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<b>set </b><font color="Maroon" title="c4">lf</font> =  <a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font>;<br/>
<b>thus </b><a NAME="E1:111_2_1"/>
 <a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font> is <a href="bilinear.html#V2" title="BILINEAR:attr.2">additiveSAF</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">A</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">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">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="bilinear.html#D13" title="BILINEAR:def.13">BILINEAR:def 13</a><br/>

<b>set </b><font color="Maroon" title="c6">flf</font> =  <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font>;<br/>
<b>consider </b><font color="Maroon" title="c7">w</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font><b> such that </b><br/><a NAME="E2:111_2_1_1"/><i><font color="Green" title="E53">A3</font></i>: 
<font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">w</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23" title="VECTSP10:th.23">VECTSP10:23</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">v</font>, <font color="Maroon" title="c9">t</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D11" title="HAHNBAN1:def.11">HAHNBAN1:def 11</a><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">t</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">t</font></span>)</span>,<font color="Maroon" title="c5">A</font>
<b>by </b><i><a class="ref" href="bilinear.html#T10" title="BILINEAR:th.10">BILINEAR:10</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">t</font></span>)</span>,<font color="Maroon" title="c7">w</font>
<b>by </b><i><a class="txt" href="hermitan.html#E2:111_2_1_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="hermitan.html#T62" target="_self" title="HERMITAN:th.62">Th62</a></i>
<br/>.= 
<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="c8">v</font>,<font color="Maroon" title="c7">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="c9">t</font>,<font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T27" title="BILINEAR:th.27">BILINEAR:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c8">v</font>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="c9">t</font>,<font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E2:111_2_1_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="hermitan.html#T62" target="_self" title="HERMITAN:th.62">Th62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c8">v</font>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">t</font>,<font color="Maroon" title="c5">A</font></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E2:111_2_1_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="hermitan.html#T62" target="_self" title="HERMITAN:th.62">Th62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">t</font>,<font color="Maroon" title="c5">A</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10" title="BILINEAR:th.10">BILINEAR:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10" title="BILINEAR:th.10">BILINEAR:10</a></i>
;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">A</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">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">W</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="bilinear.html#D15" title="BILINEAR:def.15">BILINEAR:def 15</a><br/>

<b>set </b><font color="Maroon" title="c6">flf</font> =  <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font>;<br/>
<b>consider </b><font color="Maroon" title="c7">w</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font><b> such that </b><br/><a NAME="E3:111_2_1"/><i><font color="Green" title="E53">A4</font></i>: 
<font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">w</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23" title="VECTSP10:th.23">VECTSP10:23</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a><br/><b>let </b><font color="Maroon" title="c9">r</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Scalar</a> of ;<br/>



<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span>,<font color="Maroon" title="c5">A</font>
<b>by </b><i><a class="ref" href="bilinear.html#T10" title="BILINEAR:th.10">BILINEAR:10</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span>,<font color="Maroon" title="c7">w</font>
<b>by </b><i><a class="txt" href="hermitan.html#E3:111_2_1"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="hermitan.html#T62" target="_self" title="HERMITAN:th.62">Th62</a></i>
<br/>.= 
<font color="Maroon" title="c9">r</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</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="c8">v</font>,<font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T32" title="BILINEAR:th.32">BILINEAR:32</a></i>
<br/>.= 
<font color="Maroon" title="c9">r</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c8">v</font>,<font color="Maroon" title="c5">A</font></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E3:111_2_1"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="hermitan.html#T62" target="_self" title="HERMITAN:th.62">Th62</a></i>
<br/>.= 
<font color="Maroon" title="c9">r</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" title="HERMITAN:func.7">RQ*Form</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10" title="BILINEAR:th.10">BILINEAR:10</a></i>
;<br/>


</div>
