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<b>set </b><font color="Maroon" title="c3">C</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>$2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c2">f</font>,$1</span>)</span>;<br/>
<div><i><font color="Green" title="E51">A1</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" title="c4">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>;<br/><b>reconsider </b><font color="Maroon" title="c5">y</font> =  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">x</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/><b>take </b><font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c5">y</font>;<br/><b>thus </b><a NAME="E2:99_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">y</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c4">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E3:99_1_1"/><i><font color="Green" title="E52">A2</font></i>: 
for <font color="Olive" title="b1">v</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">v</font>,<font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S3" title="FUNCT_2:sch.3">FUNCT_2:sch 3</a>(<a class="txt" href="hermitan.html#E1:99_1_1"><i><font color="Green" title="E51">A1</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c5">F</font> = <font color="Maroon" title="c4">F</font> as   <a href="hahnban1.html#NM3" title="HAHNBAN1:NM.3">RFunctional</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c5">F</font>
;<br/>

<b>thus </b><a NAME="E5:99_1_1"/>
for <font color="Olive" title="b1">v</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c5">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c2">f</font>,<font color="Olive" title="b1">v</font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:99_1_1"><i><font color="Green" title="E52">A2</font></i></a></i>;<br/>


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