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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">  for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">W</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">f</font> being  <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="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">g</font> being  <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="Olive" title="b2">W</font> holds   <a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</a> <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">g</font>)</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Olive" title="b3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Olive" title="b4">g</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font>, <font color="Maroon" title="c3">W</font> be   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</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">  for <font color="Olive" title="b1">f</font> being  <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/>  for <font color="Olive" title="b2">g</font> being  <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="c3">W</font> holds   <a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</a> <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>)</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Olive" title="b2">g</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be  <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">  for <font color="Olive" title="b1">g</font> being  <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="c3">W</font> holds   <a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</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="Olive" title="b1">g</font>)</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Olive" title="b1">g</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">g</font> be  <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="c3">W</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">  <a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</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="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c5">g</font></span>)</span>)</span><br/>







<a NAME="E1:120"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
 <a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c4">f</font></span>)</span>)</span>)</span>
 
;<br/>
<a NAME="E2:120"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c3">W</font>
 
;<br/>
<a NAME="E3:120"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A3</font></span>: 
 <a href="bilinear.html#K15" title="BILINEAR:func.15">LQForm</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="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">g</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T54" target="_self" onmouseover="rs('bilinear/T54')" onmouseout="rh()">Th54</a></span>;<br/>
<span class="kw">thus </span> <a href="bilinear.html#K17" title="BILINEAR:func.17">QForm</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="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LQForm</a> <span class="p2">(<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></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T48" target="_self" onmouseover="rs('bilinear/T48')" onmouseout="rh()">Th48</a></span>
<br/>.= 
 <a href="bilinear.html#K16" title="BILINEAR:func.16">RQForm</a> <span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p2">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c5">g</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:120"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="txt" href="#E3:120"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="ref" href="bilinear.html#T54" target="_self" onmouseover="rs('bilinear/T54')" onmouseout="rh()">Th54</a></span>
<br/>.= 
 <a href="bilinear.html#K9" title="BILINEAR:func.9">FormFunctional</a> (<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c5">g</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:120"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="bilinear.html#T55" target="_self" onmouseover="rs('bilinear/T55')" onmouseout="rh()">Th55</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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