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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:67"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> 2 <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:67"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="euclid.html#K18">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:67"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>
<font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="mathmorp.html#E4:67"><i><font color="Green">E31</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T37">EUCLID:37</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K17">+</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
;<br/>
<a NAME="E6:67"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K17">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>, B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="mathmorp.html#E4:67"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:67"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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