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<b>thus </b><a NAME="E1:146_1_1"/>
( <font color="Maroon" title="c3">f</font> is <a href="bilinear.html#V8" title="BILINEAR:attr.8">alternating</a> implies for <font color="Olive" title="b1">v</font>, <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="c2">V</font> holds  <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">v</font></span>)</span> )
 <b>by </b><i><a class="ref" href="bilinear.html#T59" target="_self" title="BILINEAR:th.59">Th59</a></i>;<br/>

<b>assume </b><a NAME="E2:146_1_1"/><i><font color="Green" title="E64">A1</font></i>: 
for <font color="Olive" title="b1">v</font>, <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="c2">V</font> holds  <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">v</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bilinear.html#D27" target="_self" title="BILINEAR:def.27">BILINEAR:def 27</a><br/>

<a NAME="E3:146_1_1"/>
<font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bilinear.html#E2:146_1_1"><i><font color="Green" title="E64">A1</font></i></a></i>;<br/>
<a NAME="E4:146_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">K</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#T63" title="VECTSP_1:th.63">VECTSP_1:63</a></i>;<br/>
<b>hence </b><a NAME="E5:146_1_1"/>
<font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">K</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D28" title="VECTSP_1:def.28">VECTSP_1:def 28</a></i>;<br/>


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