<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th40</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: BILINEAR:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   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="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">V</font>, <font color="Olive" title="b3">W</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">ModuleStr</a> over <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="bilinear.html#NM1" title="BILINEAR:NM.1">Form</a> of <font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font>  st ( <font color="Olive" title="b4">f</font> is  <a href="bilinear.html#V1" title="BILINEAR:attr.1">additiveFAF</a>  or <font color="Olive" title="b4">f</font> is  <a href="bilinear.html#V2" title="BILINEAR:attr.2">additiveSAF</a>  ) holds <br/>( <font color="Olive" title="b4">f</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  iff  for <font color="Olive" title="b5">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b6">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b3">W</font> holds  <font color="Olive" title="b4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">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="Olive" title="b1">K</font> )</div></div>
