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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E49">Th49</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: BILINEAR:49</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>, <font color="Olive" title="b3">W</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="b4">f</font> being   <a href="bilinear.html#NM2" title="BILINEAR:NM.2">bilinear-Form</a> of <font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font> holds <br/> (  <a href="bilinear.html#K10" title="BILINEAR:func.10">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K10" title="BILINEAR:func.10">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LQForm</a> <font color="Olive" title="b4">f</font></span>)</span></span>)</span> &amp;  <a href="bilinear.html#K11" title="BILINEAR:func.11">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K11" title="BILINEAR:func.11">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LQForm</a> <font color="Olive" title="b4">f</font></span>)</span></span>)</span> &amp;  <a href="bilinear.html#K10" title="BILINEAR:func.10">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K10" title="BILINEAR:func.10">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LQForm</a> <span class="p2">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Olive" title="b4">f</font></span>)</span></span>)</span> &amp;  <a href="bilinear.html#K11" title="BILINEAR:func.11">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K11" title="BILINEAR:func.11">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LQForm</a> <span class="p2">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Olive" title="b4">f</font></span>)</span></span>)</span> )</div></div>
