<?xml version="1.0"?>
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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font>, <font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>21</sub></font>, <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>23</sub></font>, <font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>26</sub></font>, <font color="Maroon">c<sub>27</sub></font>, <font color="Maroon">c<sub>28</sub></font>, <font color="Maroon">c<sub>29</sub></font>, <font color="Maroon">c<sub>30</sub></font>, <font color="Maroon">c<sub>31</sub></font>, <font color="Maroon">c<sub>32</sub></font>, <font color="Maroon">c<sub>33</sub></font>, <font color="Maroon">c<sub>34</sub></font>, <font color="Maroon">c<sub>35</sub></font>, <font color="Maroon">c<sub>36</sub></font>, <font color="Maroon">c<sub>37</sub></font>, <font color="Maroon">c<sub>38</sub></font>, <font color="Maroon">c<sub>39</sub></font>, <font color="Maroon">c<sub>40</sub></font>, <font color="Maroon">c<sub>41</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:46"/><i><font color="Green">E40</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K7" target="_self">NOR2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E2:46"/><i><font color="Green">E41</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K6" target="_self">NAND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E3:46"/><i><font color="Green">E42</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K34" target="_self">MODADD2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E4:46"/><i><font color="Green">E43</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K7" target="_self">NOR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>and </b><br/><a NAME="E5:46"/><i><font color="Green">E44</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K6" target="_self">NAND2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>and </b><br/><a NAME="E6:46"/><i><font color="Green">E45</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K34" target="_self">MODADD2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>and </b><br/><a NAME="E7:46"/><i><font color="Green">E46</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K7" target="_self">NOR2</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E8:46"/><i><font color="Green">E47</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K6" target="_self">NAND2</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E9:46"/><i><font color="Green">E48</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K34" target="_self">MODADD2</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E10:46"/><i><font color="Green">E49</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K7" target="_self">NOR2</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E11:46"/><i><font color="Green">E50</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K6" target="_self">NAND2</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E12:46"/><i><font color="Green">E51</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K34" target="_self">MODADD2</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E13:46"/><i><font color="Green">E52</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1" target="_self">NOT1</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E14:46"/><i><font color="Green">E53</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1" target="_self">NOT1</a> <font color="Maroon">c<sub>23</sub></font> )
 <b>and </b><br/><a NAME="E15:46"/><i><font color="Green">E54</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>38</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4" target="_self">XOR2</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>13</sub></font> )
 <b>and </b><br/><a NAME="E16:46"/><i><font color="Green">E55</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>25</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2" target="_self">AND2</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font> )
 <b>and </b><br/><a NAME="E17:46"/><i><font color="Green">E56</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>26</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K7" target="_self">NOR2</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <b>and </b><br/><a NAME="E18:46"/><i><font color="Green">E57</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>39</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4" target="_self">XOR2</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>16</sub></font> )
 <b>and </b><br/><a NAME="E19:46"/><i><font color="Green">E58</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>27</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2" target="_self">AND2</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>and </b><br/><a NAME="E20:46"/><i><font color="Green">E59</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>28</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8" target="_self">AND3</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font> )
 <b>and </b><br/><a NAME="E21:46"/><i><font color="Green">E60</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>29</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K13" target="_self">NOR3</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>14</sub></font> )
 <b>and </b><br/><a NAME="E22:46"/><i><font color="Green">E61</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>40</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4" target="_self">XOR2</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>19</sub></font> )
 <b>and </b><br/><a NAME="E23:46"/><i><font color="Green">E62</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>30</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2" target="_self">AND2</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 <b>and </b><br/><a NAME="E24:46"/><i><font color="Green">E63</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>31</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8" target="_self">AND3</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>and </b><br/><a NAME="E25:46"/><i><font color="Green">E64</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>32</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14" target="_self">AND4</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font> )
 <b>and </b><br/><a NAME="E26:46"/><i><font color="Green">E65</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>33</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K17" target="_self">NOR4</a> <font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 <b>and </b><br/><a NAME="E27:46"/><i><font color="Green">E66</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>41</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4" target="_self">XOR2</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>22</sub></font> )
 <b>and </b><br/><a NAME="E28:46"/><i><font color="Green">E67</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>34</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2" target="_self">AND2</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>21</sub></font> )
 <b>and </b><br/><a NAME="E29:46"/><i><font color="Green">E68</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>35</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8" target="_self">AND3</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 <b>and </b><br/><a NAME="E30:46"/><i><font color="Green">E69</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>36</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14" target="_self">AND4</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>and </b><br/><a NAME="E31:46"/><i><font color="Green">E70</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>37</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K18" target="_self">AND5</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font> )
 <b>and </b><br/><a NAME="E32:46"/><i><font color="Green">E71</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K21" target="_self">NOR5</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>34</sub></font>,<font color="Maroon">c<sub>35</sub></font>,<font color="Maroon">c<sub>36</sub></font>,<font color="Maroon">c<sub>37</sub></font> )
 ;<br/>

<a NAME="E33:46"/><i><font color="Green">E72</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E1:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="gate_1.html#D7" target="_self">Def7</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E34:46"/><i><font color="Green">E73</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> iff  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E2:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="gate_1.html#D6" target="_self">Def6</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E35:46"/><i><font color="Green">E74</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> iff ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E3:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self">Def34</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E36:46"/><i><font color="Green">E75</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E4:46"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gate_1.html#D7" target="_self">Def7</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E37:46"/><i><font color="Green">E76</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> iff  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E5:46"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gate_1.html#D6" target="_self">Def6</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E38:46"/><i><font color="Green">E77</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> iff ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E6:46"><i><font color="Green">E45</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self">Def34</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E39:46"/><i><font color="Green">E78</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E7:46"><i><font color="Green">E46</font></i></a>, <a class="ref" href="gate_1.html#D7" target="_self">Def7</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E40:46"/><i><font color="Green">E79</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> iff  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E8:46"><i><font color="Green">E47</font></i></a>, <a class="ref" href="gate_1.html#D6" target="_self">Def6</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E41:46"/><i><font color="Green">E80</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> iff ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E9:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self">Def34</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E42:46"/><i><font color="Green">E81</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E10:46"><i><font color="Green">E49</font></i></a>, <a class="ref" href="gate_1.html#D7" target="_self">Def7</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E43:46"/><i><font color="Green">E82</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> iff  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E11:46"><i><font color="Green">E50</font></i></a>, <a class="ref" href="gate_1.html#D6" target="_self">Def6</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E44:46"/><i><font color="Green">E83</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> iff ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E12:46"><i><font color="Green">E51</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self">Def34</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E45:46"/><i><font color="Green">E84</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> iff not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E13:46"><i><font color="Green">E52</font></i></a>, <a class="ref" href="gate_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E46:46"/><i><font color="Green">E85</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> iff not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E14:46"><i><font color="Green">E53</font></i></a>, <a class="ref" href="gate_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E47:46"/><i><font color="Green">E86</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>38</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E15:46"><i><font color="Green">E54</font></i></a>, <a class="ref" href="gate_1.html#D4" target="_self">Def4</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E48:46"/><i><font color="Green">E87</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>25</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E16:46"><i><font color="Green">E55</font></i></a>, <a class="ref" href="gate_1.html#D2" target="_self">Def2</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E49:46"/><i><font color="Green">E88</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>26</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>25</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E17:46"><i><font color="Green">E56</font></i></a>, <a class="ref" href="gate_1.html#D7" target="_self">Def7</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E50:46"/><i><font color="Green">E89</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>26</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>26</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>39</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E18:46"><i><font color="Green">E57</font></i></a>, <a class="ref" href="gate_1.html#D4" target="_self">Def4</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E51:46"/><i><font color="Green">E90</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>27</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E19:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="gate_1.html#D2" target="_self">Def2</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E52:46"/><i><font color="Green">E91</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>28</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E20:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="gate_1.html#D8" target="_self">Def8</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E53:46"/><i><font color="Green">E92</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>29</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>27</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>28</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E21:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="gate_1.html#D13" target="_self">Def13</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E54:46"/><i><font color="Green">E93</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>29</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>29</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>40</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E22:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="gate_1.html#D4" target="_self">Def4</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E55:46"/><i><font color="Green">E94</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>30</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E23:46"><i><font color="Green">E62</font></i></a>, <a class="ref" href="gate_1.html#D2" target="_self">Def2</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E56:46"/><i><font color="Green">E95</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>31</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E24:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="gate_1.html#D8" target="_self">Def8</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E57:46"/><i><font color="Green">E96</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>32</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E25:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="gate_1.html#D14" target="_self">Def14</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E58:46"/><i><font color="Green">E97</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>33</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>30</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>31</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>32</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E26:46"><i><font color="Green">E65</font></i></a>, <a class="ref" href="gate_1.html#D17" target="_self">Def17</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E59:46"/><i><font color="Green">E98</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>33</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>33</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>41</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E27:46"><i><font color="Green">E66</font></i></a>, <a class="ref" href="gate_1.html#D4" target="_self">Def4</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E60:46"/><i><font color="Green">E99</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>34</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E28:46"><i><font color="Green">E67</font></i></a>, <a class="ref" href="gate_1.html#D2" target="_self">Def2</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E61:46"/><i><font color="Green">E100</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>35</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E29:46"><i><font color="Green">E68</font></i></a>, <a class="ref" href="gate_1.html#D8" target="_self">Def8</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E62:46"/><i><font color="Green">E101</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>36</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E30:46"><i><font color="Green">E69</font></i></a>, <a class="ref" href="gate_1.html#D14" target="_self">Def14</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E63:46"/><i><font color="Green">E102</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>37</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E31:46"><i><font color="Green">E70</font></i></a>, <a class="ref" href="gate_1.html#D18" target="_self">Def18</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E64:46"/><i><font color="Green">E103</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>34</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>35</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>36</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>37</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E32:46"><i><font color="Green">E71</font></i></a>, <a class="ref" href="gate_1.html#D21" target="_self">Def21</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<b>thus </b><a NAME="E65:46"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>38</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#NK35" target="_self">ADD1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E35:46"><i><font color="Green">E74</font></i></a>, <a class="txt" href="gate_1.html#E45:46"><i><font color="Green">E84</font></i></a>, <a class="txt" href="gate_1.html#E46:46"><i><font color="Green">E85</font></i></a>, <a class="txt" href="gate_1.html#E47:46"><i><font color="Green">E86</font></i></a>, <a class="ref" href="gate_1.html#T18" target="_self">Th18</a></i>;<br/>

<a NAME="E66:46"/><i><font color="Green">E104</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E67:46"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>39</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10" target="_self">XOR3</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#NK36" target="_self">CARR1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E33:46"><i><font color="Green">E72</font></i></a>, <a class="txt" href="gate_1.html#E34:46"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gate_1.html#E38:46"><i><font color="Green">E77</font></i></a>, <a class="txt" href="gate_1.html#E45:46"><i><font color="Green">E84</font></i></a>, <a class="txt" href="gate_1.html#E48:46"><i><font color="Green">E87</font></i></a>, <a class="txt" href="gate_1.html#E49:46"><i><font color="Green">E88</font></i></a>, <a class="txt" href="gate_1.html#E50:46"><i><font color="Green">E89</font></i></a>, <a class="ref" href="gate_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E68:46"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>39</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K35" target="_self">ADD2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E69:46"/><i><font color="Green">E105</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#NK36" target="_self">CARR1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#NK36" target="_self">CARR1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#NK36" target="_self">CARR1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E70:46"/><b>then </b><i><font color="Green">E106</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K36" target="_self">CARR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E71:46"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>40</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10" target="_self">XOR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K36" target="_self">CARR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E33:46"><i><font color="Green">E72</font></i></a>, <a class="txt" href="gate_1.html#E34:46"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gate_1.html#E36:46"><i><font color="Green">E75</font></i></a>, <a class="txt" href="gate_1.html#E37:46"><i><font color="Green">E76</font></i></a>, <a class="txt" href="gate_1.html#E41:46"><i><font color="Green">E80</font></i></a>, <a class="txt" href="gate_1.html#E45:46"><i><font color="Green">E84</font></i></a>, <a class="txt" href="gate_1.html#E51:46"><i><font color="Green">E90</font></i></a>, <a class="txt" href="gate_1.html#E52:46"><i><font color="Green">E91</font></i></a>, <a class="txt" href="gate_1.html#E53:46"><i><font color="Green">E92</font></i></a>, <a class="txt" href="gate_1.html#E54:46"><i><font color="Green">E93</font></i></a>, <a class="ref" href="gate_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E72:46"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>40</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K37" target="_self">ADD3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E73:46"/><i><font color="Green">E107</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K36" target="_self">CARR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K36" target="_self">CARR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K36" target="_self">CARR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>42</sub></font> =  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E74:46"/><i><font color="Green">E108</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E66:46"><i><font color="Green">E104</font></i></a>, <a class="txt" href="gate_1.html#E69:46"><i><font color="Green">E105</font></i></a>, <a class="txt" href="gate_1.html#E73:46"><i><font color="Green">E107</font></i></a></i>;<br/>
<a NAME="E75:46"/>
( <!--HUMANRECFAILED-->( ( not <!--HUMANRECFAILED-->( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> &amp; ( ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) ) &amp; not <!--HUMANRECFAILED-->( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) &amp; (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) ) &amp; ( ( not <!--HUMANRECFAILED-->( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> &amp; ( ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> ) or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) &amp; (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) ) ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E33:46"><i><font color="Green">E72</font></i></a>, <a class="txt" href="gate_1.html#E34:46"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gate_1.html#E36:46"><i><font color="Green">E75</font></i></a>, <a class="txt" href="gate_1.html#E37:46"><i><font color="Green">E76</font></i></a>, <a class="txt" href="gate_1.html#E39:46"><i><font color="Green">E78</font></i></a>, <a class="txt" href="gate_1.html#E40:46"><i><font color="Green">E79</font></i></a>, <a class="txt" href="gate_1.html#E70:46"><i><font color="Green">E106</font></i></a>, <a class="txt" href="gate_1.html#E73:46"><i><font color="Green">E107</font></i></a></i>;<br/>
<a NAME="E76:46"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>41</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10" target="_self">XOR3</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E44:46"><i><font color="Green">E83</font></i></a>, <a class="txt" href="gate_1.html#E45:46"><i><font color="Green">E84</font></i></a>, <a class="txt" href="gate_1.html#E55:46"><i><font color="Green">E94</font></i></a>, <a class="txt" href="gate_1.html#E56:46"><i><font color="Green">E95</font></i></a>, <a class="txt" href="gate_1.html#E57:46"><i><font color="Green">E96</font></i></a>, <a class="txt" href="gate_1.html#E58:46"><i><font color="Green">E97</font></i></a>, <a class="txt" href="gate_1.html#E59:46"><i><font color="Green">E98</font></i></a>, <a class="ref" href="gate_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E77:46"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>41</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K39" target="_self">ADD4</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E78:46"/>
( ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) ) iff ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_1.html#E13:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="gate_1.html#E33:46"><i><font color="Green">E72</font></i></a>, <a class="txt" href="gate_1.html#E34:46"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gate_1.html#E36:46"><i><font color="Green">E75</font></i></a>, <a class="txt" href="gate_1.html#E37:46"><i><font color="Green">E76</font></i></a>, <a class="txt" href="gate_1.html#E39:46"><i><font color="Green">E78</font></i></a>, <a class="txt" href="gate_1.html#E40:46"><i><font color="Green">E79</font></i></a>, <a class="txt" href="gate_1.html#E42:46"><i><font color="Green">E81</font></i></a>, <a class="txt" href="gate_1.html#E43:46"><i><font color="Green">E82</font></i></a>, <a class="txt" href="gate_1.html#E74:46"><i><font color="Green">E108</font></i></a>, <a class="ref" href="gate_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E79:46"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K38" target="_self">CARR3</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_1.html#E60:46"><i><font color="Green">E99</font></i></a>, <a class="txt" href="gate_1.html#E61:46"><i><font color="Green">E100</font></i></a>, <a class="txt" href="gate_1.html#E62:46"><i><font color="Green">E101</font></i></a>, <a class="txt" href="gate_1.html#E63:46"><i><font color="Green">E102</font></i></a>, <a class="txt" href="gate_1.html#E64:46"><i><font color="Green">E103</font></i></a>, <a class="ref" href="gate_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E80:46"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K40" target="_self">CARR4</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>


</div>
