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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="yellow18.html#K1" target="_self">opp</a>  <a href="yellow18.html#R1" target="_self">are_equivalent</a> 
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="yellow18.html#R1" target="_self">are_equivalent</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow18.html#D6" target="_self">YELLOW18:def 6</a><br/>

<a NAME="E3:54"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="yellow18.html#K1" target="_self">opp</a>  <a href="yellow18.html#R2" target="_self">are_opposite</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="yellow18.html#K1" target="_self">opp</a>  <a href="yellow18.html#R2" target="_self">are_opposite</a>  )
 
<b>by </b><i><a class="ref" href="yellow18.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="yellow18.html#K1" target="_self">opp</a> ,<font color="Maroon">c<sub>3</sub></font> <a href="yellow18.html#K1" target="_self">opp</a>  <a href="yellow18.html#R1" target="_self">are_equivalent</a> 
 
<b>by </b><i><a class="txt" href="yellow18.html#E2:54"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow18.html#T26" target="_self">Th26</a></i>;<br/>
<b>hence </b><a NAME="E5:54"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="yellow18.html#K1" target="_self">opp</a>  <a href="yellow18.html#R1" target="_self">are_equivalent</a> 
 <b>by </b><i><a class="txt" href="yellow18.html#E1:54"><i><font color="Green">E26</font></i></a>, <a class="ref" href="yellow18.html#T4" target="_self">Th4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow18.html#D6" target="_self">YELLOW18:def 6</a><br/>


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