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<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/>

<a NAME="E1:3"/><i><font color="Green">E22</font></i>: 
the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">G</font> <a href="binop_1.html#R3">is_a_unity_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>thus </b>the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> = 
<font color="Maroon">x</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D25">VECTSP_1:def 25</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">G</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
 <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G</font>
<b>by </b><i>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>
;<br/><b>thus </b>the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>,<font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D25">VECTSP_1:def 25</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">G</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
 <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G</font>
<b>by </b><i>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:3"/>
 <a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G</font> <a href="finseqop.html#R1">is_an_inverseOp_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="finseqop.html#D1">FINSEQOP:def 1</a></i>;<br/>


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