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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="clopban1.html#NM1" title="CLOPBAN1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>;<br/>



<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E28">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</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="c2">Y</font>
 ;<br/>

<div><i><font color="Green" title="E29">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">X</font>;<br/><b>thus </b><span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> = 
<span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span>
<b>by </b><i><a class="txt" href="clopban1.html#E1:40"><i><font color="Green" title="E28">A1</font></i></a></i>
<br/>.= 
0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span>
<b>by </b><i><a class="ref" href="clvect_1.html#T103" title="CLVECT_1:th.103">CLVECT_1:103</a></i>
;<br/></div><b>end;</b></div>
<b>take </b>
0
; <i><font color="Red">:: according to </font></i><a class="ref" href="clopban1.html#D7" target="_self" title="CLOPBAN1:def.7">CLOPBAN1:def 7</a><br/>

<b>thus </b><a NAME="E3:40"/>
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 &amp; ( for <font color="Olive" title="b1">x</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">X</font> holds  <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> ) )
 <b>by </b><i><a class="txt" href="clopban1.html#E2:40"><i><font color="Green" title="E29">A2</font></i></a></i>;<br/>


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