<?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">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">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">m1</font> be    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">P</font>;<br/>







<b>assume </b><a NAME="E1:46"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">m3</font> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">m2</font>
 ;<br/>

<b>assume </b><a NAME="E2:46"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">m2</font> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">m1</font>
 ;<br/>

<a NAME="E3:46"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">m3</font> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:46"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">m2</font> <a href="pnproc_1.html#R1" target="_self">=</a> <font color="Maroon">m3</font> <a href="pnproc_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T2" target="_self">Th2</a>, <a class="txt" href="pnproc_1.html#E2:46"><i><font color="Green">E30</font></i></a></i>;<br/>
<a NAME="E5:46"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">m3</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#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">m1</font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span>
 
<b>by </b><i>, <a class="txt" href="pnproc_1.html#E3:46"><i><font color="Green">E35</font></i></a>, <a class="txt" href="pnproc_1.html#E1:46"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E6:46"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">m3</font> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">m1</font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E2"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K5" 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 class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span> <a href="pnproc_1.html#K4" target="_self">+</a> <font color="Maroon">m3</font>
<b>by </b><i>, <a class="ref" href="pnproc_1.html#T3" target="_self">Th3</a>, </i>
<br/>.= 
<font color="Maroon">m1</font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="pnproc_1.html#K5" target="_self">-</a> <font color="Maroon">m3</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:46"><i><font color="Green">E37</font></i></a>, <a class="txt" href="pnproc_1.html#E2:46"><i><font color="Green">E30</font></i></a></i>
;<br/>


</div>
