<?xml version="1.0"?>
<div class="add">

<span class="kw">thus </span><a NAME="E1:144_1_1"/>
( <font color="Maroon" title="c3">f</font> is  <a href="bilinear.html#V8" title="BILINEAR:attr.8">alternating</a>  implies  for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">f</font> <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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">v</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T58" target="_self" onmouseover="rs('bilinear/T58')" onmouseout="rh()">Th58</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"> ( (  for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">f</font> <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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">v</font>)</span>)</span> ) implies <font color="Maroon" title="c3">f</font> is  <a href="bilinear.html#V8" title="BILINEAR:attr.8">alternating</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:144_1_1"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
 for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">f</font> <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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">v</font>)</span>)</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"> <font color="Maroon" title="c3">f</font> is  <a href="bilinear.html#V8" title="BILINEAR:attr.8">alternating</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="bilinear.html#D26" target="_self" onmouseover="rs('bilinear/D26')" onmouseout="rh()">BILINEAR:def 26</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"> <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</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/>

<a NAME="E3:144_1_1"/>
<font color="Maroon" title="c3">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="c4">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">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="c4">v</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:144_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a></span>;<br/>
<a NAME="E4:144_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">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="c4">v</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">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="c4">v</font>)</span>)</span> <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 class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T16" onmouseover="rs('vectsp_1/T16')" onmouseout="rh()">VECTSP_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:144_1_1"/>
<font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</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 class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D18" onmouseover="rs('vectsp_1/D18')" onmouseout="rh()">VECTSP_1:def 18</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/>


</div>
