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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="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> ;<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#L4" title="VECTSP_1:struct.4">VectSpStr</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c5">y</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c3">W</font>;<br/><b>let </b><font color="Maroon" title="c6">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c7">f</font> be   <a href="bilinear.html#NM1" title="BILINEAR:NM.1">Form</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">W</font>;<br/>











<b>set </b><font color="Maroon" title="c8">F</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c4">v</font>;<br/>
<b>assume </b><a NAME="E1:81"/>
<font color="Maroon" title="c7">f</font> is <a href="bilinear.html#V3" title="BILINEAR:attr.3">homogeneousFAF</a>
 ;<br/>

<a NAME="E2:81"/><b>then </b><i><font color="Green" title="E33">A1</font></i>: 
 <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c4">v</font> is <a href="hahnban1.html#V2" title="HAHNBAN1:attr.2">homogeneous</a>
 
<b>by </b><i><a class="ref" href="bilinear.html#D14" target="_self" title="BILINEAR:def.14">Def14</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c5">y</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c4">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">r</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c5">y</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T9" target="_self" title="BILINEAR:th.9">Th9</a></i>
<br/>.= 
<font color="Maroon" title="c6">r</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c4">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>
<b>by </b><i><a class="txt" href="bilinear.html#E2:81"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="hahnban1.html#D12" title="HAHNBAN1:def.12">HAHNBAN1:def 12</a></i>
<br/>.= 
<font color="Maroon" title="c6">r</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">y</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T9" target="_self" title="BILINEAR:th.9">Th9</a></i>
;<br/>


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