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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pnproc_1.html#M1" target="_self">marking</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:33_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:33_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="pnproc_1.html#E22"><i><font color="Green">Lemma19</font></i></a></i>;<br/><b>hence </b><a NAME="E3:33_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/></div><b>end;</b></div>
<a NAME="E2:33"/>
 <a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">c<sub>1</sub></font> <a href="pnproc_1.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E3:33"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pnproc_1.html#K5" target="_self">-</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pnproc_1.html#R1" target="_self">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:33"><i><font color="Green">E25</font></i></a>, <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a></i>;<br/>


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