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

<span class="kw">let </span><font color="Maroon" title="c1">P</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N</font> being   <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">Petri_net</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">R1</font>, <font color="Olive" title="b3">R2</font>, <font color="Olive" title="b4">R</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">process</a> of <font color="Olive" title="b1">N</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b4">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b4">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b4">R</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be    <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">Petri_net</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">R1</font>, <font color="Olive" title="b2">R2</font>, <font color="Olive" title="b3">R</font> being  <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">process</a> of <font color="Maroon" title="c2">N</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b3">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b3">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b3">R</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">R2</font>, <font color="Maroon" title="c5">R</font> be   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">process</a> of <font color="Maroon" title="c2">N</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">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <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="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span></span><br/>









<span class="kw">thus </span><a NAME="E1:78"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <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="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span>
  <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:78_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">C</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E3:78_1"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C</font>
 <span class="kw">and </span><br/><a NAME="E4:78_1"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
 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="c7">C</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="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">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="c5">R</font> )
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">q1</font>, <font color="Maroon" title="c9">q2</font> being   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a><span class="kw"> such that </span><br/><a NAME="E6:78_1"/><span class="lab"><font color="Green" title="E47">A3</font></span>: 
<font color="Maroon" title="c7">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">q2</font>
 <span class="kw">and </span><br/><a NAME="E7:78_1"/><span class="lab"><font color="Green" title="E48">A4</font></span>: 
<font color="Maroon" title="c8">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c9">q2</font>
 <span class="kw">and </span><br/><a NAME="E8:78_1"/><span class="lab"><font color="Green" title="E49">A5</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">and </span><br/><a NAME="E9:78_1"/><span class="lab"><font color="Green" title="E50">A6</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c9">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:78_1"><span class="lab"><font color="Green" title="E46">A2</font></span></a></span>;<br/>
<a NAME="E10:78_1"/>
(  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> or  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:78_1"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E11:78_1"/><span class="kw">then </span>
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#NM5" title="PNPROC_1:NM.5">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="c3">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="c5">R</font> ) </span>}</span>  or <font color="Maroon" title="c6">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#NM5" title="PNPROC_1:NM.5">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="c4">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="c5">R</font> ) </span>}</span>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E6:78_1"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="txt" href="#E7:78_1"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="txt" href="#E9:78_1"><span class="lab"><font color="Green" title="E50">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:78_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>

<span class="kw">let </span><font color="Maroon" title="c6">x</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:78"/><span class="lab"><font color="Green" title="E45">A7</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span>)</span>
 ; <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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="78_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="E1:78_2"/>
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:78"><span class="lab"><font color="Green" title="E45">A7</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="78_2_1"><span class="kw">suppose </span></a><a NAME="E1:78_2_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">C</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E3:78_2_1"/><span class="lab"><font color="Green" title="E46">A8</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C</font>
 <span class="kw">and </span><br/><a NAME="E4:78_2_1"/><span class="lab"><font color="Green" title="E47">A9</font></span>: 
 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="c7">C</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="c3">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="c5">R</font> )
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c8">q1</font>, <font color="Maroon" title="c9">q2</font> being   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a><span class="kw"> such that </span><br/><a NAME="E6:78_2_1"/><span class="lab"><font color="Green" title="E48">A10</font></span>: 
<font color="Maroon" title="c7">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">q2</font>
 <span class="kw">and </span><br/><a NAME="E7:78_2_1"/><span class="lab"><font color="Green" title="E49">A11</font></span>: 
<font color="Maroon" title="c8">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c9">q2</font>
 <span class="kw">and </span><br/><a NAME="E8:78_2_1"/><span class="lab"><font color="Green" title="E50">A12</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font>
 <span class="kw">and </span><br/><a NAME="E9:78_2_1"/><span class="lab"><font color="Green" title="E51">A13</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c9">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:78_2_1"><span class="lab"><font color="Green" title="E47">A9</font></span></a></span>;<br/><a NAME="E10:78_2_1"/>
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:78_2_1"><span class="lab"><font color="Green" title="E50">A12</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E11:78_2_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_2_1"><span class="lab"><font color="Green" title="E46">A8</font></span></a>, <a class="txt" href="#E6:78_2_1"><span class="lab"><font color="Green" title="E48">A10</font></span></a>, <a class="txt" href="#E7:78_2_1"><span class="lab"><font color="Green" title="E49">A11</font></span></a>, <a class="txt" href="#E9:78_2_1"><span class="lab"><font color="Green" title="E51">A13</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="78_2_2"><span class="kw">suppose </span></a><a NAME="E1:78_2_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">C</font> being   <a href="pnproc_1.html#NM5" title="PNPROC_1:NM.5">firing-sequence</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E3:78_2_2"/><span class="lab"><font color="Green" title="E46">A14</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C</font>
 <span class="kw">and </span><br/><a NAME="E4:78_2_2"/><span class="lab"><font color="Green" title="E47">A15</font></span>: 
 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="c7">C</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="c4">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="c5">R</font> )
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c8">q1</font>, <font color="Maroon" title="c9">q2</font> being   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a><span class="kw"> such that </span><br/><a NAME="E6:78_2_2"/><span class="lab"><font color="Green" title="E48">A16</font></span>: 
<font color="Maroon" title="c7">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">q2</font>
 <span class="kw">and </span><br/><a NAME="E7:78_2_2"/><span class="lab"><font color="Green" title="E49">A17</font></span>: 
<font color="Maroon" title="c8">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c9">q2</font>
 <span class="kw">and </span><br/><a NAME="E8:78_2_2"/><span class="lab"><font color="Green" title="E50">A18</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">and </span><br/><a NAME="E9:78_2_2"/><span class="lab"><font color="Green" title="E51">A19</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c9">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:78_2_2"><span class="lab"><font color="Green" title="E47">A15</font></span></a></span>;<br/><a NAME="E10:78_2_2"/>
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:78_2_2"><span class="lab"><font color="Green" title="E50">A18</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E11:78_2_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c5">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_2_2"><span class="lab"><font color="Green" title="E46">A14</font></span></a>, <a class="txt" href="#E6:78_2_2"><span class="lab"><font color="Green" title="E48">A16</font></span></a>, <a class="txt" href="#E7:78_2_2"><span class="lab"><font color="Green" title="E49">A17</font></span></a>, <a class="txt" href="#E9:78_2_2"><span class="lab"><font color="Green" title="E51">A19</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>
