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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:47"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="rewrite1.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E2:47"/>
( <font color="Maroon">c<sub>1</sub></font> <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> implies ( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="rewrite1.html#R5" target="_self">are_convergent_wrt</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="rewrite1.html#R6" target="_self">are_divergent_wrt</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R5" target="_self">are_convergent_wrt</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R6" target="_self">are_divergent_wrt</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="rewrite1.html#D7" target="_self">Def7</a>, <a class="ref" href="rewrite1.html#D8" target="_self">Def8</a></i>;<br/>


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