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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: RLVECT_2:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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">S</font>, <font color="Olive" title="b3">T</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> holds   <a href="rlvect_2.html#K2" title="RLVECT_2:func.2">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">T</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" title="RLVECT_2:func.2">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">T</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b2">S</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K2" title="RLVECT_2:func.2">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">S</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b3">T</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#T12" target="_self" onmouseover="rs('rlvect_2/T12')" onmouseout="rh()">Th12</a>, <a class="ref" href="xboole_1.html#T82" onmouseover="rs('xboole_1/T82')" onmouseout="rh()">XBOOLE_1:82</a></span>;<br/></div></div>
