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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">K</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="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/> for <font color="Olive" title="b2">R1</font>, <font color="Olive" title="b3">R2</font> being   <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="Olive" title="b1">K</font> holds   <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">R1</font> <a href="fvsum_1.html#K8" title="FVSUM_1:func.8">-</a> <font color="Olive" title="b3">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Olive" title="b2">R1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Olive" title="b3">R2</font></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R1</font>, <font color="Olive" title="b2">R2</font> being   <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> holds   <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R1</font> <a href="fvsum_1.html#K8" title="FVSUM_1:func.8">-</a> <font color="Olive" title="b2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Olive" title="b1">R1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Olive" title="b2">R2</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c3">R1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c4">R2</font></span><br/>







<b>thus </b> <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</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> = 
 <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c4">R2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T89" title="FINSEQOP:th.89">FINSEQOP:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c3">R1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <span class="p2">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c4">R2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T40" target="_self" title="FVSUM_1:th.40">Th40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c3">R1</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c4">R2</font>
<b>by </b><i><a class="ref" href="fvsum_1.html#T37" target="_self" title="FVSUM_1:th.37">Th37</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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