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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:21"/>
<font color="Maroon" title="c1">i</font> <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c2">n</font>
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="ref" href="idea_1.html#D3" target="_self" title="IDEA_1:def.3">Def3</a></i>;<br/>
<b>thus </b><a NAME="E3:21"/>
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> 0,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E2:21"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>;<br/>


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