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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</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>2</sub></font>, <font color="Maroon">c<sub>3</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>assume </b><b>that </b><br/><a NAME="E1:21"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>and </b><br/><a NAME="E3:21"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/>

<a NAME="E4:21"/><i><font color="Green">E19</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E5:21"/><i><font color="Green">E20</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E6:21"/><i><font color="Green">E21</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E7:21"/><i><font color="Green">E22</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:21_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:21_1"/><b>then </b><i><font color="Green">E24</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><i><font color="Green">E25</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E1:21"><i><font color="Green">E16</font></i></a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i><a class="txt" href="binari_3.html#E1:21_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2_1_1"><b>suppose </b></a><a NAME="E1:21_1_2_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:21_1_2_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_2_1_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="binari_3.html#E2:21_1_2_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:21_1_2_1_1_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_2_1_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="binari_3.html#E3:21"><i><font color="Green">E18</font></i></a>, <a class="ref" href="binarith.html#D5">BINARITH:def 5</a>, <a class="ref" href="margrel1.html#T38">MARGREL1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:21_1_2_1_1_1_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:21_1_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E29</font></i>: 
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:21_1_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E30</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E4:21_1_2_1_1_1_1_2"/><i><font color="Green">E31</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/><a NAME="E5:21_1_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="txt" href="binari_3.html#E1:21_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binarith.html#D5">BINARITH:def 5</a></i>;<br/><a NAME="E6:21_1_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E32</font></i>: 
( <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>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></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#T45">MARGREL1:45</a></i>;<br/><span class="p1">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="binari_3.html#E2:21"><i><font color="Green">E17</font></i></a>, <a class="txt" href="binari_3.html#E3:21"><i><font color="Green">E18</font></i></a>, <a class="txt" href="binari_3.html#E1:21_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binari_3.html#T21" target="_self">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> 2
<b>by </b><i><a class="txt" href="binari_3.html#E2:21_1_2_1_1_1_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="binari_3.html#E4:21_1_2_1_1_1_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E3:21_1_2_1_1_1_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="binarith.html#D4">BINARITH:def 4</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i><a class="txt" href="binari_3.html#E3:21_1_2_1_1_1_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="binari_2.html#T8">BINARI_2:8</a></i>
<br/>.= 
 <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
;<br/><b>then </b><i><font color="Green">E33</font></i>:  <a href="margrel1.html#K8">TRUE</a>  = 
<span class="p1">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E7:21"><i><font color="Green">E22</font></i></a>, <a class="txt" href="binari_3.html#E1:21_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1_2_1_1_1_1_2"><i><font color="Green">E29</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E1:21_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="binari_3.html#E1:21_1_2_1_1_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="binarith.html#D5">BINARITH:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E6:21_1_2_1_1_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="binarith.html#T7">BINARITH:7</a></i>
<br/>.= 
<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>4</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K2">Bin1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E6:21_1_2_1_1_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="binarith.html#T7">BINARITH:7</a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E4:21"><i><font color="Green">E19</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
 <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_3.html#E8:21_1_2_1_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E5:21"><i><font color="Green">E20</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="binari_3.html#E3:21_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E1:21_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#D4">BINARITH:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:21_1_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2_1_2"><b>suppose </b></a><a NAME="E1:21_1_2_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:21_1_2_1_2"/><i><font color="Green">E27</font></i>: 
not <font color="Maroon">c<sub>4</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="binari_3.html#E1:21_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#T5">BINARITH:5</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E4:21"><i><font color="Green">E19</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
 <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_3.html#E2:21"><i><font color="Green">E17</font></i></a>, <a class="txt" href="binari_3.html#E3:21"><i><font color="Green">E18</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="binari_3.html#E1:21_1_2_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1_2_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="binari_3.html#T20" target="_self">Th20</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="binari_3.html#E5:21"><i><font color="Green">E20</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="binari_3.html#E3:21_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E1:21_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#D4">BINARITH:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="binari_3.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="binari_3.html#E2:21_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:21_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:21"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="binarith.html#K6">'not'</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T139">FINSEQ_2:139</a></i>;<br/>


</div>
