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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: VECTSP_1:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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#V1" title="VECTSP_1:attr.1">right-distributive</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">F</font> holds  <font color="Olive" title="b2">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">y</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">y</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">z</font></span>)</span></div></div>
