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<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> <a href="vectsp_1.html#V2" title="VECTSP_1:attr.2">left-distributive</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">VectSpStr</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b3">g</font> being  <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Olive" title="b2">W</font><br/> for <font color="Olive" title="b4">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b5">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Olive" title="b2">W</font> holds  <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Olive" title="b1">V</font></span>)</span>,<font color="Olive" title="b3">g</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><b>let </b><font color="Maroon" title="c2">V</font>, <font color="Maroon" title="c3">W</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">VectSpStr</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">g</font> being  <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c3">W</font><br/> for <font color="Olive" title="b2">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b3">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c3">W</font> holds  <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Olive" title="b1">g</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><b>let </b><font color="Maroon" title="c4">h</font> be   <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c3">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b2">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c3">W</font> holds  <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">h</font></span>)</span> <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>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><b>let </b><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="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c3">W</font> holds  <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">h</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><b>let </b><font color="Maroon" title="c6">y</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c3">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">h</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/>









<b>set </b><font color="Maroon" title="c7">0F</font> =  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font>;<br/>
<b>set </b><font color="Maroon" title="c8">F</font> =  <a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p1">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">h</font>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c4">h</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">y</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#D11" target="_self" title="BILINEAR:def.11">Def11</a></i>
<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="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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