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<b>let </b><font color="Maroon" title="c6">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c3">W</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bilinear.html#D13" target="_self" title="BILINEAR:def.13">BILINEAR:def 13</a><br/>

<b>set </b><font color="Maroon" title="c7">Ffg</font> =  <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="bilinear.html#K3" title="BILINEAR:func.3">*</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c6">w</font>;<br/>
<b>set </b><font color="Maroon" title="c8">Ff</font> =  <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font>;<br/>
<a NAME="E1:61_1_1"/><i><font color="Green" title="E26">A1</font></i>: 
 <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font> is <a href="hahnban1.html#V1" title="HAHNBAN1:attr.1">additive</a>
 
<b>by </b><i><a class="ref" href="bilinear.html#D13" target="_self" title="BILINEAR:def.13">Def13</a></i>;<br/>
<b>let </b><font color="Maroon" title="c9">v</font>, <font color="Maroon" title="c10">y</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">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"><font color="Maroon" title="c5">a</font> <a href="bilinear.html#K3" title="BILINEAR:func.3">*</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c6">w</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">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">y</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <span class="p2">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span></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">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">y</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T15" target="_self" title="BILINEAR:th.15">Th15</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D9" title="HAHNBAN1:def.9">HAHNBAN1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="bilinear.html#E1:61_1_1"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="hahnban1.html#D11" title="HAHNBAN1:def.11">HAHNBAN1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D9" title="HAHNBAN1:def.9">HAHNBAN1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D9" title="HAHNBAN1:def.9">HAHNBAN1:def 9</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"><font color="Maroon" title="c5">a</font> <a href="bilinear.html#K3" title="BILINEAR:func.3">*</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <span class="p3">(<span class="default"><a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T15" target="_self" title="BILINEAR:th.15">Th15</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"><font color="Maroon" title="c5">a</font> <a href="bilinear.html#K3" title="BILINEAR:func.3">*</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</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"><font color="Maroon" title="c5">a</font> <a href="bilinear.html#K3" title="BILINEAR:func.3">*</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T15" target="_self" title="BILINEAR:th.15">Th15</a></i>
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