<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">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="c2">L</font>;<br/>





<b>set </b><font color="Maroon" title="c4">J'</font> =  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c3">J</font>;<br/>
<b>set </b><font color="Maroon" title="c5">L'</font> =  <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c2">L</font>;<br/>
<a NAME="E1:66"/><i><font color="Green" title="E54">A1</font></i>: 
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> iff  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c2">L</font></span>)</span> )
 
;<br/>
<a NAME="E2:66"/>
( <font color="Maroon" title="c3">J</font> is <a href="mod_4.html#V3" title="MOD_4:attr.3">antimonomorphism</a> iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c3">J</font> is <a href="mod_4.html#V2" title="MOD_4:attr.2">monomorphism</a> )
 
<b>by </b><i><a class="ref" href="mod_4.html#T38" target="_self" title="MOD_4:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E3:66"/>
( <font color="Maroon" title="c3">J</font> is <a href="mod_4.html#V7" title="MOD_4:attr.7">antiisomorphism</a> iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c3">J</font> is <a href="mod_4.html#V6" title="MOD_4:attr.6">isomorphism</a> )
 <b>by </b><i><a class="txt" href="mod_4.html#E1:66"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="mod_4.html#D11" target="_self" title="MOD_4:def.11">Def11</a>, <a class="ref" href="mod_4.html#D12" target="_self" title="MOD_4:def.12">Def12</a></i>;<br/>


</div>
