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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">m</font> being  <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Maroon" title="c1">P</font> holds  <font color="Olive" title="b1">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <font color="Olive" title="b1">m</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">m</font> be   <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <font color="Maroon" title="c2">m</font></span><br/>



<div><span class="lab"><font color="Green" title="E23">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> implies <font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:32_1"/>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font></span>)</span></span><br/><a NAME="E2:32_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="pnproc_1.html#E22"><span class="lab"><font color="Green" title="E17">Lm6</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:32_1"/>
<font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">p</font></span>)</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/></div><span class="kw">end;</span></div>
<a NAME="E2:32"/>
 <a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#T13" target="_self" title="PNPROC_1:th.13">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:32"/>
<font color="Maroon" title="c2">m</font> <a href="pnproc_1.html#K3" title="PNPROC_1:func.3">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K1" title="PNPROC_1:func.1">{$}</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="pnproc_1.html#D6" target="_self" title="PNPROC_1:def.6">Def6</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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