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<b>let </b><font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c4">Q</font> be   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">P</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">Q</font> implies  <a href="pcs_0.html#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font> is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a> )</span><br/>

<b>set </b><font color="Maroon" title="c5">D1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font>;<br/>
<b>set </b><font color="Maroon" title="c6">D2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Q</font>;<br/>
<b>set </b><font color="Maroon" title="c7">R1</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font>;<br/>
<b>set </b><font color="Maroon" title="c8">R2</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font>;<br/>
<b>set </b><font color="Maroon" title="c9">T1</font> = the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font>;<br/>
<b>set </b><font color="Maroon" title="c10">T2</font> = the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font>;<br/>
<b>set </b><font color="Maroon" title="c11">R</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font>;<br/>
<b>set </b><font color="Maroon" title="c12">T</font> = the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font>;<br/>
<b>assume </b><a NAME="E1:139"/><i><font color="Green" title="E48">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Q</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="tsep_1.html#D3" title="TSEP_1:def.3">TSEP_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pcs_0.html#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font> is <a href="pcs_0.html#V13" title="PCS_0:attr.13">pcs-compatible</a></span><br/>

<b>let </b><font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c14">p'</font>, <font color="Maroon" title="c15">q</font>, <font color="Maroon" title="c16">q'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="pcs_0.html#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">PCS_0:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c13">p</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c15">q</font> &amp; <font color="Maroon" title="c14">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c13">p</font> &amp; <font color="Maroon" title="c16">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">q</font> implies <font color="Maroon" title="c14">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c16">q'</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:139"/><i><font color="Green" title="E49">A2</font></i>: 
<font color="Maroon" title="c13">p</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c15">q</font>
 <b>and </b><br/><a NAME="E3:139"/><i><font color="Green" title="E50">A3</font></i>: 
<font color="Maroon" title="c14">p'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c13">p</font>
 <b>and </b><br/><a NAME="E4:139"/><i><font color="Green" title="E51">A4</font></i>: 
<font color="Maroon" title="c16">q'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c14">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c16">q'</font></span><br/>

<a NAME="E5:139"/><i><font color="Green" title="E52">A5</font></i>: 
 <a href="pcs_0.html#K19" title="PCS_0:func.19">pcs-sum</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">Q</font>)
 
<b>by </b><i><a class="ref" href="pcs_0.html#T15" target="_self" title="PCS_0:th.15">Th15</a></i>;<br/>
<a NAME="E6:139"/><b>then </b><i><font color="Green" title="E53">A6</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font>
 
<b>by </b><i><a class="txt" href="#E2:139"><i><font color="Green" title="E49">A2</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="139_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:139_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c4">Q</font> )
 </span><b>by </b><i><a class="txt" href="#E6:139"><i><font color="Green" title="E53">A6</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="139_1_1"><b>suppose </b></a><a NAME="E1:139_1_1"/><i><font color="Green" title="E54">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c14">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c16">q'</font></span><br/><div class="add"><a NAME="E2:139_1_1"/><b>then </b><i><font color="Green" title="E55">A8</font></i>: 
( <font color="Maroon" title="c13">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 <font color="Maroon" title="c3">P</font> &amp; <font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">p1</font> = <font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c18">q1</font> = <font color="Maroon" title="c15">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> <b>by </b><i><a class="txt" href="#E1:139_1_1"><i><font color="Green" title="E54">A7</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E4:139_1_1"/><i><font color="Green" title="E56">A9</font></i>: 
<font color="Maroon" title="c17">p1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c18">q1</font>
 <b>by </b><i><a class="txt" href="#E1:139_1_1"><i><font color="Green" title="E54">A7</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/><a NAME="E5:139_1_1"/><i><font color="Green" title="E57">A10</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">p'</font>,<font color="Maroon" title="c13">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 <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">q'</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font> )
 <b>by </b><i><a class="txt" href="#E3:139"><i><font color="Green" title="E50">A3</font></i></a>, <a class="txt" href="#E4:139"><i><font color="Green" title="E51">A4</font></i></a>, <a class="txt" href="#E5:139"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c19">p'1</font> = <font color="Maroon" title="c14">p'</font>, <font color="Maroon" title="c20">q'1</font> = <font color="Maroon" title="c16">q'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">P</font> <b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="#E2:139_1_1"><i><font color="Green" title="E55">A8</font></i></a>, <a class="txt" href="pcs_0.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E7:139_1_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">p'</font>,<font color="Maroon" title="c13">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 <font color="Maroon" title="c3">P</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">q'</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font> )
 <b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="#E2:139_1_1"><i><font color="Green" title="E55">A8</font></i></a>, <a class="txt" href="#E5:139_1_1"><i><font color="Green" title="E57">A10</font></i></a>, <a class="txt" href="pcs_0.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E8:139_1_1"/><b>then </b>
( <font color="Maroon" title="c19">p'1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">p1</font> &amp; <font color="Maroon" title="c20">q'1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">q1</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/><a NAME="E9:139_1_1"/><b>then </b>
<font color="Maroon" title="c19">p'1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c20">q'1</font>
 <b>by </b><i><a class="txt" href="#E4:139_1_1"><i><font color="Green" title="E56">A9</font></i></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></i>;<br/><a NAME="E10:139_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">p'1</font>,<font color="Maroon" title="c20">q'1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font>
 <b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/><a NAME="E11:139_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">p'1</font>,<font color="Maroon" title="c20">q'1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E12:139_1_1"/>
<font color="Maroon" title="c14">p'</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c16">q'</font>
 <b>by </b><i><a class="txt" href="#E5:139"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="139_1_2"><b>suppose </b></a><a NAME="E1:139_1_2"/><i><font color="Green" title="E54">A11</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">p</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c4">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c14">p'</font> <a href="pcs_0.html#R1" title="PCS_0:pred.1">(--)</a> <font color="Maroon" title="c16">q'</font></span><br/><div class="add"><a NAME="E2:139_1_2"/><b>then </b><i><font color="Green" title="E55">A12</font></i>: 
( <font color="Maroon" title="c13">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 <font color="Maroon" title="c4">Q</font> &amp; <font color="Maroon" title="c15">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 <font color="Maroon" title="c4">Q</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">p1</font> = <font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c18">q1</font> = <font color="Maroon" title="c15">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Q</font> <b>by </b><i><a class="txt" href="#E1:139_1_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E4:139_1_2"/><i><font color="Green" title="E56">A13</font></i>: 
<font color="Maroon" title="c17">p1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c18">q1</font>
 <b>by </b><i><a class="txt" href="#E1:139_1_2"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/><a NAME="E5:139_1_2"/><i><font color="Green" title="E57">A14</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">p'</font>,<font color="Maroon" title="c13">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 <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">q'</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">Q</font> )
 <b>by </b><i><a class="txt" href="#E3:139"><i><font color="Green" title="E50">A3</font></i></a>, <a class="txt" href="#E4:139"><i><font color="Green" title="E51">A4</font></i></a>, <a class="txt" href="#E5:139"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c19">p'1</font> = <font color="Maroon" title="c14">p'</font>, <font color="Maroon" title="c20">q'1</font> = <font color="Maroon" title="c16">q'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Q</font> <b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="#E2:139_1_2"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="pcs_0.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E7:139_1_2"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">p'</font>,<font color="Maroon" title="c13">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 <font color="Maroon" title="c4">Q</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">q'</font>,<font color="Maroon" title="c15">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 <font color="Maroon" title="c4">Q</font> )
 <b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="#E2:139_1_2"><i><font color="Green" title="E55">A12</font></i></a>, <a class="txt" href="#E5:139_1_2"><i><font color="Green" title="E57">A14</font></i></a>, <a class="txt" href="pcs_0.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E8:139_1_2"/><b>then </b>
( <font color="Maroon" title="c19">p'1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">p1</font> &amp; <font color="Maroon" title="c20">q'1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">q1</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/><a NAME="E9:139_1_2"/><b>then </b>
<font color="Maroon" title="c19">p'1</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c20">q'1</font>
 <b>by </b><i><a class="txt" href="#E4:139_1_2"><i><font color="Green" title="E56">A13</font></i></a>, <a class="ref" href="pcs_0.html#D22" target="_self" title="PCS_0:def.22">Def22</a></i>;<br/><a NAME="E10:139_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">p'1</font>,<font color="Maroon" title="c20">q'1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font>
 <b>by </b><i><a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>;<br/><a NAME="E11:139_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">p'1</font>,<font color="Maroon" title="c20">q'1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c3">P</font> <a href="pcs_0.html#K2" title="PCS_0:func.2">\/</a> the <a href="pcs_0.html#U1" title="PCS_0:sel.1">ToleranceRel</a> of <font color="Maroon" title="c4">Q</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E12:139_1_2"/>
<font color="Maroon" title="c14">p'</font> <a href="pcs_0.html#R2" title="PCS_0:pred.2">(--)</a> <font color="Maroon" title="c16">q'</font>
 <b>by </b><i><a class="txt" href="#E5:139"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="pcs_0.html#D7" target="_self" title="PCS_0:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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