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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   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> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">W</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="bilinear.html#NM2" title="BILINEAR:NM.2">bilinear-Form</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font> holds   <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Olive" title="b3">f</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font>, <font color="Maroon" title="c3">W</font> be   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="bilinear.html#NM2" title="BILINEAR:NM.2">bilinear-Form</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">W</font> holds   <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Olive" title="b1">f</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="bilinear.html#NM2" title="BILINEAR:NM.2">bilinear-Form</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">W</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Maroon" title="c4">f</font></span>)</span></span><br/>





 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span> = 
 <a href="bilinear.html#K10" title="BILINEAR:func.10">leftker</a> <font color="Maroon" title="c4">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D18" target="_self" onmouseover="rs('bilinear/D18')" onmouseout="rh()">Def18</a></span>
<br/>.= 
 <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> <font color="Maroon" title="c4">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T45" target="_self" onmouseover="rs('bilinear/T45')" onmouseout="rh()">Th45</a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <span class="p2">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D18" target="_self" onmouseover="rs('bilinear/D18')" onmouseout="rh()">Def18</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:111"/>
 <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K13" title="BILINEAR:func.13">LKer</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <font color="Maroon" title="c4">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T29" onmouseover="rs('vectsp_4/T29')" onmouseout="rh()">VECTSP_4:29</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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