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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c4">D</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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>  &amp; <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c4">D</font> <a href="yellow18.html#R2" title="YELLOW18:pred.2">are_opposite</a>  &amp; <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  implies <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c4">D</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  )</span><br/>

<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E20">A1</font></i>: 
( <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>  &amp; <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c4">D</font> <a href="yellow18.html#R2" title="YELLOW18:pred.2">are_opposite</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  or <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c4">D</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  )</span><br/>

<a NAME="E2:43"/><b>then </b>
( <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  implies <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font> <a href="functor0.html#R1" title="FUNCTOR0:pred.1">are_isomorphic</a>  )
 
<b>by </b><i><a class="ref" href="yellow18.html#T18" target="_self" title="YELLOW18:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E3:43"/>
(  not <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  or <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c4">D</font> <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a>  )
 <b>by </b><i><a class="txt" href="#E1:43"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="yellow18.html#T18" target="_self" title="YELLOW18:th.18">Th18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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