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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">n</font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>



<b>set </b><font color="Maroon">B</font> = <font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0;<br/>
<b>set </b><font color="Maroon">nB</font> =  <a href="binarith.html#K4">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:20_1"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span></span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:20_1"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span></span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:20_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span></span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><i><font color="Green">E38</font></i>: <font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0 = 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="binari_3.html#T26">BINARI_3:26</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="finseq_2.html#K2">|-&gt;</a> 0
<b>by </b><i><a class="ref" href="euclid.html#D4">EUCLID:def 4</a></i>
;<br/><a NAME="E5:20_1"/><i><font color="Green">E39</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/><a NAME="E6:20_1"/>
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, , , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><a NAME="E7:20_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i>, , , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><span class="p1">(<span class="default"><a href="binarith.html#K4">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x</font> = 
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="binarith.html#D4">BINARITH:def 4</a></i>
<br/>.= 
 <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i/>
;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span></span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<a href="margrel1.html#K8">TRUE</a>  <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20"/>
<span class="p1">(<span class="default"><a href="binarith.html#K4">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span></span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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