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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">m</font> being   <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">marking</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">t1</font>, <font color="Olive" title="b3">t2</font> being   <a href="pnproc_1.html#M3" title="PNPROC_1:mode.3">transition</a> of <font color="Maroon" title="c1">P</font>  st <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b2">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b3">t2</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Olive" title="b1">m</font> holds <br/> <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Olive" title="b3">t2</font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Olive" title="b2">t1</font>,<font color="Olive" title="b1">m</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b2">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b3">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Olive" title="b2">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Olive" title="b3">t2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">m</font> be    <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">marking</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">t1</font>, <font color="Olive" title="b2">t2</font> being   <a href="pnproc_1.html#M3" title="PNPROC_1:mode.3">transition</a> of <font color="Maroon" title="c1">P</font>  st <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b1">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b2">t2</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m</font> holds <br/> <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Olive" title="b2">t2</font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Olive" title="b1">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b1">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Olive" title="b2">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Olive" title="b1">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Olive" title="b2">t2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">t1</font>, <font color="Maroon" title="c4">t2</font> be    <a href="pnproc_1.html#M3" title="PNPROC_1:mode.3">transition</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"> ( <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m</font> implies  <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c4">t2</font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c4">t2</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:53"/><i><font color="Green" title="E37">A1</font></i>: 
<span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c4">t2</font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><br/>

<a NAME="E2:53"/><i><font color="Green" title="E38">A2</font></i>: 
 <a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self" title="PNPROC_1:th.16">Th16</a></i>;<br/>
<a NAME="E3:53"/><b>then </b><i><font color="Green" title="E39">A3</font></i>: 
 <a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:53"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="pnproc_1.html#T14" target="_self" title="PNPROC_1:th.14">Th14</a></i>;<br/>
<a NAME="E4:53"/><b>then </b><i><font color="Green" title="E40">A4</font></i>: 
 <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c3">t1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D8" target="_self" title="PNPROC_1:def.8">Def8</a></i>;<br/>
<a NAME="E5:53"/><i><font color="Green" title="E41">A5</font></i>: 
 <a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T19" target="_self" title="PNPROC_1:th.19">Th19</a></i>;<br/>
<a NAME="E6:53"/><i><font color="Green" title="E42">A6</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:53"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E2:53"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="pnproc_1.html#T20" target="_self" title="PNPROC_1:th.20">Th20</a></i>;<br/>
<a NAME="E7:53"/>
<font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c3">t1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self" title="PNPROC_1:th.16">Th16</a></i>;<br/>
<a NAME="E8:53"/><b>then </b>
 <a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a>  <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:53"><i><font color="Green" title="E40">A4</font></i></a>, <a class="txt" href="pnproc_1.html#E5:53"><i><font color="Green" title="E41">A5</font></i></a>, <a class="txt" href="pnproc_1.html#E6:53"><i><font color="Green" title="E42">A6</font></i></a>, <a class="ref" href="pnproc_1.html#T14" target="_self" title="PNPROC_1:th.14">Th14</a></i>;<br/>
<b>hence </b> <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c4">t2</font>,<span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c4">t2</font></span>)</span>
<b>by </b><i><a class="ref" href="pnproc_1.html#D8" target="_self" title="PNPROC_1:def.8">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c4">t2</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E3:53"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="pnproc_1.html#D8" target="_self" title="PNPROC_1:def.8">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><a href="pnproc_1.html#K4" title="PNPROC_1:func.4">Pre</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K5" title="PNPROC_1:func.5">Post</a> <font color="Maroon" title="c4">t2</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:53"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E2:53"><i><font color="Green" title="E38">A2</font></i></a>, <a class="txt" href="pnproc_1.html#E5:53"><i><font color="Green" title="E41">A5</font></i></a>, <a class="ref" href="pnproc_1.html#T20" target="_self" title="PNPROC_1:th.20">Th20</a>, <a class="ref" href="pnproc_1.html#T21" target="_self" title="PNPROC_1:th.21">Th21</a></i>
;<br/> <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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