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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="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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being   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> <br/>  for <font color="Olive" title="b2">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="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b2">J</font> is  <a href="mod_4.html#V6" title="MOD_4:attr.6">antiepimorphism</a>  iff  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Olive" title="b2">J</font> is  <a href="mod_4.html#V5" title="MOD_4:attr.5">epimorphism</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">L</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="firebrick">::  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="c2">L</font> holds <br/> ( <font color="Olive" title="b1">J</font> is  <a href="mod_4.html#V6" title="MOD_4:attr.6">antiepimorphism</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#V5" title="MOD_4:attr.5">epimorphism</a>  )</span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">J</font> is  <a href="mod_4.html#V6" title="MOD_4:attr.6">antiepimorphism</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#V5" title="MOD_4:attr.5">epimorphism</a>  )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">J9</font> =  <a href="mod_4.html#K7" title="MOD_4:func.7">opp</a> <font color="Maroon" title="c3">J</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">L9</font> =  <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c2">L</font>;<br/>
<a NAME="E1:69"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
( <font color="Maroon" title="c3">J</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</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="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )
 
;<br/>
<a NAME="E2:69"/>
( <font color="Maroon" title="c3">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="c3">J</font> is  <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#T29" target="_self" title="MOD_4:th.29">Th36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:69"/>
( <font color="Maroon" title="c3">J</font> is  <a href="mod_4.html#V6" title="MOD_4:attr.6">antiepimorphism</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#V5" title="MOD_4:attr.5">epimorphism</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="mod_4.html#D10" target="_self" title="MOD_4:def.10">Def10</a>, <a class="ref" href="mod_4.html#D11" target="_self" title="MOD_4:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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