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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">J</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c1">K</font> holds <br/> ( <font color="Olive" title="b1">J</font> is  <a href="mod_4.html#V11" title="MOD_4:attr.11">automorphism</a>  iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Olive" title="b1">J</font> is  <a href="mod_4.html#V8" title="MOD_4:attr.8">antiisomorphism</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">J</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c1">K</font>; <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="c2">J</font> is  <a href="mod_4.html#V11" title="MOD_4:attr.11">automorphism</a>  iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c2">J</font> is  <a href="mod_4.html#V8" title="MOD_4:attr.8">antiisomorphism</a>  )</span><br/>



<a NAME="E1:80"/>
( <font color="Maroon" title="c2">J</font> is  <a href="mod_4.html#V7" title="MOD_4:attr.7">isomorphism</a>  iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c2">J</font> is  <a href="mod_4.html#V8" title="MOD_4:attr.8">antiisomorphism</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#T41" target="_self" title="MOD_4:th.41">Th41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:80"/>
( <font color="Maroon" title="c2">J</font> is  <a href="mod_4.html#V11" title="MOD_4:attr.11">automorphism</a>  iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c2">J</font> is  <a href="mod_4.html#V8" title="MOD_4:attr.8">antiisomorphism</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#D16" target="_self" title="MOD_4:def.16">Def16</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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