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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="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="algstr_1.html#V1" title="ALGSTR_1:attr.1">left_zeroed</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</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="E1:39"/><i><font color="Green" title="E25">A1</font></i>: 
(  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font> &amp; the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">K</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T9" target="_self" title="FVSUM_1:th.9">Th9</a>, <a class="ref" href="fvsum_1.html#T10" target="_self" title="FVSUM_1:th.10">Th10</a></i>;<br/>
<a NAME="E2:39"/>
( the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</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="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</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#K6" title="VECTSP_1:func.6">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 NAME="E3:39"/>
( <font color="Maroon" title="c3">R1</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c4">R2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span> implies ( <font color="Maroon" title="c3">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c4">R2</font> &amp; <font color="Maroon" title="c4">R2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c3">R1</font> ) )
 <b>by </b><i><a class="txt" href="fvsum_1.html#E1:39"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="finseqop.html#T78" title="FINSEQOP:th.78">FINSEQOP:78</a></i>;<br/>


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