<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">P</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">m1</font> be    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">P</font>;<br/><b>let </b><font color="Maroon">m2</font> be    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">P</font>;<br/><b>let </b><font color="Maroon">m3</font> be    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">P</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pnproc_1.html#D2" target="_self">PNPROC_1:def 2</a><br/>









<b>assume </b><a NAME="E1:39"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/>

<b>then </b><i><font color="Green">E30</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m2</font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m3</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m2</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:39"><i><font color="Green">E29</font></i></a>, </i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m3</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:39"><i><font color="Green">E29</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m3</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:39"><i><font color="Green">E29</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">m3</font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font></span>)</span>

;<br/>
<b>hence </b><a NAME="E4:39"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m2</font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m3</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E2:39"><i><font color="Green">E30</font></i></a></i>;<br/>


</div>
