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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="E1:37"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R2" target="_self">are_convertible_wrt</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:37"/><b>then </b>
( <a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="relat_1.html#K4">~</a> </span>)</span> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <a href="xboole_0.html#K1">{}</a>  <a href="relat_1.html#K4">~</a>  )
 
<b>by </b><i><a class="ref" href="rewrite1.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
<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="ref" href="rewrite1.html#T14" target="_self">Th14</a></i>;<br/>


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