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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#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#V7" title="GROUP_1:attr.7">commutative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">distributive</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">left_unital</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">R</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="E1:75"/><i><font color="Green" title="E38">A1</font></i>: 
<span class="p1">(<span class="default"><a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c2">K</font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D25" title="VECTSP_1:def.25">VECTSP_1:def 25</a></i>;<br/>
<a NAME="E2:75"/><i><font color="Green" title="E39">A2</font></i>: 
(  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c2">K</font> &amp; the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</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#T7" target="_self" title="FVSUM_1:th.7">Th7</a>, <a class="ref" href="fvsum_1.html#T11" target="_self" title="FVSUM_1:th.11">Th11</a></i>;<br/>
<a NAME="E3:75"/><i><font color="Green" title="E40">A3</font></i>: 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="binop_1.html#R6" title="BINOP_1:pred.6">is_distributive_wrt</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">K</font>
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T12" target="_self" title="FVSUM_1:th.12">Th12</a></i>;<br/>
<a NAME="E4:75"/><i><font color="Green" title="E41">A4</font></i>: 
( 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>  &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="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#K7" title="VECTSP_1:func.7">comp</a> <font color="Maroon" title="c2">K</font> )
 
<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="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>reconsider </b><font color="Maroon" title="c4">a</font> =  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c2">K</font></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font> ;<br/>
<b>thus </b><a NAME="E6:75"/>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c3">R</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">R</font>
 <b>by </b><i><a class="txt" href="fvsum_1.html#E1:75"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="fvsum_1.html#E2:75"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="fvsum_1.html#E3:75"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="fvsum_1.html#E4:75"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="finseqop.html#T72" title="FINSEQOP:th.72">FINSEQOP:72</a></i>;<br/>


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