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<b>let </b><font color="Maroon">k</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">seq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E53</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">k</font>
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E55</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</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">m</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:23"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<a NAME="E5:23"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E6:23"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="sin_cos.html#K10" target="_self">Sift</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">k</font> = 
<font color="Maroon">seq</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">seq</font> <a href="comseq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i>, , <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/><br/>


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