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<b>let </b><font color="Maroon">F</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><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>assume </b><a NAME="E1:55"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="afinsq_1.html#K2">dom</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E2:55"/>
( <a href="binop_2.html#K47">addnat</a>  <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K47">addnat</a>  <a href="stirl2_1.html#K4">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="stirl2_1.html#K8">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K47">addnat</a>  <a href="stirl2_1.html#K4">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> &amp; <a href="binop_2.html#K47">addnat</a>  <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K47">addnat</a>  <a href="stirl2_1.html#K4">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="stirl2_1.html#K8">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K47">addnat</a>  <a href="stirl2_1.html#K4">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="stirl2_1.html#K8">.</a> <font color="Maroon">n</font></span>)</span> &amp; <a href="binop_2.html#K47">addnat</a>  <a href="stirl2_1.html#K4">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="stirl2_1.html#K7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <font color="Maroon">n</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1"><i><font color="Green">Lemma44</font></i></a>, , <a class="ref" href="binop_2.html#D23">BINOP_2:def 23</a>, <a class="ref" href="stirl2_1.html#D4">STIRL2_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:55"/>
<span class="p1">(<span class="default"><a href="stirl2_1.html#K7">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="stirl2_1.html#K8">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="stirl2_1.html#K7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="card_fin.html#K4" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="stirl2_1.html#D4">STIRL2_1:def 4</a></i>;<br/>


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