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<b>let </b><font color="Maroon">T</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">E39</font></i>: 
<font color="Maroon">T</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_1.html#K13">*</a> 
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">y</font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">n</font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E2:25"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E3:25"/><i><font color="Green">E41</font></i>: 
 <a href="binarith.html#K4">'not'</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> <a href="trees_2.html#K2">-level</a> <font color="Maroon">n</font>
 
<b>by </b><i>, </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#K4">'not'</a> <font color="Maroon">y</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K4">'not'</a> <font color="Maroon">y</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">n</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">F</font> =  <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="binarith.html#K4">'not'</a> <font color="Maroon">y</font></span>)</span> as   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">n</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">E42</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="binarith.html#K4">'not'</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="binarith.html#K4">'not'</a> <font color="Maroon">y</font>
 
<b>by </b><i>, <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">n</font>,<font color="Maroon">T</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="binarith.html#K4">'not'</a> <font color="Maroon">y</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <font color="Maroon">F</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i>, </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">n</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, , <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">n</font>

;<br/>


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