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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">P1</font>, <font color="Olive" title="b4">R2</font>, <font color="Olive" title="b5">P2</font> being  <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Olive" title="b1">N</font>  st <font color="Olive" title="b2">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">P1</font> &amp; <font color="Olive" title="b4">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">P2</font> holds <br/><font color="Olive" title="b2">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b4">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b5">P2</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">P1</font>, <font color="Olive" title="b3">R2</font>, <font color="Olive" title="b4">P2</font> being  <a href="pnproc_1.html#NM7" title="PNPROC_1:NM.7">process</a> of <font color="Maroon" title="c2">N</font>  st <font color="Olive" title="b1">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P1</font> &amp; <font color="Olive" title="b3">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">P2</font> holds <br/><font color="Olive" title="b1">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">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Olive" title="b4">P2</font></span><br/><b>let </b><font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">P1</font>, <font color="Maroon" title="c5">R2</font>, <font color="Maroon" title="c6">P2</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="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1</font> &amp; <font color="Maroon" title="c5">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P2</font> implies <font color="Maroon" title="c3">R1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c5">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c6">P2</font> )</span><br/>











<b>assume </b><a NAME="E1:101"/><i><font color="Green" title="E65">A1</font></i>: 
( <font color="Maroon" title="c3">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1</font> &amp; <font color="Maroon" title="c5">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P2</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="c5">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c6">P2</font></span><br/>

<b>let </b><font color="Maroon" title="c7">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="c7">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="c5">R2</font> or <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c6">P2</font> )</span><br/>

<b>assume </b><a NAME="E2:101"/>
<font color="Maroon" title="c7">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="c5">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="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c6">P2</font></span><br/>

<b>then consider </b><font color="Maroon" title="c8">C1</font>, <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="E4:101"/><i><font color="Green" title="E66">A2</font></i>: 
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">C1</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Maroon" title="c9">C2</font> &amp; <font color="Maroon" title="c8">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="c9">C2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">R2</font> )
 ;<br/>
<b>thus </b><a NAME="E5:101"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P1</font> <a href="pnproc_1.html#K10" title="PNPROC_1:func.10">before</a> <font color="Maroon" title="c6">P2</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:101"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E4:101"><i><font color="Green" title="E66">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/>


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