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<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being  non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V14</a>() <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c4">ff</font> =  <a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c3">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V7" title="BILINEAR:attr.7">symmetric</a>  &amp; not <font color="Maroon" title="c4">ff</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  &amp; not <font color="Maroon" title="c4">ff</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V1" title="BILINEAR:attr.1">additiveFAF</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V3" title="BILINEAR:attr.3">homogeneousFAF</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V2" title="BILINEAR:attr.2">additiveSAF</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V4" title="BILINEAR:attr.4">homogeneousSAF</a>  )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">v</font>, <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="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font> = 
<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="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">w</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D11" target="_self" title="BILINEAR:def.11">Def11</a></span>
<br/>.= 
<font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D11" target="_self" title="BILINEAR:def.11">Def11</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:135_1_1"/>
( <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V7" title="BILINEAR:attr.7">symmetric</a>  &amp; not <font color="Maroon" title="c4">ff</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  &amp; not <font color="Maroon" title="c4">ff</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V1" title="BILINEAR:attr.1">additiveFAF</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V3" title="BILINEAR:attr.3">homogeneousFAF</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V2" title="BILINEAR:attr.2">additiveSAF</a>  &amp; <font color="Maroon" title="c4">ff</font> is  <a href="bilinear.html#V4" title="BILINEAR:attr.4">homogeneousSAF</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D26" target="_self" title="BILINEAR:def.26">Def26</a></span>; <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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