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<b>let </b><font color="Maroon">c<sub>1</sub></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/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:18"/>
 <a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_2.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E2:18"/><b>then </b>
<span class="p1">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rlsub_2.html#T78">RLSUB_2:78</a></i>;<br/>
<b>hence </b><a NAME="E3:18"/>
 <a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rlsub_2.html#T78">RLSUB_2:78</a></i>;<br/>


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