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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">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#V2" title="RLVECT_1:attr.2">Abelian</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#L2" title="ALGSTR_0:struct.2">addLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">R2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">K</font>;<br/>







<a NAME="E1:86"/>
( the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">K</font> <a href="finseqop.html#NR2" title="FINSEQOP:NR.2">has_an_inverseOp</a>  &amp;  <a href="finseqop.html#K6" title="FINSEQOP:func.6">the_inverseOp_wrt</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">K</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">comp</a> <font color="Maroon" title="c2">K</font> )
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T17" target="_self" title="FVSUM_1:th.17">Th17</a>, <a class="ref" href="fvsum_1.html#T18" target="_self" title="FVSUM_1:th.18">Th18</a></i>;<br/>
<b>hence </b> <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="fvsum_1.html#K8" title="FVSUM_1:func.8">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K2" title="FVSUM_1:func.2">diffield</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <font color="Maroon" title="c3">R1</font></span>)</span>,<span class="p1">(<span class="default">the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c4">R2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T10" target="_self" title="FVSUM_1:th.10">Th10</a>, <a class="ref" href="setwop_2.html#T48" title="SETWOP_2:th.48">SETWOP_2:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <font color="Maroon" title="c3">R1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <font color="Maroon" title="c4">R2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T14" target="_self" title="FVSUM_1:th.14">Th14</a></i>
;<br/><br/>


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