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<b>let </b><font color="Maroon" title="c4">M1</font>, <font color="Maroon" title="c5">M2</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"> ( ( for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> holds <br/><font color="Olive" title="b1">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> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> ) &amp; ( for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> holds <br/><font color="Olive" title="b1">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> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> ) implies <font color="Maroon" title="c4">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:31_1_2"/><i><font color="Green" title="E24">A5</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> holds <br/><font color="Olive" title="b1">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> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:31_1_2"/><i><font color="Green" title="E25">A6</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> holds <br/><font color="Olive" title="b1">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> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span>
 ; <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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M2</font></span><br/>

<b>let </b><font color="Maroon" title="c6">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="c6">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="c6">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="c6">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  )</span><br/>

<b>assume </b><a NAME="E3:31_1_2"/><i><font color="Green" title="E26">A7</font></i>: 
<font color="Maroon" title="c6">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="c6">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="c6">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span><br/>

<b>hence </b><font color="Maroon" title="c6">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E1:31_1_2"><i><font color="Green" title="E24">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> 
<b>by </b><i><a class="txt" href="#E2:31_1_2"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="#E3:31_1_2"><i><font color="Green" title="E26">A7</font></i></a></i>
;<br/> <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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