<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c4">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bilinear.html#D13" title="BILINEAR:def.13">BILINEAR:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font> is <a href="hahnban1.html#V1" title="HAHNBAN1:attr.1">additive</a></span><br/><b>let </b><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">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> <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#K10" title="BILINEAR:func.10">FunctionalSAF</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>,<font color="Maroon" title="c4">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="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">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="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">t</font></span>)</span></span><br/>



<b>set </b><font color="Maroon" title="c7">fg</font> =  <a href="bilinear.html#K10" title="BILINEAR:func.10">FunctionalSAF</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font>;<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="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">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="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">t</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">t</font></span>)</span>,<font color="Maroon" title="c4">w</font>
<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"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">t</font></span>)</span>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 
<b>by </b><i><a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="c5">v</font>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<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="c6">t</font>,<font color="Maroon" title="c4">w</font></span>)</span></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 
<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"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </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"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">t</font>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="complfld.html#T87" title="COMPLFLD:th.87">COMPLFLD:87</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">w</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"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">t</font>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">w</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"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">t</font>,<font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</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="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">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"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">t</font>,<font color="Maroon" title="c4">w</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"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">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"><font color="Maroon" title="c3">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>,<font color="Maroon" title="c4">w</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">t</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10" title="BILINEAR:th.10">BILINEAR:10</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
