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<span class="kw">let </span><font color="Maroon" title="c5">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="Red">:: according to </font></span><a class="ref" href="hermitan.html#D4" target="_self" title="HERMITAN:def.4">HERMITAN:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font> is  <a href="hermitan.html#V1" title="HERMITAN:attr.1">cmplxhomogeneous</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">fg</font> =  <a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">F</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">y</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="Red">:: according to </font></span><a class="ref" href="hermitan.html#D1" target="_self" title="HERMITAN:def.1">HERMITAN:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Scalar</a> of  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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">r</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Scalar</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">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="c9">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font></span>)</span></span><br/>



<a NAME="E1:62_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Maroon" title="c4">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T25" title="BILINEAR:th.25">BILINEAR:25</a></span>;<br/>
<span class="kw">hence </span><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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">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="c9">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">y</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<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">y</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hahnban1.html#D9" title="HAHNBAN1:def.9">HAHNBAN1:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#D1" target="_self" title="HERMITAN:def.1">Def1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="hahnban1.html#D9" title="HAHNBAN1:def.9">HAHNBAN1:def 9</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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