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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c1">F</font>
 ;<br/>

<a NAME="E2:55"/>
( <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> &amp; <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> <font color="Maroon" title="c2">n</font></span>)</span> &amp; <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stirl2_1.html#K7" title="STIRL2_1:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c2">n</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1:55"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="card_fin.html#T42" target="_self" title="CARD_FIN:th.42">Th42</a>, <a class="ref" href="binop_2.html#D23" title="BINOP_2:def.23">BINOP_2:def 23</a>, <a class="ref" href="stirl2_1.html#D4" title="STIRL2_1:def.4">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" title="STIRL2_1:func.7">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stirl2_1.html#K7" title="STIRL2_1:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="stirl2_1.html#D4" title="STIRL2_1:def.4">STIRL2_1:def 4</a></i>;<br/>


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