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<b>let </b><font color="Maroon" title="c5">R</font>, <font color="Maroon" title="c6">R1</font>, <font color="Maroon" title="c7">R2</font> be   <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C</font> where <font color="Olive" title="b1">C</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> ) </span>}</span>  implies <font color="Maroon" title="c5">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C</font> where <font color="Olive" title="b1">C</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span>  )</span><br/>





<b>assume </b><a NAME="E1:78_1_2"/><i><font color="Green" title="E48">A1</font></i>: 
<font color="Maroon" title="c5">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C1</font> where <font color="Olive" title="b1">C1</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> ) </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C</font> where <font color="Olive" title="b1">C</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span> </span><br/>

<b>thus </b><a NAME="E2:78_1_2"/>
<font color="Maroon" title="c5">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C2</font> where <font color="Olive" title="b1">C2</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C</font> where <font color="Olive" title="b1">C</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">R</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C2</font> where <font color="Olive" title="b1">C2</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:78_1_2_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C2</font> where <font color="Olive" title="b1">C2</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c9">C1</font> being   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font><b> such that </b><br/><a NAME="E3:78_1_2_1"/><i><font color="Green" title="E49">A2</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">C1</font> &amp;  ex <font color="Olive" title="b1">q1</font>, <font color="Olive" title="b2">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Maroon" title="c9">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">q2</font> &amp; <font color="Olive" title="b1">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b1">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> ) )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:78_1_2"><i><font color="Green" title="E48">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">X</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">C2</font> where <font color="Olive" title="b1">C2</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span> ;<br/>
<b>thus </b><a NAME="E4:78_1_2_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C2</font> where <font color="Olive" title="b1">C2</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:78_1_2_1"><i><font color="Green" title="E49">A2</font></i></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>

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C</font> where <font color="Olive" title="b1">C</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span>  or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font> )</span><br/>

<b>assume </b><a NAME="E3:78_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">C2</font> where <font color="Olive" title="b1">C2</font> is   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> :  ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Olive" title="b1">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">q2</font> &amp; <font color="Olive" title="b2">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b3">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font></span><br/>

<b>then consider </b><font color="Maroon" title="c9">C2</font> being   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font><b> such that </b><br/><a NAME="E5:78_1_2"/><i><font color="Green" title="E49">A3</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">C2</font> &amp;  ex <font color="Olive" title="b1">q1</font>, <font color="Olive" title="b2">q2</font> being  <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> st <br/>( <font color="Maroon" title="c9">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">q2</font> &amp; <font color="Olive" title="b1">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b1">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b2">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">R1</font> ) )
 ;<br/>
<b>thus </b><a NAME="E6:78_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:78_1_2"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E5:78_1_2"><i><font color="Green" title="E49">A3</font></i></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>
