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<b>let </b><font color="Maroon">V</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">f</font> be  <a href="hermitan.html#V5" target="_self">diagReR+0valued</a> <a href="hermitan.html#NM3">hermitan-Form</a> of <font color="Maroon">V</font>;<br/>



<b>thus </b><a NAME="E1:104"/>
 <a href="bilinear.html#K14">diagker</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K13">rightker</a> <font color="Maroon">f</font>
  <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="104_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</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="E1:104_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K14">diagker</a> <font color="Maroon">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:104_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">a</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="104_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">w</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><a NAME="E1:104_1_1"/>
( <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">a</font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">w</font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> 0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">a</font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a>  )
 <b>by </b><i><a class="ref" href="hermitan.html#T17" target="_self">Th17</a>, <a class="txt" href="hermitan.html#E17"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="complfld.html#T93">COMPLFLD:93</a>, <a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E2:104_1_1"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">a</font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E3:104_1_1"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">a</font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:104_1_1"/>
<font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="complfld.html#T94">COMPLFLD:94</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:104_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K13">rightker</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="hermitan.html#T17" target="_self">Th17</a></i>;<br/>


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

<b>thus </b><a NAME="E2:104"/>
 <a href="bilinear.html#K13">rightker</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="bilinear.html#K14">diagker</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="bilinear.html#T42">BILINEAR:42</a></i>;<br/>


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