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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:55"/>
 <a href="afinsq_1.html#K1">len</a> <span class="p1"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="afinsq_1.html#K9">%&gt;</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="afinsq_1.html#T37">AFINSQ_1:37</a></i>;<br/>
<a NAME="E2:55"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <span class="p1"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="afinsq_1.html#K9">%&gt;</a></span> <a href="funct_1.html#K1">.</a> 0 &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>2</sub></font> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="afinsq_1.html#K1">len</a> <span class="p1"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="afinsq_1.html#K9">%&gt;</a></span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="afinsq_1.html#K9">%&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="afinsq_1.html#K9">%&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K10">-</a> 1</span>)</span> )
 
<b>by </b><i><a class="ref" href="stirl2_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:55"/>
<font color="Maroon">c<sub>2</sub></font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="afinsq_1.html#K9">%&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="afinsq_1.html#T38">AFINSQ_1:38</a></i>;<br/>


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