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<div><span class="kw">theorem </span><a NAME="T14"><span class="comment"><font color="firebrick">:: VECTSP12:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">G</font>, <font color="Olive" title="b3">F</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#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#L1" title="VECTSP_1:struct.1">ModuleStr</a> over <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">x</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1"><a href="vectsp12.html#K9" title="VECTSP12:func.9">[:</a><span class="default"><font color="Olive" title="b2">G</font>,<font color="Olive" title="b3">F</font></span><a href="vectsp12.html#K9" title="VECTSP12:func.9">:]</a></span><br/>  for <font color="Olive" title="b5">x1</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">G</font><br/>  for <font color="Olive" title="b6">x2</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b3">F</font>  st <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_3.html#K5" title="PRVECT_3:func.5">[</a><span class="default"><font color="Olive" title="b5">x1</font>,<font color="Olive" title="b6">x2</font></span><a href="prvect_3.html#K5" title="PRVECT_3:func.5">]</a></span> holds <br/> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_3.html#K5" title="PRVECT_3:func.5">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b5">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b6">x2</font></span>)</span></span><a href="prvect_3.html#K5" title="PRVECT_3:func.5">]</a></span></div></div>
