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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:19_1"/><i><font color="Green">E12</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="armstrng.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><b>hence </b><a NAME="E2:19_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="armstrng.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:19_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</sub></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"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E4:19_1"/><i><font color="Green">E14</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="armstrng.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><i><font color="Green">E15</font></i>: <font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0 = 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="binari_3.html#T26">BINARI_3:26</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></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="E6:19_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="armstrng.html#E1:19_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="armstrng.html#E3:19_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><a NAME="E7:19_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="txt" href="armstrng.html#E1:19_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="armstrng.html#E3:19_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="armstrng.html#E4:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a>, <a class="ref" href="margrel1.html#D13">MARGREL1:def 13</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<a href="margrel1.html#K7">FALSE</a>  <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="armstrng.html#E1:19_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="armstrng.html#E3:19_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="armstrng.html#D5" target="_self">Def5</a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i><a class="ref" href="margrel1.html#T49">MARGREL1:49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="armstrng.html#E1:19_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="armstrng.html#E3:19_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="armstrng.html#E5:19_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="margrel1.html#D13">MARGREL1:def 13</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:19"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0</span>)</span> <a href="armstrng.html#K3" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> 0
 <b>by </b><i><a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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