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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow18.html#R2" title="YELLOW18:pred.2">are_opposite</a>  implies <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:40"/>
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow18.html#R2" title="YELLOW18:pred.2">are_opposite</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a> </span><br/>

<a NAME="E2:40"/><span class="kw">then </span>
 <a href="yellow18.html#K2" title="YELLOW18:func.2">dualizing-func</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> is  <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow18.html#T16" target="_self" title="YELLOW18:th.16">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:40"/>
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D41" title="FUNCTOR0:def.41">FUNCTOR0:def 41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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