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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> ;<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>;<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>;<br/>





<b>thus </b><a NAME="E1:124"/>
<font color="Maroon" title="c3">R</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</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="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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="124_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><br/>

<b>assume </b><a NAME="E1:124_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> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</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>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">C1</font>, <font color="Maroon" title="c6">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="E3:124_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">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c6">C</font> &amp; <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> &amp; <font color="Maroon" title="c6">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font> )
 ;<br/>
<a NAME="E4:124_1"/>
<font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E3:124_1"><i><font color="Green" title="E82">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:124_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#E3:124_1"><i><font color="Green" title="E82">A1</font></i></a>, <a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<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><br/>

<b>assume </b><a NAME="E2:124"/><i><font color="Green" title="E82">A2</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>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">C</font> = <font color="Maroon" title="c4">x</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">N</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  ;<br/>
<a NAME="E4:124"/>
(  <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pnproc_1.html#K13" title="PNPROC_1:func.13">NeutralProcess</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <font color="Maroon" title="c2">N</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:124"/>
<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 href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</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>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E2:124"><i><font color="Green" title="E82">A2</font></i></a></i>;<br/>


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