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

<b>assume </b><a NAME="E1:50"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R5" target="_self">are_convergent_wrt</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R6" target="_self">are_divergent_wrt</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_1"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R5" target="_self">are_convergent_wrt</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:50_1"/><i><font color="Green">E49</font></i>: 
(  <a href="xboole_0.html#K1">{}</a>  <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="rewrite1.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E4:50_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="rewrite1.html#E3:50_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rewrite1.html#T14" target="_self">Th14</a></i>;<br/><b>hence </b><a NAME="E5:50_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_2"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R6" target="_self">are_divergent_wrt</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:50_2"/><i><font color="Green">E49</font></i>: 
(  <a href="xboole_0.html#K1">{}</a>  <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="rewrite1.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:50_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="rewrite1.html#E3:50_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rewrite1.html#T14" target="_self">Th14</a></i>;<br/><b>hence </b><a NAME="E5:50_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:50"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rewrite1.html#E1:50"><i><font color="Green">E47</font></i></a>, <a class="txt" href="rewrite1.html#E2:50"><i><font color="Green">E48</font></i></a></i>;<br/>


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