<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" target="_self">TOP-REAL</a> 2</span>)</span>;<br/>



<b>reconsider </b><font color="Maroon">p1</font> = <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> 2 ;<br/>
<a NAME="E2:79"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="euclid.html#K9" target="_self">*</a> <font color="Maroon">p1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:79"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">p</font> <a href="euclid.html#K21" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> 1 &amp; <font color="Maroon">p</font> <a href="euclid.html#K22" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> 2 )
 
<b>by </b><i><a class="ref" href="euclid.html#T2" target="_self">Th2</a>, <a class="ref" href="euclid.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:79"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<i><font color="Green">E52</font></i>: <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="euclid.html#K21" target="_self">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K9" target="_self">*</a> <font color="Maroon">p1</font></span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="euclid.html#E5:79"><i><font color="Green">E52</font></i></a>, <a class="ref" href="euclid.html#T2" target="_self">Th2</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21" target="_self">`1</a> </span>)</span>
<b>by </b><i>, <a class="txt" href="euclid.html#E13"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="rvsum_1.html#T66">RVSUM_1:66</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="euclid.html#K22" target="_self">`2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K9" target="_self">*</a> <font color="Maroon">p1</font></span>)</span> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="euclid.html#E5:79"><i><font color="Green">E52</font></i></a>, <a class="ref" href="euclid.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22" target="_self">`2</a> </span>)</span>
<b>by </b><i>, <a class="txt" href="euclid.html#E13"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="rvsum_1.html#T66">RVSUM_1:66</a></i>
;<br/>
<b>hence </b><a NAME="E7:79"/>
<font color="Maroon">x</font> <a href="euclid.html#K18" target="_self">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23" target="_self">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22" target="_self">`2</a> </span>)</span></span>)</span></span><a href="euclid.html#K23" target="_self">]|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T8" target="_self">Th8</a>, <a class="ref" href="euclid.html#T5" target="_self">Th5</a></i>;<br/>


</div>
