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<b>set </b><font color="Maroon" title="c5">L</font> =  <a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font>;<br/>
<b>set </b><font color="Maroon" title="c6">vq</font> =  <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c7">f1</font>, <font color="Maroon" title="c8">f2</font> be  <a href="bilinear.html#V2" title="BILINEAR:attr.2">additiveSAF</a> <a href="bilinear.html#V4" title="BILINEAR:attr.4">homogeneousSAF</a> <a href="bilinear.html#NM1" title="BILINEAR:NM.1">Form</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">W</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:106_1_2"/><i><font color="Green" title="E44">A14</font></i>: 
for <font color="Olive" title="b1">A</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span><br/> for <font color="Olive" title="b2">w</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c3">W</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span> holds <br/><font color="Maroon" title="c7">f1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">w</font>
 <b>and </b><br/><a NAME="E2:106_1_2"/><i><font color="Green" title="E45">A15</font></i>: 
for <font color="Olive" title="b1">A</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span><br/> for <font color="Olive" title="b2">w</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c3">W</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span> holds <br/><font color="Maroon" title="c8">f2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">w</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">A</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon" title="c10">w</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c3">W</font>;<br/><b>consider </b><font color="Maroon" title="c11">a</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E2:106_1_2_1"/><i><font color="Green" title="E46">A16</font></i>: 
<font color="Maroon" title="c9">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c4">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23" title="VECTSP10:th.23">VECTSP10:23</a></i>;<br/><b>thus </b><font color="Maroon" title="c7">f1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c10">w</font> = 
<font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">w</font>
<b>by </b><i><a class="txt" href="bilinear.html#E1:106_1_2"><i><font color="Green" title="E44">A14</font></i></a>, <a class="txt" href="bilinear.html#E2:106_1_2_1"><i><font color="Green" title="E46">A16</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c8">f2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c10">w</font>
<b>by </b><i><a class="txt" href="bilinear.html#E2:106_1_2"><i><font color="Green" title="E45">A15</font></i></a>, <a class="txt" href="bilinear.html#E2:106_1_2_1"><i><font color="Green" title="E46">A16</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:106_1_2"/>
<font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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