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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">m2</font>, <font color="Olive" title="b2">m3</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">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Olive" title="b2">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Olive" title="b3">m1</font> holds <br/><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="b1">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Olive" title="b2">m3</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <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="b1">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Olive" title="b2">m3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">m2</font>, <font color="Maroon" title="c3">m3</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">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c4">m1</font> implies <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="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</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="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:45"/>
<font color="Maroon" title="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</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"> <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="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</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="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span></span><br/>

<b>then </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="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font>
<b>by </b><i><a class="ref" href="pnproc_1.html#T27" target="_self" title="PNPROC_1:th.27">Th27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">m1</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font>
<b>by </b><i><a class="ref" href="pnproc_1.html#T23" target="_self" title="PNPROC_1:th.23">Th23</a></i>
<br/>.= 
<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="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span></span>)</span> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font>
<b>by </b><i><a class="ref" href="pnproc_1.html#T28" target="_self" title="PNPROC_1:th.28">Th28</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="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">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>hence </b><a NAME="E3:45"/>
<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="c2">m2</font></span>)</span> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <font color="Maroon" title="c3">m3</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</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="c2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m3</font></span>)</span>
 ; <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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