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<span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="bilinear.html#D11" title="BILINEAR:def.11">BILINEAR:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">w</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="c2">W</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="grcat_1.html#D8" title="GRCAT_1:def.8">GRCAT_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</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">w</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#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">w</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#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</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/>



<span class="kw">set </span><font color="Maroon" title="c7">fg</font> =  <a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</font>);<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</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">w</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> (<font color="Maroon" title="c4">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T8" title="BILINEAR:th.8">BILINEAR:8</a></span>
<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="c4">v</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">t</font></span>)</span>)</span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a></span>
<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="c4">v</font>,<font color="Maroon" title="c5">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="c4">v</font>,<font color="Maroon" title="c6">t</font>)</span>)</span></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T27" title="BILINEAR:th.27">BILINEAR:27</a></span>
<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="c4">v</font>,<font color="Maroon" title="c5">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="c4">v</font>,<font color="Maroon" title="c6">t</font>)</span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#T51" title="COMPLFLD:th.51">COMPLFLD:51</a></span>
<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="c4">v</font>,<font color="Maroon" title="c5">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="c4">v</font>,<font color="Maroon" title="c6">t</font>)</span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a></span>
<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="c4">v</font>,<font color="Maroon" title="c5">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="c4">v</font>,<font color="Maroon" title="c6">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">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="c4">v</font>,<font color="Maroon" title="c6">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T8" title="BILINEAR:th.8">BILINEAR:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">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"><a href="bilinear.html#K7" title="BILINEAR:func.7">FunctionalFAF</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">v</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 class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T8" title="BILINEAR:th.8">BILINEAR:8</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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