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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">N</font> being   <a href="pnproc_1.html#M4" title="PNPROC_1:mode.4">Petri_net</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">R</font> being  <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Olive" title="b1">N</font> holds  <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">R</font></span><br/><b>let </b><font color="Maroon" title="c2">N</font> be    <a href="pnproc_1.html#M4" title="PNPROC_1:mode.4">Petri_net</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Maroon" title="c2">N</font> holds  <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">R</font></span><br/><b>let </b><font color="Maroon" title="c3">R</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"> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">R</font></span><br/>





<b>thus </b><a NAME="E1:125"/>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">R</font>
  <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"> <font color="Maroon" title="c3">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="125_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> )</span><br/>

<b>assume </b><a NAME="E1:125_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">C</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="E3:125_1"/><i><font color="Green" title="E82">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</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="c5">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> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &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="c3">R</font> ) )
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">q1</font>, <font color="Maroon" title="c7">q2</font> being   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a><b> such that </b><br/><a NAME="E5:125_1"/><i><font color="Green" title="E83">A2</font></i>: 
( <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">q2</font> &amp; <font color="Maroon" title="c6">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">q2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c7">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:125_1"><i><font color="Green" title="E82">A1</font></i></a></i>;<br/>
<a NAME="E6:125_1"/>
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E5:125_1"><i><font color="Green" title="E83">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:125_1"/><b>then </b>
<font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E2"><i><font color="Green" title="E2">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:125_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E3:125_1"><i><font color="Green" title="E82">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E5:125_1"><i><font color="Green" title="E83">A2</font></i></a>, <a class="ref" href="finseq_3.html#T125" title="FINSEQ_3:th.125">FINSEQ_3:125</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="c4">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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font> )</span><br/>

<b>assume </b><a NAME="E2:125"/><i><font color="Green" title="E82">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c5">C</font> = <font color="Maroon" title="c4">x</font> as   <a href="pnproc_1.html#NM6" title="PNPROC_1:NM.6">firing-sequence</a> of <font color="Maroon" title="c2">N</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">q1</font> =  <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font>, <font color="Maroon" title="c7">q2</font> = <font color="Maroon" title="c5">C</font> as   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> ;<br/>
<a NAME="E5:125"/>
<font color="Maroon" title="c6">q1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c7">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E6:125"/><b>then </b>
(  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c7">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1</font> &amp; <font color="Maroon" title="c6">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c6">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">q2</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T125" title="FINSEQ_3:th.125">FINSEQ_3:125</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E7:125"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E2:125"><i><font color="Green" title="E82">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>
