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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">m3</font>, <font color="Olive" title="b2">m2</font>, <font color="Olive" title="b3">m1</font> being  <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">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/><span class="kw">let </span><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#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"> ( <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/>







<span class="kw">assume </span><a NAME="E1:45"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E2:45"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:45"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#T16" target="_self" title="PNPROC_1:th.16">Th16</a></span>;<br/>
<a NAME="E4:45"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="pnproc_1.html#T27" target="_self" title="PNPROC_1:th.27">Th27</a></span>;<br/>
<a NAME="E5:45"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E3:45"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="pnproc_1.html#T26" target="_self" title="PNPROC_1:th.26">Th26</a></span>;<br/>
<a NAME="E6:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#T28" target="_self" title="PNPROC_1:th.28">Th28</a></span>;<br/>
<span class="kw">thus </span><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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="pnproc_1.html#T29" target="_self" title="PNPROC_1:th.29">Th29</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:45"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="pnproc_1.html#T27" target="_self" title="PNPROC_1:th.27">Th27</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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