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<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  the   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">V17</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#K9" title="BILINEAR:func.9">FormFunctional</a> ( the   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">V17</a>() <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>, the   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">V17</a>() <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="132_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">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="Olive" title="b2">w</font>,<font color="Olive" title="b1">v</font>)</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#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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"> the   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">V17</a>() <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</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"> the   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">V17</a>() <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</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#D10" target="_self" onmouseover="rs('bilinear/D10')" onmouseout="rh()">Def10</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#D10" target="_self" onmouseover="rs('bilinear/D10')" onmouseout="rh()">Def10</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:132_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>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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