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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>, <font color="Maroon">c<sub>3</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>assume </b><a NAME="E2:58"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K17" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16" target="_self">0.REAL</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  ;<br/>
<font color="Maroon">c<sub>6</sub></font> <a href="rvsum_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="euclid.html#K16" target="_self">0.REAL</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="euclid.html#E2:58"><i><font color="Green">E37</font></i></a>, <a class="ref" href="euclid.html#D10" target="_self">Def10</a></i>
<br/>.= 
 <a href="euclid.html#K5" target="_self">0*</a> <font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0

;<br/>
<a NAME="E5:58"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T41">RVSUM_1:41</a></i>;<br/>
<b>hence </b><a NAME="E6:58"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K19" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K19" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="euclid.html#D12" target="_self">Def12</a></i>;<br/>


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