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<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">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</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">n</font>
 ;<br/>

<a NAME="E2:34"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">k</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">n</font></span>)</span> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/>
<a NAME="E3:34"/>
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <a href="margrel1.html#K6">BOOLEAN</a>  <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:34"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="margrel1.html#K6">BOOLEAN</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E5:34"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <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">y</font> =  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> 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="txt" href="binari_3.html#E1:34"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E7:34"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E8:34"/><b>then </b>
<font color="Maroon">n</font> <a href="binari_3.html#K1" target="_self">-BinarySequence</a> <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="binarith.html#K4">'not'</a> <font color="Maroon">y</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:34"/><b>then </b>
 <a href="binarith.html#K9">add_ovfl</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1" target="_self">-BinarySequence</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E10:34"/>
 <a href="binarith.html#K9">add_ovfl</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1" target="_self">-BinarySequence</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>;<br/>


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