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<b>let </b><font color="Maroon">h</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="int_1.html#NM1">Integer</a>;<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>assume </b><a NAME="E1:43"/><i><font color="Green">E39</font></i>: 
(  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> &amp; <font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 &amp; <font color="Maroon">h</font> <a href="xxreal_0.html#R1">&lt;</a> 0 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a> 0 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">h</font> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> )
 ;<br/>

<b>set </b><font color="Maroon">H</font> =  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">n</font>,<font color="Maroon">h</font>;<br/>
<b>set </b><font color="Maroon">I</font> =  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">n</font>,<font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">H1</font> =  <a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font>;<br/>
<b>set </b><font color="Maroon">I1</font> =  <a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">F</font> =  <a href="margrel1.html#K7">FALSE</a> ;<br/>
<b>set </b><font color="Maroon">T</font> =  <a href="margrel1.html#K8">TRUE</a> ;<br/>
<a NAME="E2:43"/>
( <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
;<br/>
<a NAME="E3:43"/><b>then </b><i><font color="Green">E40</font></i>: 
(  <a href="real_1.html#K1">-</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="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> &amp; <font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&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="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E4:43"/><b>then </b><i><font color="Green">E41</font></i>: 
(  <a href="real_1.html#K1">-</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="xxreal_0.html#R1">&lt;</a> <font color="Maroon">h</font> &amp;  <a href="real_1.html#K1">-</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="xxreal_0.html#R1">&lt;</a> <font color="Maroon">i</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:43"/><b>then </b>
(  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">h</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span> &amp;  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E6:43"/><b>then </b><i><font color="Green">E42</font></i>: 
(  <a href="prepower.html#K1">abs</a> <font color="Maroon">h</font> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font> &amp;  <a href="prepower.html#K1">abs</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&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="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E7:43"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E8:43"/><b>then </b>
2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="power.html#T44">POWER:44</a></i>;<br/>
<a NAME="E9:43"/><b>then </b>
(  <a href="prepower.html#K1">abs</a> <font color="Maroon">h</font> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp;  <a href="prepower.html#K1">abs</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E10:43"/><b>then </b><i><font color="Green">E43</font></i>: 
(  <a href="binari_4.html#K1" target="_self">MajP</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">h</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="binari_4.html#K1" target="_self">MajP</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i/>;<br/>
<a NAME="E11:43"/><i><font color="Green">E44</font></i>: 
( <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">h</font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 &amp; <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 )
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<i><font color="Green">E45</font></i>: <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> 1</span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="power.html#T32">POWER:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font>

;<br/>
<a NAME="E13:43"/><b>then </b><i><font color="Green">E50</font></i>: 
( 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">h</font> &amp; 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> )
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E14:43"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">h</font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> )
 
<b>by </b><i>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">NH</font> = <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">h</font>, <font color="Maroon">NI</font> = <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<b>consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a> <b> such that </b><br/><a NAME="E17:43"/><i><font color="Green">E51</font></i>: 
 <a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">n</font>,<font color="Maroon">h</font></span>)</span> <a href="binarith.html#K10">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a> <b> such that </b><br/><a NAME="E19:43"/><i><font color="Green">E52</font></i>: 
 <a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">n</font>,<font color="Maroon">i</font></span>)</span> <a href="binarith.html#K10">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i/>;<br/>
<a NAME="E20:43"/><i><font color="Green">E74</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E21:43"/><i><font color="Green">E75</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<b>then </b><i><font color="Green">E91</font></i>: <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">h</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">NH</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
 <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i>, , <a class="ref" href="binari_3.html#T30">BINARI_3:30</a></i>
;<br/>
<i><font color="Green">E92</font></i>: <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="txt" href="binari_4.html#E1:43"><i><font color="Green">E39</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">NI</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
 <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i>, , <a class="ref" href="binari_3.html#T30">BINARI_3:30</a></i>
;<br/>
<i><font color="Green">E93</font></i>:  <a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">h</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">NH</font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<i><font color="Green">E94</font></i>:  <a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">NI</font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<i><font color="Green">E95</font></i>:  <a href="binari_2.html#K4">Intval</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E3:43"><i><font color="Green">E40</font></i></a>, <a class="ref" href="binari_2.html#D3">BINARI_2:def 3</a></i>
<br/>.= 
<font color="Maroon">NH</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="binari_4.html#E6:43"><i><font color="Green">E42</font></i></a>, <a class="ref" href="binari_3.html#T36">BINARI_3:36</a></i>
<br/>.= 
<font color="Maroon">h</font>

;<br/>
<i><font color="Green">E103</font></i>:  <a href="binari_2.html#K4">Intval</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K7">Absval</a> <span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E4:43"><i><font color="Green">E41</font></i></a>, <a class="ref" href="binari_2.html#D3">BINARI_2:def 3</a></i>
<br/>.= 
<font color="Maroon">NI</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="binari_4.html#E10:43"><i><font color="Green">E43</font></i></a>, <a class="ref" href="binari_3.html#T36">BINARI_3:36</a></i>
<br/>.= 
<font color="Maroon">i</font>

;<br/>
<a NAME="E28:43"/><i><font color="Green">E104</font></i>: 
<span class="p1">(<span class="default"><a href="binarith.html#K5">carry</a> <span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span>,<span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i>, , </i>;<br/>
<b>then </b><i><font color="Green">E105</font></i>:  <a href="binari_2.html#K5">Int_add_ovfl</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="margrel1.html#K7">FALSE</a>  <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <a href="margrel1.html#K8">TRUE</a> </span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_4.html#E3:43"><i><font color="Green">E40</font></i></a>, <a class="txt" href="binari_4.html#E4:43"><i><font color="Green">E41</font></i></a>, <a class="ref" href="binari_2.html#D4">BINARI_2:def 4</a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 

;<br/>
 <a href="binari_2.html#K6">Int_add_udfl</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span>,<span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="margrel1.html#K8">TRUE</a>  <a href="margrel1.html#K10">'&amp;'</a> <a href="margrel1.html#K8">TRUE</a> </span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <a href="margrel1.html#K8">TRUE</a> </span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E3:43"><i><font color="Green">E40</font></i></a>, <a class="txt" href="binari_4.html#E4:43"><i><font color="Green">E41</font></i></a>, <a class="ref" href="binari_4.html#T4" target="_self">Th4</a>, <a class="ref" href="binari_2.html#D5">BINARI_2:def 5</a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 

;<br/>
<b>then </b> <a href="binari_2.html#K4">Intval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span> <a href="binarith.html#K8">+</a> <span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <a href="margrel1.html#K7">FALSE</a> ,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K2">IFEQ</a> <a href="margrel1.html#K7">FALSE</a> ,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binari_4.html#T1" target="_self">Th1</a>, <a class="ref" href="binari_4.html#T2" target="_self">Th2</a>, <a class="txt" href="binari_4.html#E11:43"><i><font color="Green">E44</font></i></a>, <a class="txt" href="binari_4.html#E12:43"><i><font color="Green">E45</font></i></a>, <a class="ref" href="binari_4.html#T5" target="_self">Th5</a>, <a class="ref" href="binari_2.html#T14">BINARI_2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> 0

;<br/>
<b>hence </b><a NAME="E32:43"/>
 <a href="binari_2.html#K4">Intval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">h</font></span>)</span> <a href="binarith.html#K8">+</a> <span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font>
 ;<br/>


</div>
