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<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span>;<br/>

<b>consider </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E2:5"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="euclid_5.html#T1" target="_self" title="EUCLID_5:th.1">Th1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c1">p</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <b>by </b><i><a class="ref" href="euclid.html#T27" title="EUCLID:th.27">EUCLID:27</a></i>;<br/>
<i><font color="Green" title="E8">A2</font></i>: <font color="Maroon" title="c1">p</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  = 
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="ref" href="euclid_5.html#D1" target="_self" title="EUCLID_5:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="euclid_5.html#E2:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green" title="E9">A3</font></i>: <font color="Maroon" title="c1">p</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  = 
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="ref" href="euclid_5.html#D2" target="_self" title="EUCLID_5:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="txt" href="euclid_5.html#E2:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon" title="c1">p</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  = 
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3
<b>by </b><i><a class="ref" href="euclid_5.html#D3" target="_self" title="EUCLID_5:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c4">z</font>
<b>by </b><i><a class="txt" href="euclid_5.html#E2:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E7:5"/>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
 <b>by </b><i><a class="txt" href="euclid_5.html#E2:5"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="euclid_5.html#E4:5"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="euclid_5.html#E5:5"><i><font color="Green" title="E9">A3</font></i></a></i>;<br/>


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