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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">m3</font>, <font color="Olive" title="b2">m2</font>, <font color="Olive" title="b3">m1</font> being   <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">marking</a> of <font color="Maroon" title="c1">P</font>  st <font color="Olive" title="b1">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Olive" title="b2">m2</font> &amp; <font color="Olive" title="b2">m2</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Olive" title="b3">m1</font> holds <br/><font color="Olive" title="b3">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Olive" title="b1">m3</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Olive" title="b2">m2</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Olive" title="b1">m3</font></span><br/><b>let </b><font color="Maroon" title="c2">m3</font>, <font color="Maroon" title="c3">m2</font>, <font color="Maroon" title="c4">m1</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"> ( <font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c3">m2</font> &amp; <font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c4">m1</font> implies <font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c2">m3</font> )</span><br/>







<b>assume </b><a NAME="E1:46"/><i><font color="Green" title="E33">A1</font></i>: 
<font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c3">m2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c4">m1</font> or <font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c2">m3</font> )</span><br/>

<b>assume </b><a NAME="E2:46"/><i><font color="Green" title="E34">A2</font></i>: 
<font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c4">m1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c2">m3</font></span><br/>

<a NAME="E3:46"/><i><font color="Green" title="E35">A3</font></i>: 
<font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</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="E4:46"/><i><font color="Green" title="E36">A4</font></i>: 
<font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:46"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="pnproc_1.html#T27" target="_self" title="PNPROC_1:th.27">Th27</a></i>;<br/>
<a NAME="E5:46"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E2:46"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="pnproc_1.html#E3:46"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="pnproc_1.html#T26" target="_self" title="PNPROC_1:th.26">Th26</a></i>;<br/>
<a NAME="E6:46"/><b>then </b><i><font color="Green" title="E37">A5</font></i>: 
<font color="Maroon" title="c2">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T28" target="_self" title="PNPROC_1:th.28">Th28</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c2">m3</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c2">m3</font>
<b>by </b><i><a class="txt" href="pnproc_1.html#E2:46"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="pnproc_1.html#E4:46"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="pnproc_1.html#T29" target="_self" title="PNPROC_1:th.29">Th29</a></i>
<br/>.= 
<font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m3</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E6:46"><i><font color="Green" title="E37">A5</font></i></a>, <a class="ref" href="pnproc_1.html#T27" target="_self" title="PNPROC_1:th.27">Th27</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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