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<b>set </b><font color="Maroon">C</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">f</font>,<font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<div><i><font color="Green">E30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/><b>reconsider </b><font color="Maroon">y</font> =  <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/><b>take </b><font color="Maroon">y</font> = <font color="Maroon">y</font>;<br/><b>thus </b><a NAME="E2:99_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>, <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E3:99_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">v</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">v</font>,<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>(<a class="ref" href="hermitan.html#T15" target="_self">Th15</a>);<br/></i>
<b>reconsider </b><font color="Maroon">F</font> = <font color="Maroon">F</font> as   <a href="hahnban1.html#NM3">RFunctional</a> of <font color="Maroon">V</font> ;<br/>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E5:99_1_1"/>
for <font color="Olive">v</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> holds  <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">f</font>,<font color="Olive">v</font></span>)</span>
 <b>by </b><i/>;<br/>


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