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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: RLVECT_1:41</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#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">F</font>, <font color="Olive" title="b3">G</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b1">V</font> holds   <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <font color="Olive" title="b3">G</font></span>)</span></div></div>
