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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/><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="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:28"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:28"/><b>then </b><i><font color="Green">E21</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>;<br/>
<i><font color="Green">E22</font></i>:  <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"><font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></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>5</sub></font> =  <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></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="E5:28"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</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="finseq_1.html#D11">FINSEQ_1:def 11</a>, <a class="ref" href="margrel1.html#D12">MARGREL1:def 12</a></i>;<br/>
<a NAME="E6:28"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is    <a href="bintree2.html#M1" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="bintree2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="bintree2.html#M1" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="bintree2.html#E3:28"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E8:28"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</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="ref" href="trees_2.html#D6">TREES_2:def 6</a></i>;<br/>
<a NAME="E9:28"/>
<font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_6.html#T29">FINSEQ_6:29</a></i>;<br/>
<a NAME="E10:28"/><b>then </b><i><font color="Green">E24</font></i>: 
<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> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K9">Absval</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="bintree2.html#E8:28"><i><font color="Green">E23</font></i></a>, <a class="ref" href="bintree2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E11:28"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <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>
 
<b>by </b><i><a class="txt" href="bintree2.html#E8:28"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:28"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="bintree2.html#E2:28"><i><font color="Green">E21</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E13:28"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<a NAME="E14:28"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="bintree2.html#E2:28"><i><font color="Green">E21</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<b>then </b><i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><a href="binarith.html#K9">Absval</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="binari_3.html#T36">BINARI_3:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <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#E2:28"><i><font color="Green">E21</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>

;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="bintree2.html#K2" target="_self">FinSeqLevel</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> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<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#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="bintree2.html#E10:28"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bintree2.html#E11:28"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bintree2.html#E15:28"><i><font color="Green">E26</font></i></a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>
;<br/>


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