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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:31_1_1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="pnproc_1.html#S1" target="_self">PNPROC_1:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E3:31_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E4:31_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:31"><i><font color="Green">E23</font></i></a>, <a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E2:31_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="pnproc_1.html#E3:31_1_1"><i><font color="Green">E25</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E4:31_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/>


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