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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">VectSpStr</a> of  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="bilinear.html#NM1" title="BILINEAR:NM.1">Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c1">V</font> holds   <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="bilinear.html#NM1" title="BILINEAR:NM.1">Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">K</font> =  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/>
<span class="kw">thus </span><a NAME="E1:107"/>
 <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:107_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">v</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E3:107_1"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font>
 <span class="kw">and </span><br/><a NAME="E4:107_1"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c5">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> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/>
<a NAME="E5:107_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c5">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> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:107_1"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a>, <a class="ref" href="complfld.html#T83" title="COMPLFLD:th.83">COMPLFLD:83</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:107_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:107_1"><span class="lab"><font color="Green" title="E48">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:107"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">v</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E4:107"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font>
 <span class="kw">and </span><br/><a NAME="E5:107"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c5">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> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ;<br/>
<a NAME="E6:107"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:107"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="hermitan.html#D8" target="_self" title="HERMITAN:def.8">Def8</a>, <a class="ref" href="complfld.html#T83" title="COMPLFLD:th.83">COMPLFLD:83</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:107"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:107"><span class="lab"><font color="Green" title="E48">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
