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<span class="kw">set </span><font color="Maroon" title="c6">fg</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>);<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E2:55_1_1"/>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font>
 <span class="kw">and </span><br/><a NAME="E3:55_1_1"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp10.html#T28" onmouseover="rs('vectsp10/T28')" onmouseout="rh()">VECTSP10:28</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c3">W</font><span class="kw"> such that </span><br/><a NAME="E5:55_1_1"/>
<font color="Maroon" title="c8">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">W</font>
 <span class="kw">and </span><br/><a NAME="E6:55_1_1"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp10.html#T28" onmouseover="rs('vectsp10/T28')" onmouseout="rh()">VECTSP10:28</a></span>;<br/>
<a NAME="E7:55_1_1"/>
<span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">v</font>,<font color="Maroon" title="c8">w</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">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="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">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/>
<a NAME="E8:55_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A3</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">v</font>,<font color="Maroon" title="c8">w</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:55_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E6:55_1_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="vectsp_1.html#T12" onmouseover="rs('vectsp_1/T12')" onmouseout="rh()">VECTSP_1:12</a></span>;<br/>
<span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">W</font></span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">W</font></span>)</span></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/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</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="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">W</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hahnban1.html#D9" onmouseover="rs('hahnban1/D9')" onmouseout="rh()">HAHNBAN1:def 9</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>

;<br/>
<span class="kw">hence </span><a NAME="E10:55_1_1"/>
 not  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>) is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:55_1_1"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="binop_1.html#T19" onmouseover="rs('binop_1/T19')" onmouseout="rh()">BINOP_1:19</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/>


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