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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</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">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">p1</font> be   <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">n</font></span>)</span>, <font color="Maroon">q</font> be   <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">n</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p1</font>
 ;<br/>

<b>thus </b><font color="Maroon">p</font> = 
<font color="Maroon">p</font> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T31">EUCLID:31</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K20">-</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T46">EUCLID:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K20">-</a> <font color="Maroon">p1</font>
<b>by </b><i><a class="ref" href="euclid.html#T49">EUCLID:49</a></i>
<br/>.= 
<font color="Maroon">q</font> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="euclid.html#K20">-</a> <font color="Maroon">p1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="euclid.html#T49">EUCLID:49</a></i>
<br/>.= 
<font color="Maroon">q</font> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T46">EUCLID:46</a></i>
<br/>.= 
<font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="euclid.html#T31">EUCLID:31</a></i>
;<br/>


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