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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">d1</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">d2</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>







<a NAME="E1:61"/>
 <a href="afinsq_1.html#K1">len</a> <span class="p1"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="afinsq_1.html#T42">AFINSQ_1:42</a></i>;<br/>
<b>then consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font><b> such that </b><br/><a NAME="E3:61"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <span class="p1"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="funct_1.html#K1">.</a> 0
 <b>and </b><br/><a NAME="E4:61"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 holds <br/><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:61"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K10">-</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="stirl2_1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E6:61"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> 0</span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> &amp; <span class="p1"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> )
 
<b>by </b><i><a class="ref" href="stirl2_1.html#T6" target="_self">Th6</a>, <a class="ref" href="afinsq_1.html#T42">AFINSQ_1:42</a></i>;<br/>
<b>hence </b><a NAME="E7:61"/>
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1"><a href="stirl2_1.html#K5" target="_self">&lt;%</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="stirl2_1.html#K5" target="_self">%&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="stirl2_1.html#T5" target="_self">Th5</a>, <a class="ref" href="stirl2_1.html#T8" target="_self">Th8</a></i>;<br/>


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