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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V10" title="MOD_4:attr.10">antiendomorphism</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="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )</span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">J</font> is <a href="mod_4.html#V10" title="MOD_4:attr.10">antiendomorphism</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="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )</span><br/>



<a NAME="E1:74"/>
( <font color="Maroon" title="c2">J</font> is <a href="mod_4.html#V2" title="MOD_4:attr.2">antilinear</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="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )
 
<b>by </b><i><a class="ref" href="mod_4.html#T36" target="_self" title="MOD_4:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E2:74"/>
( <font color="Maroon" title="c2">J</font> is <a href="mod_4.html#V10" title="MOD_4:attr.10">antiendomorphism</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="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )
 <b>by </b><i><a class="ref" href="mod_4.html#D15" target="_self" title="MOD_4:def.15">Def15</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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