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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">m1</font>, <font color="Olive" title="b2">m2</font>, <font color="Olive" title="b3">m3</font> being   <a href="pnproc_1.html#M2" title="PNPROC_1:mode.2">marking</a> of <font color="Maroon" title="c1">P</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</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="b3">m3</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <font color="Olive" title="b1">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Olive" title="b3">m3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">m1</font>, <font color="Maroon" title="c3">m2</font>, <font color="Maroon" title="c4">m3</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</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="c4">m3</font> <a href="pnproc_1.html#R1" title="PNPROC_1:pred.1">=</a> <font color="Maroon" title="c2">m1</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#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c4">m3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pnproc_1.html#D2" target="_self" title="PNPROC_1:def.2">PNPROC_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">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="c5">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  )</span><br/>









<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span><br/>

<b>then </b><i><font color="Green" title="E30">A2</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</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="c4">m3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span>
<b>by </b><i><a class="ref" href="pnproc_1.html#D5" target="_self" title="PNPROC_1:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="pnproc_1.html#D5" target="_self" title="PNPROC_1:def.5">Def5</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</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#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c4">m3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c4">m3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="pnproc_1.html#D5" target="_self" title="PNPROC_1:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">m3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="pnproc_1.html#D5" target="_self" title="PNPROC_1:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font></span>)</span>

;<br/>
<b>hence </b><a NAME="E4:39"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</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="c4">m3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</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#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c4">m3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E30">A2</font></i></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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