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<b>let </b><font color="Maroon" title="c5">w</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="bilinear.html#D14" target="_self" title="BILINEAR:def.14">BILINEAR:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p1">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">w</font> is <a href="hahnban1.html#V2" title="HAHNBAN1:attr.2">homogeneous</a></span><br/>

<b>set </b><font color="Maroon" title="c6">Ffg</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p1">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">w</font>;<br/>
<b>set </b><font color="Maroon" title="c7">Ff</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">w</font>;<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="c3">W</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> holds  <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p2">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></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#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p3">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c9">a</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Scalar</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p2">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">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">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p3">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span></span><br/>



<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p2">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">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">a</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="hahnban1.html#K4" title="HAHNBAN1:func.4">-</a> <span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">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">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T18" target="_self" title="BILINEAR:th.18">Th18</a></i>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">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">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D7" title="HAHNBAN1:def.7">HAHNBAN1:def 7</a></i>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">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#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a></i>
<br/>.= 
<font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T40" title="VECTSP_1:th.40">VECTSP_1:40</a></i>
<br/>.= 
<font color="Maroon" title="c9">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="hahnban1.html#K4" title="HAHNBAN1:func.4">-</a> <span class="p3">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">w</font></span>)</span></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="hahnban1.html#D7" title="HAHNBAN1:def.7">HAHNBAN1:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c9">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#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p3">(<span class="default"><a href="bilinear.html#K4" title="BILINEAR:func.4">-</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">w</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#T18" target="_self" title="BILINEAR:th.18">Th18</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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