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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> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green">E39</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>1</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green">E40</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>and </b><br/><a NAME="E3:37"/><i><font color="Green">E41</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>and </b><br/><a NAME="E4:37"/><i><font color="Green">E42</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>and </b><br/><a NAME="E5:37"/><i><font color="Green">E43</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>and </b><br/><a NAME="E6:37"/><i><font color="Green">E44</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E7:37"/><i><font color="Green">E45</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>and </b><br/><a NAME="E8:37"/><i><font color="Green">E46</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E9:37"/><i><font color="Green">E47</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K18" target="_self">AND5</a> <font color="Maroon">c<sub>1</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> )
 <b>and </b><br/><a NAME="E10:37"/><i><font color="Green">E48</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 <b>and </b><br/><a NAME="E11:37"/><i><font color="Green">E49</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>18</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> )
 ;<br/>

<b>thus </b><a NAME="E12:37"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> implies  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E11:37"><i><font color="Green">E49</font></i></a>, <a class="ref" href="gate_1.html#D3" target="_self">Def3</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/>

<b>assume </b><a NAME="E13:37"/>
 <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font>
 ;<br/>

<a NAME="E14:37"/><b>then </b>
 <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3" target="_self">OR2</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="gate_1.html#E10:37"><i><font color="Green">E48</font></i></a></i>;<br/>
<a NAME="E15:37"/><b>then </b><i><font color="Green">E50</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T7" target="_self">Th7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1"/>
 <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font>
 ;<br/><a NAME="E2:37_1"/><b>then </b>
 <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K18" target="_self">AND5</a> <font color="Maroon">c<sub>1</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>
 <b>by </b><i><a class="txt" href="gate_1.html#E9:37"><i><font color="Green">E47</font></i></a></i>;<br/><a NAME="E3:37_1"/><b>then </b>
(  <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>14</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>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D18" target="_self">Def18</a></i>;<br/><a NAME="E4:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</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>6</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>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E5:37"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E5:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E6:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</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>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E1:37"><i><font color="Green">E39</font></i></a></i>;<br/><a NAME="E7:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</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>7</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E6:37"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E8:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E9:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E2:37"><i><font color="Green">E40</font></i></a></i>;<br/><a NAME="E10:37_1"/><b>then </b>
(  <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>4</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>17</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E7:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E11:37_1"/><b>then </b>
(  <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>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E12:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E3:37"><i><font color="Green">E41</font></i></a></i>;<br/><a NAME="E13:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> &amp; (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> ) )
 <b>by </b><i><a class="txt" href="gate_1.html#E8:37"><i><font color="Green">E46</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self">Th7</a></i>;<br/><b>hence </b><a NAME="E14:37_1"/>
 <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11" target="_self">MAJ3</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E17:37"/>
 <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="gate_1.html#E4:37"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gate_1.html#E15:37"><i><font color="Green">E50</font></i></a></i>;<br/>


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