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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="relat_1.html#NM1">Relation</a>;<br/>

<b>assume </b><a NAME="E1:69"/><i><font color="Green">E57</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> holds <br/>ex <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D18" target="_self">REWRITE1:def 18</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D17" target="_self">REWRITE1:def 17</a><br/>

<b>assume </b><a NAME="E2:69"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E3:69"/><b>then </b>
( <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>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="rewrite1.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E4:69"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</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>5</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="rewrite1.html#E1:69"><i><font color="Green">E57</font></i></a></i>;<br/>


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