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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">R1</font>, <font color="Olive" title="b3">R2</font> being  <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Olive" title="b1">N</font> holds  <font color="Olive" title="b2">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b3">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b3">R2</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">R1</font>, <font color="Olive" title="b2">R2</font> being  <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Maroon" title="c2">N</font> holds  <font color="Olive" title="b1">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b2">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">R1</font> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <font color="Olive" title="b2">R2</font></span><br/><b>let </b><font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">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="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c4">R2</font></span><br/><b>let </b><font color="Maroon" title="c5">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="c5">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#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</font> or <font color="Maroon" title="c5">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="c4">R2</font> )</span><br/>









<b>assume </b><a NAME="E1:100"/><i><font color="Green" title="E65">A1</font></i>: 
<font color="Maroon" title="c5">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#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c4">R2</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">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="c4">R2</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c5">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>consider </b><font color="Maroon" title="c7">C1</font>, <font color="Maroon" title="c8">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="E4:100"/><i><font color="Green" title="E66">A2</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c8">C2</font> &amp; <font color="Maroon" title="c7">C1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> &amp; <font color="Maroon" title="c8">C2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> )
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:100"><i><font color="Green" title="E65">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">q1</font> = <font color="Maroon" title="c7">C1</font>;<br/>
<b>set </b><font color="Maroon" title="c10">q2</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">C1</font></span>)</span> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c8">C2</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">q1</font> = <font color="Maroon" title="c7">C1</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<a NAME="E6:100"/>
( <font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">q1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">C1</font></span>)</span> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c8">C2</font></span>)</span> &amp; <font color="Maroon" title="c11">q1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">C1</font></span>)</span> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c8">C2</font> &amp;  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c11">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">C1</font></span>)</span> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c8">C2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> )
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:100"><i><font color="Green" title="E66">A2</font></i></a>, <a class="ref" href="pnproc_1.html#T61" target="_self" title="PNPROC_1:th.61">Th61</a>, <a class="ref" href="pnproc_1.html#T64" target="_self" title="PNPROC_1:th.64">Th64</a>, <a class="ref" href="pnproc_1.html#T65" target="_self" title="PNPROC_1:th.65">Th65</a>, <a class="ref" href="finseq_3.html#T125" title="FINSEQ_3:th.125">FINSEQ_3:125</a></i>;<br/>
<b>hence </b><a NAME="E7:100"/>
<font color="Maroon" title="c5">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="c4">R2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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