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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="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E18</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E19</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:23"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sin_cos.html#E1:23"><i><font color="Green">E18</font></i></a>, <a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<a NAME="E5:23"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="txt" href="sin_cos.html#E4:23"><i><font color="Green">E20</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="sin_cos.html#K10" target="_self">Sift</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="sin_cos.html#E4:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="sin_cos.html#D12" target="_self">Def12</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E2:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="sin_cos.html#E5:23"><i><font color="Green">E21</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/>


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