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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="bintree2.html#V1" target="_self">full</a> <a href="trees_1.html#NM1">Tree</a>;<br/>

<a NAME="E1:25"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="bintree2.html#D2" target="_self">Def2</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">c<sub>2</sub></font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E2:25"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:25"/><i><font color="Green">E20</font></i>: 
 <a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="trees_2.html#K2">-level</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="bintree2.html#E1:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="bintree2.html#T11" target="_self">Th11</a></i>;<br/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">c<sub>2</sub></font>,<a href="margrel1.html#K6">BOOLEAN</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E6:25"/><i><font color="Green">E21</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="bintree2.html#E2:25"><i><font color="Green">E19</font></i></a>, <a class="ref" href="binari_3.html#T10">BINARI_3:10</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="bintree2.html#K1" target="_self">NumberOnLevel</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K9">Absval</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="bintree2.html#E3:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="bintree2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="bintree2.html#E2:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="bintree2.html#E6:25"><i><font color="Green">E21</font></i></a>, <a class="ref" href="binari_3.html#T8">BINARI_3:8</a></i>
<br/>.= 
2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font>

;<br/>


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