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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: VECTSP10:25</font></span><br/></a><div class="add"> 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="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">W</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b4">A</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font>)</span>)</span><br/>  for <font color="Olive" title="b5">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b6">a</font> being   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">Scalar</a> of   st <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Olive" title="b3">W</font> holds <br/><font color="Olive" title="b6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Olive" title="b3">W</font></div></div>
