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<b>set </b><font color="Maroon">L</font> =  <a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">vq</font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">W</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span>;<br/>
<b>let </b><font color="Maroon">f1</font> be  <a href="bilinear.html#V1" target="_self">additiveFAF</a> <a href="bilinear.html#V3" target="_self">homogeneousFAF</a> <a href="bilinear.html#NM1">Form</a> of <font color="Maroon">V</font>,<span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span></span>)</span>, <font color="Maroon">f2</font> be  <a href="bilinear.html#V1" target="_self">additiveFAF</a> <a href="bilinear.html#V3" target="_self">homogeneousFAF</a> <a href="bilinear.html#NM1">Form</a> of <font color="Maroon">V</font>,<span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:107_1_2"/><i><font color="Green">E136</font></i>: 
for <font color="Olive">A</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span></span>)</span><br/> for <font color="Olive">v</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><br/> for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">W</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span> holds <br/><font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">v</font>,<font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Olive">v</font>,<font color="Olive">a</font>
 <b>and </b><br/><a NAME="E2:107_1_2"/><i><font color="Green">E137</font></i>: 
for <font color="Olive">A</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span></span>)</span><br/> for <font color="Olive">v</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><br/> for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">W</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span> holds <br/><font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">v</font>,<font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Olive">v</font>,<font color="Olive">a</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">W</font><b> such that </b><br/><a NAME="E2:107_1_2_1"/><i><font color="Green">E138</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" target="_self">RKer</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">A</font> = 
<font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="bilinear.html#T1" target="_self">Th1</a>, </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">A</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:107_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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