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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m</font> being  <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">t2</font>, <font color="Olive" title="b3">t1</font> being   <a href="pnproc_1.html#M1" title="PNPROC_1:mode.1">transition</a> of <font color="Maroon" title="c1">P</font> holds   <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="b3">t1</font>,<font color="Olive" title="b1">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Olive" title="b2">t2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Olive" title="b3">t1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">m</font> be   <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t2</font>, <font color="Olive" title="b2">t1</font> being   <a href="pnproc_1.html#M1" title="PNPROC_1:mode.1">transition</a> of <font color="Maroon" title="c1">P</font> holds   <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Olive" title="b1">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="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Olive" title="b1">t2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Olive" title="b2">t1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">t2</font>, <font color="Maroon" title="c4">t1</font> be    <a href="pnproc_1.html#M1" title="PNPROC_1:mode.1">transition</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">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="c4">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c4">t1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font></span><br/>







<a NAME="E1:55"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c4">t1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">P</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#D9" target="_self" title="PNPROC_1:def.9">Def9</a></span>;<br/>
<a NAME="E2:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c4">t1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></span>;<br/>
<span class="kw">thus </span> <a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c3">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="c4">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K6" title="PNPROC_1:func.6">fire</a> <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c2">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#D9" target="_self" title="PNPROC_1:def.9">Def9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c4">t1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#D9" target="_self" title="PNPROC_1:def.9">Def9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c3">t2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="pnproc_1.html#K7" title="PNPROC_1:func.7">fire</a> <font color="Maroon" title="c4">t1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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