_1"/><span class="lab"><font color="Green" title="E58">A38</font></span>: 
<font color="Maroon" title="c21">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c16">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E27:119_1_1"/><span class="lab"><font color="Green" title="E59">A39</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">Z2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:119_1_1"><span class="lab"><font color="Green" title="E57">A37</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c22">j</font> = <font color="Maroon" title="c21">j</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c15">I</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:119_1_1"><span class="lab"><font color="Green" title="E58">A38</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E29:119_1_1"/><span class="lab"><font color="Green" title="E60">A40</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">j</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D20" target="_self" title="PCS_0:def.20">Def20</a></span>;<br/>
<a NAME="E30:119_1_1"/><span class="lab"><font color="Green" title="E61">A41</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K4" title="PCS_0:func.4">pcs-InternalRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">j</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D6" target="_self" title="PCS_0:def.6">Def6</a></span>;<br/>
<a NAME="E31:119_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A42</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E32:119_1_1"/><span class="lab"><font color="Green" title="E63">A43</font></span>: 
<font color="Maroon" title="c11">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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c23">qj</font> = <font color="Maroon" title="c11">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E34:119_1_1"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:119_1_1"><span class="lab"><font color="Green" title="E47">A27</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="c24">Z3</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E36:119_1_1"/><span class="lab"><font color="Green" title="E64">A44</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> <font color="Maroon" title="c24">Z3</font>
 <span class="kw">and </span><br/><a NAME="E37:119_1_1"/><span class="lab"><font color="Green" title="E65">A45</font></span>: 
<font color="Maroon" title="c24">Z3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c25">k</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E39:119_1_1"/><span class="lab"><font color="Green" title="E66">A46</font></span>: 
<font color="Maroon" title="c25">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E40:119_1_1"/><span class="lab"><font color="Green" title="E67">A47</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">Z3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:119_1_1"><span class="lab"><font color="Green" title="E65">A45</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c26">k</font> = <font color="Maroon" title="c25">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c15">I</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:119_1_1"><span class="lab"><font color="Green" title="E66">A46</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E42:119_1_1"/><span class="lab"><font color="Green" title="E68">A48</font></span>: 
<span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">k</font> <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 <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pcs_0.html#D20" target="_self" title="PCS_0:def.20">Def20</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">pk</font> = <font color="Maroon" title="c9">p</font>, <font color="Maroon" title="c28">qk</font> = <font color="Maroon" title="c11">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E44:119_1_1"/><span class="lab"><font color="Green" title="E69">A49</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c16">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E45:119_1_1"/><span class="lab"><font color="Green" title="E70">A50</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c16">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E46:119_1_1"/><span class="lab"><font color="Green" title="E71">A51</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c16">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E47:119_1_1"/><span class="lab"><font color="Green" title="E72">A52</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pcs_0.html#K7" title="PCS_0:func.7">pcs-ToleranceRels</a> <font color="Maroon" title="c16">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E48:119_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A53</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="#E18:119_1_1"><span class="lab"><font color="Green" title="E54">A34</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></span>;<br/>
<a NAME="E49:119_1_1"/><span class="lab"><font color="Green" title="E74">A54</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="#E29:119_1_1"><span class="lab"><font color="Green" title="E60">A40</font></span></a>, <a class="txt" href="#E47:119_1_1"><span class="lab"><font color="Green" title="E72">A52</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></span>;<br/>
<a NAME="E50:119_1_1"/><span class="lab"><font color="Green" title="E75">A55</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="#E37:119_1_1"><span class="lab"><font color="Green" title="E65">A45</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:119_1_1_2"/>
( ( <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> &amp; <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> ) or ( <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> &amp; <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> ) or ( <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> &amp; <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> ) or ( <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> &amp; <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> ) or ( <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> &amp; <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> ) or ( <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> &amp; <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:119_1_1"><span class="lab"><font color="Green" title="E69">A49</font></span></a>, <a class="txt" href="#E45:119_1_1"><span class="lab"><font color="Green" title="E70">A50</font></span></a>, <a class="txt" href="#E46:119_1_1"><span class="lab"><font color="Green" title="E71">A51</font></span></a>, <a class="ref" href="pcs_0.html#D35" target="_self" title="PCS_0:def.35">Def35</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2_1"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:119_1_1_2_1"/><span class="lab"><font color="Green" title="E76">A56</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_2_1"/><span class="lab"><font color="Green" title="E77">A57</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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/><div class="add"><a NAME="E3:119_1_1_2_1"/><span class="lab"><font color="Green" title="E78">A58</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_1"><span class="lab"><font color="Green" title="E77">A57</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E4:119_1_1_2_1"/>
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_1"><span class="lab"><font color="Green" title="E76">A56</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E5:119_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A59</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a></span>;<br/><a NAME="E6:119_1_1_2_1"/><span class="kw">then </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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_1"><span class="lab"><font color="Green" title="E78">A58</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c29">p9k</font> = <font color="Maroon" title="c10">p9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E8:119_1_1_2_1"/>
<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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="txt" href="#E3:119_1_1_2_1"><span class="lab"><font color="Green" title="E78">A58</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c30">q9k</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E10:119_1_1_2_1"/><span class="lab"><font color="Green" title="E80">A60</font></span>: 
<font color="Maroon" title="c29">p9k</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c27">pk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_1"><span class="lab"><font color="Green" title="E78">A58</font></span></a>, <a class="txt" href="#E5:119_1_1_2_1"><span class="lab"><font color="Green" title="E79">A59</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E11:119_1_1_2_1"/><span class="lab"><font color="Green" title="E81">A61</font></span>: 
<font color="Maroon" title="c30">q9k</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c28">qk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="txt" href="#E3:119_1_1_2_1"><span class="lab"><font color="Green" title="E78">A58</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E12:119_1_1_2_1"/>
<font color="Maroon" title="c27">pk</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c28">qk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/><a NAME="E13:119_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">p9k</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c30">q9k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1_2_1"><span class="lab"><font color="Green" title="E80">A60</font></span></a>, <a class="txt" href="#E11:119_1_1_2_1"><span class="lab"><font color="Green" title="E81">A61</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/><a NAME="E14:119_1_1_2_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c29">p9k</font>,<font color="Maroon" title="c30">q9k</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E15:119_1_1_2_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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:119_1_1"><span class="lab"><font color="Green" title="E75">A55</font></span></a></span>; <span class="comment"><font color="Red">:: 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="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2_2"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:119_1_1_2_2"/><span class="lab"><font color="Green" title="E76">A62</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_2_2"/><span class="lab"><font color="Green" title="E77">A63</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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/><div class="add"><a NAME="E3:119_1_1_2_2"/><span class="lab"><font color="Green" title="E78">A64</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_2"><span class="lab"><font color="Green" title="E77">A63</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E4:119_1_1_2_2"/><span class="lab"><font color="Green" title="E79">A65</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_2"><span class="lab"><font color="Green" title="E76">A62</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E5:119_1_1_2_2"/>
<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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="txt" href="#E3:119_1_1_2_2"><span class="lab"><font color="Green" title="E78">A64</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c29">p9k</font> = <font color="Maroon" title="c10">p9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E7:119_1_1_2_2"/><span class="lab"><font color="Green" title="E80">A66</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="txt" href="#E4:119_1_1_2_2"><span class="lab"><font color="Green" title="E79">A65</font></span></a></span>;<br/><a NAME="E8:119_1_1_2_2"/><span class="kw">then </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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_2"><span class="lab"><font color="Green" title="E78">A64</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c30">q9k</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E10:119_1_1_2_2"/><span class="lab"><font color="Green" title="E81">A67</font></span>: 
<font color="Maroon" title="c29">p9k</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c27">pk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="txt" href="#E3:119_1_1_2_2"><span class="lab"><font color="Green" title="E78">A64</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E11:119_1_1_2_2"/><span class="lab"><font color="Green" title="E82">A68</font></span>: 
<font color="Maroon" title="c30">q9k</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c28">qk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_2"><span class="lab"><font color="Green" title="E78">A64</font></span></a>, <a class="txt" href="#E7:119_1_1_2_2"><span class="lab"><font color="Green" title="E80">A66</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E12:119_1_1_2_2"/>
<font color="Maroon" title="c27">pk</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c28">qk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/><a NAME="E13:119_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c29">p9k</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c30">q9k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1_2_2"><span class="lab"><font color="Green" title="E81">A67</font></span></a>, <a class="txt" href="#E11:119_1_1_2_2"><span class="lab"><font color="Green" title="E82">A68</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/><a NAME="E14:119_1_1_2_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c29">p9k</font>,<font color="Maroon" title="c30">q9k</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E15:119_1_1_2_2"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:119_1_1"><span class="lab"><font color="Green" title="E75">A55</font></span></a></span>; <span class="comment"><font color="Red">:: 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="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2_3"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:119_1_1_2_3"/><span class="lab"><font color="Green" title="E76">A69</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_2_3"/><span class="lab"><font color="Green" title="E77">A70</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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/><div class="add"><a NAME="E3:119_1_1_2_3"/><span class="lab"><font color="Green" title="E78">A71</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_3"><span class="lab"><font color="Green" title="E77">A70</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E4:119_1_1_2_3"/><span class="lab"><font color="Green" title="E79">A72</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_3"><span class="lab"><font color="Green" title="E77">A70</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E5:119_1_1_2_3"/>
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_3"><span class="lab"><font color="Green" title="E76">A69</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E6:119_1_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A73</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a></span>;<br/><a NAME="E7:119_1_1_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A74</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_3"><span class="lab"><font color="Green" title="E78">A71</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c29">p9j</font> = <font color="Maroon" title="c10">p9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">q9j</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">pj</font> = <font color="Maroon" title="c9">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:119_1_1_2_3"><span class="lab"><font color="Green" title="E81">A74</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E11:119_1_1_2_3"/><span class="lab"><font color="Green" title="E82">A75</font></span>: 
<font color="Maroon" title="c29">p9j</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c31">pj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_3"><span class="lab"><font color="Green" title="E78">A71</font></span></a>, <a class="txt" href="#E6:119_1_1_2_3"><span class="lab"><font color="Green" title="E80">A73</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E12:119_1_1_2_3"/><span class="lab"><font color="Green" title="E83">A76</font></span>: 
<font color="Maroon" title="c30">q9j</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c23">qj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E13:119_1_1_2_3"/>
<font color="Maroon" title="c31">pj</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c23">qj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="txt" href="#E4:119_1_1_2_3"><span class="lab"><font color="Green" title="E79">A72</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/><a NAME="E14:119_1_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c29">p9j</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c30">q9j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:119_1_1_2_3"><span class="lab"><font color="Green" title="E82">A75</font></span></a>, <a class="txt" href="#E12:119_1_1_2_3"><span class="lab"><font color="Green" title="E83">A76</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/><a NAME="E15:119_1_1_2_3"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c29">p9j</font>,<font color="Maroon" title="c30">q9j</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E16:119_1_1_2_3"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:119_1_1"><span class="lab"><font color="Green" title="E74">A54</font></span></a></span>; <span class="comment"><font color="Red">:: 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="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2_4"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:119_1_1_2_4"/><span class="lab"><font color="Green" title="E76">A77</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_2_4"/><span class="lab"><font color="Green" title="E77">A78</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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/><div class="add"><a NAME="E3:119_1_1_2_4"/><span class="lab"><font color="Green" title="E78">A79</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_4"><span class="lab"><font color="Green" title="E77">A78</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E4:119_1_1_2_4"/><span class="lab"><font color="Green" title="E79">A80</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_4"><span class="lab"><font color="Green" title="E77">A78</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E5:119_1_1_2_4"/><span class="lab"><font color="Green" title="E80">A81</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_4"><span class="lab"><font color="Green" title="E76">A77</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E6:119_1_1_2_4"/><span class="lab"><font color="Green" title="E81">A82</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="txt" href="#E3:119_1_1_2_4"><span class="lab"><font color="Green" title="E78">A79</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c29">p9j</font> = <font color="Maroon" title="c10">p9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">q9j</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">pj</font> = <font color="Maroon" title="c9">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1_2_4"><span class="lab"><font color="Green" title="E81">A82</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E10:119_1_1_2_4"/>
<font color="Maroon" title="c11">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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c32">qi</font> = <font color="Maroon" title="c11">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_4"><span class="lab"><font color="Green" title="E76">A77</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><a NAME="E12:119_1_1_2_4"/><span class="lab"><font color="Green" title="E82">A83</font></span>: 
<font color="Maroon" title="c29">p9j</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c31">pj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="txt" href="#E3:119_1_1_2_4"><span class="lab"><font color="Green" title="E78">A79</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E13:119_1_1_2_4"/><span class="lab"><font color="Green" title="E83">A84</font></span>: 
<font color="Maroon" title="c30">q9j</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c23">qj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E14:119_1_1_2_4"/>
<font color="Maroon" title="c18">pi1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c32">qi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="txt" href="#E5:119_1_1_2_4"><span class="lab"><font color="Green" title="E80">A81</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/><a NAME="E15:119_1_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c31">pj</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c23">qj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:119_1_1_2_4"><span class="lab"><font color="Green" title="E79">A80</font></span></a>, <a class="ref" href="pcs_0.html#T9" target="_self" title="PCS_0:th.9">Th9</a></span>;<br/><a NAME="E16:119_1_1_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c29">p9j</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c30">q9j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:119_1_1_2_4"><span class="lab"><font color="Green" title="E82">A83</font></span></a>, <a class="txt" href="#E13:119_1_1_2_4"><span class="lab"><font color="Green" title="E83">A84</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/><a NAME="E17:119_1_1_2_4"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c29">p9j</font>,<font color="Maroon" title="c30">q9j</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E18:119_1_1_2_4"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:119_1_1"><span class="lab"><font color="Green" title="E74">A54</font></span></a></span>; <span class="comment"><font color="Red">:: 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="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2_5"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:119_1_1_2_5"/><span class="lab"><font color="Green" title="E76">A85</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_2_5"/><span class="lab"><font color="Green" title="E77">A86</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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/><div class="add"><a NAME="E3:119_1_1_2_5"/><span class="lab"><font color="Green" title="E78">A87</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_5"><span class="lab"><font color="Green" title="E77">A86</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E4:119_1_1_2_5"/><span class="lab"><font color="Green" title="E79">A88</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_5"><span class="lab"><font color="Green" title="E76">A85</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E5:119_1_1_2_5"/><span class="lab"><font color="Green" title="E80">A89</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_5"><span class="lab"><font color="Green" title="E77">A86</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">q9i</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:119_1_1"><span class="lab"><font color="Green" title="E62">A42</font></span></a>, <a class="txt" href="#E2:119_1_1_2_5"><span class="lab"><font color="Green" title="E77">A86</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">qi</font> = <font color="Maroon" title="c11">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:119_1_1"><span class="lab"><font color="Green" title="E63">A43</font></span></a>, <a class="txt" href="#E2:119_1_1_2_5"><span class="lab"><font color="Green" title="E77">A86</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><a NAME="E8:119_1_1_2_5"/>
<font color="Maroon" title="c9">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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c31">pj</font> = <font color="Maroon" title="c9">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_5"><span class="lab"><font color="Green" title="E76">A85</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><a NAME="E10:119_1_1_2_5"/><span class="lab"><font color="Green" title="E81">A90</font></span>: 
<font color="Maroon" title="c19">p9i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">pi1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E11:119_1_1_2_5"/><span class="lab"><font color="Green" title="E82">A91</font></span>: 
<font color="Maroon" title="c29">q9i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c30">qi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="txt" href="#E5:119_1_1_2_5"><span class="lab"><font color="Green" title="E80">A89</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E12:119_1_1_2_5"/>
<font color="Maroon" title="c31">pj</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c23">qj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="txt" href="#E4:119_1_1_2_5"><span class="lab"><font color="Green" title="E79">A88</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/><a NAME="E13:119_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c18">pi1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c30">qi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_1_2_5"><span class="lab"><font color="Green" title="E78">A87</font></span></a>, <a class="ref" href="pcs_0.html#T9" target="_self" title="PCS_0:th.9">Th9</a></span>;<br/><a NAME="E14:119_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c19">p9i</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c29">q9i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1_2_5"><span class="lab"><font color="Green" title="E81">A90</font></span></a>, <a class="txt" href="#E11:119_1_1_2_5"><span class="lab"><font color="Green" title="E82">A91</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/><a NAME="E15:119_1_1_2_5"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">p9i</font>,<font color="Maroon" title="c29">q9i</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E16:119_1_1_2_5"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:119_1_1"><span class="lab"><font color="Green" title="E73">A53</font></span></a></span>; <span class="comment"><font color="Red">:: 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="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1_2_6"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:119_1_1_2_6"/><span class="lab"><font color="Green" title="E76">A92</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font>
 <span class="kw">and </span><br/><a NAME="E2:119_1_1_2_6"/><span class="lab"><font color="Green" title="E77">A93</font></span>: 
<font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font> <a href="pcs_0.html#R3" title="PCS_0:pred.3">c=</a> <font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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/><div class="add"><a NAME="E3:119_1_1_2_6"/><span class="lab"><font color="Green" title="E78">A94</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_6"><span class="lab"><font color="Green" title="E77">A93</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E4:119_1_1_2_6"/><span class="lab"><font color="Green" title="E79">A95</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:119_1_1_2_6"><span class="lab"><font color="Green" title="E77">A93</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><a NAME="E5:119_1_1_2_6"/><span class="lab"><font color="Green" title="E80">A96</font></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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_6"><span class="lab"><font color="Green" title="E76">A92</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">q9k</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:119_1_1"><span class="lab"><font color="Green" title="E62">A42</font></span></a>, <a class="txt" href="#E1:119_1_1_2_6"><span class="lab"><font color="Green" title="E76">A92</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><a NAME="E7:119_1_1_2_6"/><span class="lab"><font color="Green" title="E81">A97</font></span>: 
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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c22">j</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c26">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_1_2_6"><span class="lab"><font color="Green" title="E76">A92</font></span></a>, <a class="ref" href="pcs_0.html#D34" target="_self" title="PCS_0:def.34">Def34</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c30">q9i</font> = <font color="Maroon" title="c12">q9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:119_1_1"><span class="lab"><font color="Green" title="E62">A42</font></span></a>, <a class="txt" href="#E2:119_1_1_2_6"><span class="lab"><font color="Green" title="E77">A93</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">qi</font> = <font color="Maroon" title="c11">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:119_1_1"><span class="lab"><font color="Green" title="E63">A43</font></span></a>, <a class="txt" href="#E2:119_1_1_2_6"><span class="lab"><font color="Green" title="E77">A93</font></span></a>, <a class="txt" href="#E7:119_1_1_2_6"><span class="lab"><font color="Green" title="E81">A97</font></span></a>, <a class="txt" href="pcs_0.html#E47"><span class="lab"><font color="Green" title="E39">Lm3</font></span></a></span>;<br/><a NAME="E10:119_1_1_2_6"/><span class="lab"><font color="Green" title="E82">A98</font></span>: 
<font color="Maroon" title="c29">q9k</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c28">qk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:119_1_1"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E27:119_1_1"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E30:119_1_1"><span class="lab"><font color="Green" title="E61">A41</font></span></a>, <a class="txt" href="#E5:119_1_1_2_6"><span class="lab"><font color="Green" title="E80">A96</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E11:119_1_1_2_6"/><span class="lab"><font color="Green" title="E83">A99</font></span>: 
<font color="Maroon" title="c19">p9i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">pi1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:119_1_1"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="txt" href="#E14:119_1_1"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="txt" href="#E19:119_1_1"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E12:119_1_1_2_6"/><span class="lab"><font color="Green" title="E84">A100</font></span>: 
<font color="Maroon" title="c30">q9i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c31">qi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:119_1_1_2_6"><span class="lab"><font color="Green" title="E79">A95</font></span></a>, <a class="txt" href="#E10:119_1_1_2_6"><span class="lab"><font color="Green" title="E82">A98</font></span></a>, <a class="ref" href="pcs_0.html#T8" target="_self" title="PCS_0:th.8">Th8</a></span>;<br/><a NAME="E13:119_1_1_2_6"/>
<font color="Maroon" title="c18">pi1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c31">qi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:119_1_1"><span class="lab"><font color="Green" title="E64">A44</font></span></a>, <a class="txt" href="#E40:119_1_1"><span class="lab"><font color="Green" title="E67">A47</font></span></a>, <a class="txt" href="#E42:119_1_1"><span class="lab"><font color="Green" title="E68">A48</font></span></a>, <a class="txt" href="#E3:119_1_1_2_6"><span class="lab"><font color="Green" title="E78">A94</font></span></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></span>;<br/><a NAME="E14:119_1_1_2_6"/><span class="kw">then </span>
<font color="Maroon" title="c19">p9i</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c30">q9i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:119_1_1_2_6"><span class="lab"><font color="Green" title="E83">A99</font></span></a>, <a class="txt" href="#E12:119_1_1_2_6"><span class="lab"><font color="Green" title="E84">A100</font></span></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></span>;<br/><a NAME="E15:119_1_1_2_6"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">p9i</font>,<font color="Maroon" title="c30">q9i</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="c16">C</font> <a href="pcs_0.html#K16" title="PCS_0:func.16">.</a> <font color="Maroon" title="c17">i</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E16:119_1_1_2_6"/>
<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"><a href="pcs_0.html#K17" title="PCS_0:func.17">pcs-union</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:119_1_1"><span class="lab"><font color="Green" title="E73">A53</font></span></a></span>; <span class="comment"><font color="Red">:: 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="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
