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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[ <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E1:24_1_1"/><i><font color="Green">E72</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="topmetr.html#K5">I[01]</a>   ex <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="topalg_2.html#K3">R^1</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>

<b>take </b>
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>
;<br/>

<b>thus </b><a NAME="E1:24_1_1_1"/>
( <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="topalg_2.html#K3">R^1</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>] )
 <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:24_1_1"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> ,the <a href="struct_0.html#U1">carrier</a> of <a href="topalg_2.html#K3">R^1</a>  st <br/>for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="topmetr.html#K5">I[01]</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>]
 
<b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>();<br/></i>
<b>hence </b><a NAME="E3:24_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<a href="topalg_2.html#K3">R^1</a>  st <br/>for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  holds  <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">x</font>
 ;<br/>


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