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

<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="complfld.html#K1">F_Complex</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="vectsp_1.html#NM6">VectSp</a> of  <a href="complfld.html#K1">F_Complex</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="hermitan.html#NM2">sesquilinear-Form</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="bilinear.html#K17">LQForm</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>thus </b><a NAME="E1:122"/>
 <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_1"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T64" target="_self">Th64</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_1"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:122_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_1"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:122"/>
 <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_2"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T64" target="_self">Th64</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_2"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:122_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_2"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:122"/>
 <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_3"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_3"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T64" target="_self">Th64</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_3"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:122_3"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_3"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:122"/>
 <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_4"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_4"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T64" target="_self">Th64</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <span class="p2">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_4"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:122_4"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_4"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:122"/>
 <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_5"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_5"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T65" target="_self">Th65</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_5"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:122_5"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_5"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:122"/>
 <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_6"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_6"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T65" target="_self">Th65</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_6"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:122_6"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_6"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:122"/>
 <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:122_7"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:122_7"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T65" target="_self">Th65</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E3:122_7"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:122_7"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:122_7"><i><font color="Green">E65</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E8:122"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E10:122"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  ) )
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <span class="p3">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T65" target="_self">Th65</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> = 
<span class="p1">(<span class="default"><a href="bilinear.html#K17">LQForm</a> <span class="p2">(<span class="default"><a href="hermitan.html#K7" target="_self">RQ*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T66" target="_self">Th66</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="hermitan.html#E10:122"><i><font color="Green">E65</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:122"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E10:122"><i><font color="Green">E65</font></i></a></i>;<br/>


</div>
