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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><a NAME="E1:53"/><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#R2" target="_self">are_opposite</a> 
 ;<br/>

<a NAME="E2:53"/><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#R3" target="_self">are_dual</a>  iff <font color="Maroon">c<sub>2</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="ref" href="yellow18.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E3:53"/>
<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/>
<b>hence </b><a NAME="E4:53"/>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="yellow18.html#R1" target="_self">are_equivalent</a>  iff <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="yellow18.html#R3" target="_self">are_dual</a>  )
 <b>by </b><i><a class="txt" href="yellow18.html#E1:53"><i><font color="Green">E26</font></i></a>, <a class="txt" href="yellow18.html#E2:53"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow18.html#T26" target="_self">Th26</a></i>;<br/>


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